Umberto Grandi

Emiliano Lorini

Timothy Parker

Rachid Alami

Logic-Based Ethical Planning

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In ethical planning the planning agent has to find a plan for promoting a certain number of ethical values. The latter include both abstract values such as justice, fairness, reciprocity, equity, respect for human integrity and more concrete ones such as "greenhouse gas emissions are reduced". Unlike classical planning in which the goal to be achieved is unique, in ethical planning the agent can have multiple and possibly conflicting values, that is, values that cannot be concomitantly satisfied. It is typical of ethical planning the problem of facing a moral struggle which is "...provoked by inconsistencies between value commitments and information concerning the kinds of decision problems which arise..." [18, p. 8]. Consequently, in ethical planning the agent needs to evaluate and compare the ideality (or goodness) of different plans depending on how many and which values are promoted by each of them.

In this paper our intended application field is that of robotics. Including ethical considerations in robotics planning requires (at least) three steps. First, identify ethically sensitive situations in the robotics realm, and how are these situations represented. Planning seems to be the first candidate in which to include ethical considerations, thus we assume that values or ethical judgments are expressed about the results of plans. Second, design a language to express such values, bearing in mind that they can be, and often are, potentially conflicting in multiple ways: among values, between a value and a goal, or between a value and good practices. Such a value representation language needs to be compact and computationally tractable. Third, complete the picture of ethical planning by designing algorithms that compare plans based on the ethical values.

In this paper we put forward a framework for ethical planning based on a simple temporal logic language to express both an agent's values and goals. For ease of exposition we focus on single-agent planning with deterministic sequential actions in a known environment. Our model borrows from the existing literature on planning and combines it in an original way with research in compact representation languages for preferences. The latter is a widely studied topic in knowledge representation, where logical and graphical languages are proposed to represent compactly the preferences of an agent over a combinatorial space of alternatives, often described by means of variables. In particular, we commit to a prioritised or lexicographic approach to solve the possible arising inconsistencies among goals, desires, and good practices in a unified planning model.

Related Work

There is considerable research in the field of ethics and AI, see Müller [START_REF] Müller | Ethics of Artificial Intelligence and Robotics[END_REF] for a general overview. Popular ethical theories for application are consequentialism, deontology, and virtue ethics. 3 Our approach should be able to work with any notion of "good actions" but is probably a most natural fit for pluralistic consequentialism [START_REF] Sen | On Ethics and Economics[END_REF].

While there is a lot of work at the theoretical/abstract level, there is comparatively less that examines how ethical reasoning in artificial agents could actually be done in practice. There are approaches both in terms of formal models [START_REF] Dennis | A defeasible logic implementation of ethical reasoning[END_REF] and allowing agents to learn ethical values [START_REF] Anderson | Geneth: a general ethical dilemma analyzer[END_REF]. Yu et al. [START_REF] Yu | Building ethics into artificial intelligence[END_REF] provides a recent survey of this research area. The closest approaches to ours are the recent work on (i) logics for ethical reasoning and (ii) the combination of a compact representation language, such as conditional preference networks, with decision-making in an ethically sensitive domain. The former are based on different methodologies including event calculus (ASP) [START_REF] Berreby | A declarative modular framework for representing and applying ethical principles[END_REF], epistemic logic and preference logic [START_REF] Lorini | A logic for reasoning about moral agents[END_REF][START_REF] Lorini | A logic of evaluation[END_REF], BDI (belief, desire, intention) agent language [START_REF] Dennis | Formal verification of ethical choices in autonomous systems[END_REF], classical higher-order logic (HOL) [START_REF] Benzmüller | Designing normative theories for ethical and legal reasoning: LogiKEy framework, methodology, and tool support[END_REF]. The latter was presented in "blue sky" papers [START_REF] Loreggia | Modelling ethical theories compactly[END_REF][START_REF] Rossi | Building ethically bounded AI[END_REF] complemented with a technical study of distances between CP-nets [START_REF] Loreggia | On the distance between cp-nets[END_REF] and, more recently, with an empirical study on human ethical decision-making [START_REF] Awad | When is it acceptable to break the rules? Knowledge representation of moral judgement based on empirical data[END_REF]. CP-nets are a compact formalism to order states of the world described by variables.

We take inspiration from these lines of work, but depart from them under two aspects. First, robotics applications are dynamic ones, and ethical principles must be expressed over time. Hence, unlike existing logics for ethical reasoning, our focus is on a specification language for values based on linear temporal logic. Second, ethical decision-making in robotic applications requires mixing potentially conflicting values with desires of the agent and to express the notion of plan, and CP-nets alone are not sufficient.

In the field of robotics, there are approaches to enabling artificial agents to compute ethical plans. The evaluative component, which consists in assessing the "goodness" of an action or a plan in relation to the robot's values, is made explicit by Arkin et al. [START_REF] Arkin | Moral decision making in autonomous systems: Enforcement, moral emotions, dignity, trust, and deception[END_REF] and Vanderelst and Winfield [START_REF] Vanderelst | An architecture for ethical robots inspired by the simulation theory of cognition[END_REF]. Evans et al. [START_REF] Evans | Ethical decision making in autonomous vehicles: The av ethics project[END_REF] focuses on a collision scenario involving an autonomous vehicle, proposing to prioritise the ethical claims depending on the situation, e.g. by giving more priorities to the claims of the more endangered agents. Related work explores the design of planning algorithms designed to help robots produce socially acceptable plans by assigning weights to social rules [START_REF] Alili | A task planner for an autonomous social robot[END_REF] .

In preference-based planning by Bienvenu et al. [START_REF] Bienvenu | Planning with qualitative temporal preferences[END_REF] plans are compared relative to a single (possibly lexicographic) preference formula about temporal properties. Similarly, Lindner et al. [START_REF] Lindner | Moral permissibility of action plans[END_REF] evaluate the permissibility of plans according to a specific ethical principle such as the deontological principle, the utilitarian principle, the do-no-harm or the double effect principle. In our approach plans are compared relative to sets of values. Comparison of alternatives (e.g., plans, states, histories) relative to a set of values is an essential aspect of ethics which is not considered in these two works. As we will show in Section 3.5, it opens up the possibility of formalizing the notion of moral conflict.

Model

In this section, we present the formal model of ethical evaluation and planning which consist, respectively, in comparing the goodness of plans and in finding the best plan relative to a given base of ethical values.

LTL Language

Let Prop be a countable set of atomic propositions and let Act be a finite nonempty set of action names. Elements of Prop are noted p, q, . . ., while elements of Act are noted a, b, . . .. We assume the existence of a special action skip. The set of states is S = 2 Prop with elements s, s ′ , . . .

In order to represent the agent's values, we introduce the language of LTL f (Linear Temporal Logic over Finite Traces) [START_REF] Pnueli | The temporal logic of programs[END_REF][START_REF] De Giacomo | Linear temporal logic and linear dynamic logic on finite traces[END_REF], noted L LTL f (Prop) (or L LTL f ), defined by the following grammar:

φ ::= p | ¬φ | φ 1 ∧ φ 2 | Xφ | φ 1 U φ 2 ,
with p ranging over Prop. X and U are the operators "next" and "until" of LTL f . Operators "henceforth" (G) and "eventually" (F) are defined in the usual way:

Gφ def = ¬(⊤ U φ) and Fφ def = ¬G¬φ. The propositional logic fragment of L LTL f is noted L PL and
is defined in the usual way. We will use L PL to describe the effect preconditions of the agent's actions.

Histories

The notion of history is needed for interpreting formulas in L LTL f . We define a k-history to be a pair H = (H st , H act ) with

H st : [0, k] -→ S and H act : [1, k] -→ Act.
A history specifies the actual configuration of the environment at a certain time point and the action executed by the agent that leads to the next state. The set of k-histories is noted Hist k . The set of histories is Hist = k∈N Hist k . Semantic interpretation of formulas in L LTL f relative to a k-history H ∈ Hist and a time point t ∈ [0, k] goes as follows (we omit boolean cases which are defined as usual):

H, t

Action Theory

We suppose actions in Act are described by an action theory γ = (γ + , γ -), where γ + and γ -are, respectively, the positive and negative effect precondition function γ + : Act × Prop -→ L PL and γ -: Act × Prop -→ L PL . The fact γ + (a, p) guarantees that proposition p will be true in the next state when action a is executed, while γ -(a, p) guarantees that proposition p will be false in the next state when action a is executed. We stipulate that if γ + (a, p) and γ -(a, p) are concomitantly true at a given state and action a is executed, then the truth value of p will not change in the next state. The latter captures an inertial principle for fluents.

Definition 1 (Action-compatible histories). Let γ = (γ + , γ -) be an action theory and let H = (H st , H act ) be a k-history. We say H is compatible with γ if the following condition holds, for every t ∈ [1, k] and for every a ∈ Act :

if H act (t) = a then H st (t) = H st (t -1) \ p ∈ Prop : H, t -1 |= ¬γ + (a, p)∧ γ -(a, p) ∪ p ∈ Prop : H, t -1 |= γ + (a, p)∧ ¬γ -(a, p) .
The set of γ-compatible histories is noted Hist (γ).

Plans

Let us now move from the notion of action to the notion of plan. Given k ∈ N, a k-plan is a function π : {1, . . . , k} -→ Act.

The set of k-plans is noted Plan k . The set of plans is Plan = k∈N Plan k . The following definition introduces the notion of history generated by a k-plan π at an initial state s 0 . It is the action-compatible k-history along which the agent executes the plan π starting at state s 0 .

Definition 2 (History generated by a k-plan). Let γ = (γ + , γ -) be an action theory, s 0 ∈ S and π ∈ Plan k . Then, the history generated by plan π from state s 0 in conformity with the action theory γ is the k-history H π,s0,γ = (H π,s0,γ st , H π,s0,γ act ) such that:

(i) H π,s0,γ ∈ Hist (γ), (ii) H π,s0,γ st (0) = s 0 , (iii) ∀k ′ s.t. 1 ≤ k ′ ≤ k : H π,s0,γ act (k ′ ) = π(k ′ ),
Given a set of LTL f -formulas Σ, we define Sat(Σ,π,s 0 ,γ) to be the set of formulas from Σ that are guaranteed to be true by the execution of plan π at state s 0 under the action theory γ. That is,

Sat(Σ,π,s 0 ,γ) = φ ∈ Σ : H π,s0,γ , 0 |= φ .

Moral Conflicts

An ethical planning agent is likely to have multiple values that it wishes to satisfy when making plans. Some of these values will be ethical in nature ("do not harm humans"), and some may not be ("do not leave doors open"). However, the more values the robot has the more likely it is to experience scenarios where it cannot satisfy all of its values with any given plan, and must violate some of them. In such a scenario, the agent must first work out which subsets of its value base are jointly satisfiable, and then which of those subsets it should choose to satisfy.

To this end we define a notion of a moral conflict (note that in line with Levi [START_REF] Levi | Hard Choices: Decision Making Under Unresolved Conflict[END_REF] we refer to any conflict between an agent's values as a "moral conflict" even if some or all of those values are not strictly moral/ethical in nature).

Definition 3 (Moral problem).

A moral problem is a tuple M = (Ω, γ, s 0 ) where:

-Ω ⊆ L LTL f is a set of values (which may or may not be strictly moral in nature); γ = (γ + , γ -) is an action theory and s 0 is an initial state, as described above.

Definition 4 (Moral conflict). A moral problem

M = (Ω, γ, s 0 ) is a moral conflict if: -∀k ∈ N, there is no k-plan π such that Sat(Ω,π,s 0 ,γ) = Ω.
In other words, a moral conflict occurs when it is not possible to satisfy all of our values with any given plan. In some cases, a moral conlict may not depend on any particular feature of the start state, but may result simply from the value base and action theory, or even the value base alone. This allows us to define two further notions of moral problem.

Definition 5 (Physical moral problem).

A physical moral problem is a pair (Ω, γ) where:

-Ω ⊆ L LTL f is a set of values; -γ is an action theory. Definition 6 (Logical moral problem). A logical moral problem is a set of values Ω ⊆ L LTL f .
We can also define moral conflict for these moral problems. A physical (logical) moral problem is a physical (logical) value conflict if for every possible start state s 0 (and every possible action theory γ), the resultant moral value problem M = (Ω, γ, s 0 ) is a moral conflict. By our definition, conflict mirrors the concept of necessity. Necessity would imply that every possible plan satisfies all the values in Ω, whereas conflict implies that no plan satisfies all values. Thus it is interesting to note that our definitions of conflict have mirrors in philosophical literature [START_REF] Kment | Varieties of Modality[END_REF]. A physical moral conflict mirrors the notion of nomic necessity (necessary given the laws of nature) (at least from the perspective of the robot, for whom the action theory comprises the laws of nature) whereas a logical moral conflict mirrors the notion of logical necessity (necessary given the nature of logic).

If an agent is experiencing a moral conflict, one response would be to "temporarily forget" values until it has a satisfiable set.

Definition 7 (Contraction). If M = (Ω, γ, s 0 ) is a moral problem and M ′ = (Ω ′ , γ, s 0 ) is a moral problem, we say that M ′ is a contraction of M if: -Ω ′ ⊆ Ω -M ′ is not a moral conflict.
Note that if M = (Ω, γ, s 0 ) is a moral problem, π is a plan, and Ω ′ = Sat(Ω,π,s 0 ,γ) then M ′ = (Ω ′ , γ, s 0 ) must be a contraction of M .

In this case, we refer to M ′ as the contraction generated by π. This also illustrates that the current notion of contraction is unhelpful for an agent attempting to select a plan in a moral conflict, as all plans generate contractions. What would be helpful is some notion of a "minimal" or "ideal" contraction that sacrifices as few values as possible.

Definition 8 (Minimal contraction). If M = (Ω, γ, s 0 ) is a moral problem and M ′ = (Ω ′ , γ, s 0 ) is a contraction of M , M is: -A qual-minimal contraction if there is no contraction M ′′ = (Ω ′′ , γ, s 0 ) such that Ω ′ ⊂ Ω ′′ ; -A quant-minimal contraction if there is no contraction M ′′ such that |Ω ′ | < |Ω ′′ | Proposition 1. If M = (Ω, γ, s 0
) is a moral problem and is not a moral conflict, then the only qual-minimal and quant-minimal contraction of M is M .

For either notion of minimality, we will have cases where there are multiple minimal contractions of a given moral conflict. This can produce unintuitive results, as if there is some moral conflict with Ω = {"do not kill humans", "do not leave the door open"} with contractions {"do not kill humans"} and {"do not leave the door open"} then either notion of minimality will tell you that both contractions are ideal. On the other hand, it does seem that any stronger notion of minimality should at least respect qualitative minimality, since (intuitively), if plan π 1 fulfills all of the values fulfilled by π 2 , and fulfills more values, then π 1 should be preferred to π 2 .

Proposition 2. Given a moral conflict M , a contraction M ′ is quant-minimal only if it is qual-minimal.

One way to resolve this is to recognise, in line with Levi [START_REF] Levi | Hard Choices: Decision Making Under Unresolved Conflict[END_REF], that some of our values are only used as tiebreakers to separate otherwise-equivalent plans, and should not be considered directly alongside our more important values. To model this, our values exist in lexicographically ordered sets, where each set is examined only if the sets above cannot deliver a verdict.

Lexicographic Value Base

Together with an action theory and an initial state, an agent's value base constitutes an ethical planning domain.

Definition 9 (Ethical planning domain). An ethical planning domain is a tuple ∆ = (γ, s 0 , Ω) where:

γ = (γ + , γ -) is an action theory and s 0 is an initial state, as specified above; -Ω = (Ω 1 , . . . , Ω m ) is the agent's value base with Ω k ⊆ L LTL f for every

1 ≤ k ≤ m.
Ω 1 is the agent's set of values with priority 1, Ω 2 is the agent's set of values with priority 2, and so on. For notational convenience, given a value base Ω = (Ω 1 , . . . , Ω m ), we note dg(Ω) its degree (or arity).

Agent's values are used to compute the relative ideality of plans, namely, whether a plan π 2 is at least as ideal as another plan π 1 . Following [START_REF] Lorini | A logic of evaluation[END_REF], we call evaluation the operation of computing an ideality ordering over plans from a value base. Building on classical preference representation languages [START_REF] Lang | Logical preference representation and combinatorial vote[END_REF], we define the following qualitative criterion of evaluation, noted ⪯ qual ∆ , which compares two plans lexicographically on the basis of inclusion between sets of values.

Definition 10 (Qualitative ordering of plans). Let ∆ = (γ, s 0 , Ω) be an ethical planning domain with Ω = (Ω 1 , . . . , Ω m ) and π 1 , π 2 ∈ Plan . Then, π 1 ⪯ qual ∆ π 2 if and only if:

(i) ∃1 ≤ k ≤ m s.t. Sat(Ω k ,π 1 ,s 0 ,γ) ⊂ Sat(Ω k ,π 2 ,s 0 ,γ), and
∀1 ≤ k ′ < k, Sat(Ω k ′ ,π 1 ,s 0 ,γ) = Sat(Ω k ′ ,π 2 ,s 0 ,γ); or (ii) ∀1 ≤ k ≤ m, Sat(Ω k ,π 1 ,s 0 ,γ) = Sat(Ω k ,π 2 ,s 0 ,γ).
Note that a quantitative criterion could also be defined by counting the number of satisfied values in each level and, in line with the previous definition, compare these values lexicographically.

The quantitative criterion, noted ⪯ quant ∆ , compares two plans lexicographically on the basis of comparative cardinality between sets of values.

Definition 11 (Quantitative ordering of plans). Let ∆ = (γ, s 0 , Ω) be an ethical planning domain with Ω = (Ω 1 , . . . , Ω m ) and π 1 , π 2 ∈ Plan . Then, π 1 ⪯ quant ∆ π 2 if and only if:

(i) ∃1 ≤ k ≤ m s.t. |Sat(Ω k ,π 1 ,s 0 ,γ)| < |Sat(Ω k ,π 2 ,s 0 ,γ)|, and
∀1 ≤ k ′ < k, |Sat(Ω k ′ ,π 1 ,s 0 ,γ)| = |Sat(Ω k ′ ,π 2 ,s 0 ,γ)|; or (ii) ∀1 ≤ k ≤ m, |Sat(Ω k ,π ,s 0 ,γ)| = |Sat(Ω k ,π 2 ,s 0 ,γ)|.
This allows us to define another notion of minimal contraction for a moral conflict, namely a minimal contraction with respect to a lexicographic value base.

Definition 12 (Lexicographic-minimal contraction). If M = (Ω, γ, s 0 ) is a moral problem, and Ω = (Ω 1 , ..., Ω m ) is a value base such that ∪Ω = Ω then M ′ = (Ω ′ , γ, s 0 ) is a Ω-qual-minimal contraction of M if and only if:

(i) Ω ′ ⊆ Ω; (ii) M ′ is not a moral conflict; (iii) If M ′′ = (Ω ′′ , γ, s 0 ) is also a contraction of M, ∄k : (a) 1 ≤ k ≤ m and Ω ′ ∩ Ω k ⊂ Ω ′′ ∩ Ω k , and (b) ∀1 ≤ i < k, Ω ′ ∩ Ω i = Ω ′′ ∩ Ω i .
Note that by combining definitions 11 and 12 we can define a notion of Ωquant-minimal contraction.

Proposition 3. Given a moral conflict M , a contraction M ′ is Ω-qual-minimal or Ω-quant-minimal only if it is qual-minimal.

Adding Desires

The behavior of autonomous ethical agents is driven not only by ethical values aimed at promoting the good for society but also by their endogenous motivations, also called desires or goals. Following existing theories of ethical preferences in philosophy, economics and logic [START_REF] Searle | Rationality in Action[END_REF][START_REF] Harsanyi | Utilitarianism and beyond[END_REF][START_REF] Lorini | Logics for games, emotions and institutions[END_REF], we assume that (i) desires and values are competing motivational attitudes, and (ii) the agent's degree of morality is a function of its disposition to promote the fulfilment of its values at the expense of the satisfaction of its desires. The following definition extends the notion of ethical planning domain by the notions of desire and introduces the novel concept of degree of morality.

Definition 13 (Mixed-motive planning domain).

A mixed-motive planning domain is a tuple Γ = (γ, s 0 , Ω, Ω D , µ) where -(γ, s 0 , Ω) is an ethical planning domain (Definition 9); -Ω D ⊆ L LTL f is the agent's set of desires or goals; µ ∈ {1, . . . , dg(Ω) + 1} is the agent's degree of morality.

A mixed-motive planning domain induces an ethical planning domain whereby the agent's set of desires is treated as a set of values whose priority level depends on the agent's degree of morality. Specifically, the lower the agent's of morality, the higher the priority of the agent's set of desires in the induced ethical planning domain. In many practical applications it is likely to be desirable to restrict the range of values that µ can take, in order to prevent (for example) the robot's goal from overriding its safety values. Definition 14 (Induced ethical planning domain). Let Γ = (γ, s 0 , Ω, Ω D , µ) be a mixed-motive planning domain. The ethical planning domain induced by Γ is the tuple ∆ = (γ, s 0 , Ω ′ ) such that dg(Ω ′ ) = dg(Ω) + 1 with:

(i) Ω ′ µ = Ω D ; (ii)Ω ′ k = Ω k for 1 ≤ k < µ; (iii)Ω ′ k = Ω k-1 for µ < k ≤ dg(Ω) + 1.

An Example

Consider a blood delivery robot in a hospital. The robot mostly makes deliveries between different storage areas, and sometimes delivers blood to surgeries. The robot may have to deal with various kinds of obstacles to complete its deliveries, but we will consider only one: people blocking the robot. The robot has two methods to resolve this obstacle, it can ask for them to move and then wait for them to move (ask), or it can use a loud air-horn to "force" them to move (horn). Once the person has moved, the robot can reach its destination (move).

We suppose that the robot can tell some things about its environment, it knows if it is blocked (blocked), if it is near the operating theatre (theatre) and if it has reached its destination (destination). We can then define the action model as follows:

γ + (move, destination) = ¬blocked γ -(ask, blocked) = blocked γ + (ask, delayed) = ⊤ γ -(horn, blocked) = blocked γ + (horn, annoyed) = ⊤ γ + (horn, dangerous) = theatre otherwise,γ ± (a, p) = ⊥
The propositions delayed, annoyed and dangerous are used to keep track of the robot's actions, we suppose that using the horn near the operating theatre is dangerous. The values and desires of the robot can be presented as follows:

Ω = {Ω 1 , Ω 2 } Ω 1 = {G¬dangerous} Ω 2 = {G¬annoyed} Ω D = {Fdestination, F(destination ∧ ¬delayed)}
In words, the robot's goal is to reach its destination without delays, with the primary value to never do anything dangerous, and the secondary value to never be annoying. Let Ω ′ be the value base induced by Ω, Ω D and µ = 3.

Now we can compare the following 2-plans π 1 = (ask, move) and π 2 = (horn, move). If we assume that in the initial state the robot is blocked but far from an operating theatre, we can represent the histories generated from these plans as follows (each block contains exactly the propositions that are true in that state):

In this case Sat(Ω ′ ,π 1 ,s 0 ,γ) = {G¬dangerous, G¬annoyed, Fdestination} = A ⊇ Ω 1 ∪Ω 2 whereas Sat(Ω ′ ,π 2 ,s 0 ,γ) = {G¬dangerous, Fdestination, F(destination∧ ¬delayed)} = B ⊇ Ω 1 ∪ Ω D .
Therefore π 1 will be preferred to π 2 . However, if we change the morality level to 2, perhaps to represent an urgent delivery to an ongoing surgery, then we see that the robot will choose plan π 2 rather than π 1 . This illustrates how we can adjust the morality level of the robot to reflect the urgency of its goals. If we move the example to the operating theatre (so now theatre ∈ s 0 instead of ¬theatre ∈ s 0 ), then the robot would not sound its horn even if the delivery was urgent, as Ω 1 still overrides Ω D . This also means that for this robot we should restrict µ to 2 or 3 to ensure that being safe is always prioritised over goals. Furthermore, notice that for any lexicographic value structure containing exactly these values and goals, the set of non-dominated plan will always contain either π 1 , π 2 or both, since A and B are exactly the qual-minimal contractions of ∪Ω ′ given an initial state where the robot is blocked.

Computational Complexity

In this section we initiate the study of the computational complexity of ethical planning in our setting. We borrow our terminology from the work of Lang [START_REF] Lang | Logical preference representation and combinatorial vote[END_REF] on compact preference representation, but the problems we study have obvious counterparts in the planning literature, as should be clear from the proofs. In the interest of space all proofs can be found in the appendix.

We begin by studying the problem Conflict, which determines if a moral problem is also a moral conflict.

Conflict

Input: Moral problem M = (Ω, γ, s 0 ) Question: Is there some k ∈ N such that there is a k-plan π ′ such that Sat(Ω,π,s 0 ,γ) = Ω?

Theorem 1. Conflict is PSPACE-complete.
We then study the case of contractions, in particular, determining if a given moral problem is a qual-minimal contraction.

Minimal-Contraction

Input: Moral problem M = (Ω, γ, s 0 ), moral problem M ′ = (Ω ′ , γ, s 0 ) Question: Is M ′ a qual-minimal contraction of M ? Theorem 2. Minimal-Contraction is PSPACE-complete.
Neither of these results are particularly technically advanced, indeed Conflict is almost exactly equivalent to PLANSAT from classical planning [START_REF] Bylander | The computational complexity of propositional STRIPS planning[END_REF]. The purpose of these results is to indicate that quite apart from the issue of how a robot should select the best option when faced with a moral conflict, the task of identifying that the robot is facing a moral conflict and determining all of its options is extremely computationally difficult.

On the subject of planning, we begin by studying the problem Comparison, which given two k-plans π 1 and π 2 , asks whether π 1 ⪯ qual ∆ π 2 . Despite the apparent complexity of our setting this problem can be solved efficiently:

Comparison Input: Ethical planning domain ∆ = (γ, s 0 , Ω), k ∈ N, k-plans π 1 , π 2 Question: is it the case that π 1 ⪯ qual ∆ π 2 ?
Theorem 3. Comparison is in P.

We then move to the problem of non-dominance, i.e., the problem of determining if given a g-plan π 1 there exists a better k-plan wrt. ⪯ qual ∆ (where g ≤ k).

Non-dominance

Input: Ethical planning domain ∆ = (γ, s 0 , Ω), k ∈ N, g-plan π for g ≤ k Question: is there a k-plan π ′ such that π ⪯ qual ∆ π ′ and π ′ ̸ ⪯ qual ∆ π?
We show that this problem, as most instances of classical planning satisfaction, is PSPACE-complete:

Theorem 4. Non-Dominance is PSPACE-complete.
Proposition 4. Given an ethical planning domain ∆ = (γ, s 0 , Ω), a k-plan π and S = Sat(∪Ω,π,s 0 ,γ) π is non-dominated for ∆ if and only if M = (S, γ, s 0 ) is a Ω-qual-minimal contraction for (∪Ω, γ, s 0 ).

Theorems 3 and 4 are to be interpreted as baseline results showing the computational feasibility of our setting for ethical planning with LTL f . One clear direction for future work would expand on the computational complexity analysis, identifying tractable fragments and exploring their expressivity in ethical applications.

An important property for an ethical planner is explainability. While explaining why a particular plan was chosen is difficult to do succinctly (even for humans), a simpler problem is to explain why the chosen plan was better than another proposed alternative. Our approach enables this in a way that is both computationally straightforward and intuitively understandable to humans, since by the lexicographic ordering of plans there always exists a single value or set of values that decides between two plans.

Conclusion

We put forward a novel setting for ethical planning obtained by combining a simple logical temporal language with lexicographic preference modelling. Our setting applies to planning situations with a single agent who has deterministic and instantaneous actions to be performed sequentially in a static and known environment. Aside from the addition of values, our framework differs from classical planning in two aspects, by having multiple goals and by allowing temporal goals. In particular, the expressiveness of LTL means that we can express a wide variety of goals and values, including complex temporal values such as "if the weather is cold, close external doors immediately after opening them", with a computational complexity equivalent to that of standard planners. As a limitation, the system is less able to express values that tend to be satisfied by degree rather than absolutely or not at all. Among the multiple directions for future work that our definitions open, we plan to study the multi-agent extension with possibly conflicting values among agents, moving from plans to strategies (functions from states or histories to actions), from complete to incomplete information, and, most importantly, test our model by implementing it in simple robotics scenarios. Furthermore, given the computational complexity of Conflict, Mininal-Contraction and Non-Dominance, it may often be the case that in practical applications we cannot guarantee finding a non-dominated plan. Therefore, it would be valuable to find more tractable algorithms that at least guarantee some degree of approximation of a non-dominated plan, or restrictions (likely to the language or action theory) that improve tractability of the problem.

Appendix: Missing proofs

Proof of Proposition 3

Proof. Let M = (Ω, γ, s 0 ) and let Ω be a lexicographic ordering of Ω of degree m. Suppose M ′ = (Ω, γ, s 0 ) is a Ω-qual-minimal contraction of M . Suppose for contradiction that M ′ is not qual-minimal. Then there exists some contraction M ′′ = (Ω ′′ , γ, s 0 ) such that Ω ′ ⊂ Ω ′′ . Therefore there exists some value φ ∈ Ω such that φ ∈ Ω ′′ and φ / ∈ Ω ′ . Let p be the priority level of φ in Ω (so φ ∈ Ω p ). Since Ω ′ ⊂ Ω ′′ , we know that for all

1 ≤ k ≤ m, either Ω ′ ∩ Ω k ⊂ Ω ′′ ∩ Ω k or Ω ′ ∩ Ω k = Ω ′′ ∩ Ω k .
We also know that Ω ′ ∩ Ω p ⊂ Ω ′′ ∩ Ω p . Therefore there must be some p ′ ≤ p such that:

1 ≤ p ′ ≤ m and Ω ′ ∩ Ω p ′ ⊂ Ω ′′ ∩ Ω p ′ and ∀1 ≤ k ′ < p ′ , Ω ′ ∩ Ω ′ k = Ω ′′ ∩ Ω ′ k .
By a very similar method, we can derive a contradiction if we suppose that M ′ is Ω-quant-minimal but not qual-minimal.

Proof of Theorem 1

Proof. To show that Conflict is PSPACE-hard, we show a reduction from the classical planning problem PLANSAT for propositional STRIPS planning [START_REF] Bylander | The computational complexity of propositional STRIPS planning[END_REF]. In this problem we have a set of conditions (propositions) that can be true of false, an initial state which is a collection of conditions, a set of operators (actions) that have preconditions and postconditions as sets of satisfiable conjunctions of positive and negative conditions, and a single goal which is a conjunction of positive and negative conditions. We then attempt to find a finite sequence of operators that acheives the goal from the starting state. For a more complete description and complexity results, see [START_REF] Bylander | The computational complexity of propositional STRIPS planning[END_REF].

To perform the reduction, set Ω = {ω} where ω is our goal. Creating an action theory γ from the set of operators and a start state s 0 can be done in polynomial time. Then Conflict applied to (Ω, γ, s 0 ) returns true if and only if PLANSAT would return false.

To show that Conflict is PSPACE-complete, we show a reduction from Conflict to PLANSAT. Given a moral problem M = (Ω, γ, s 0 ) define φ as the conjunction of all formulas in Ω, then set φ as our goal. We can generate a set of operators from γ and an initial state from s 0 in polynomial time. Then PLANSAT returns true if and only if Conflict would return false.

Proof of Theorem 2

Proof. To show that Minimal-Contraction is PSPACE-hard, we show a reduction from Conflict . Given a value problem N , set M = M ′ = N . Then by proposition 1, Minimal-Contraction will return true if and only if Conflict would return false.

To show that Minimal-Contraction is PSPACE-complete, we provide a basic algorithm that uses polynomial space. First, use Conflict to check if M ′ is a conflict, if it is, return false. If not, let A = Ω\Ω ′ . For each a ∈ A, run Conflict on (Ω ′ ∪ a, γ, s 0 ). If Conflict returns false on any of these checks, return false, else, return true.

Proof of Theorem 3

Proof. Recall that to compare two plans π 1 and π 2 we need an ethical planning domain ∆ = (γ, s 0 , Ω) where γ is an action theory, s 0 is an initial state and Ω is a value base. Following Definition 10, plan π 1 is better than π 2 if the history generated by π 1 is lexicographically preferred to the history generated by π 2 according to the ranked values in Ω.

We begin by showing that generating the unique history associated to a kplan can be done in polynomial time. Then we show that evaluating an LTL f formula over this history can be done in polynomial time, concluding that Comparison is in P since we can give an answer by model checking all formulas in Ω over the histories generated by the two plans.

Generating H act associated to π can be done by making a copy of the plan π that returns skip whenever the input is greater than k. This can be done in polynomial time. We then set H st (0) = s 0 , then for each H st (i) we use γ to generate H st (i + 1) in polynomial time by model checking all formulas in γ. We only have to do this k times.

Let us now show that LTL f formulas can be checked in polynomial time on the history generated by a k-plan. Suppose we have an LTL f formula φ of length n, and a history H associated with some k-plan π. We proceed by strong induction on n. For the purpose of this proof, suppose an algorithm that takes φ and H as inputs. Let H j be the history such that H j act (i) = H act (i + j) and H j st (i) = H st (i + j).

Base case. Suppose n = 1, then φ = p for some p ∈ Prop. Then we can determine if p ∈ H st (0) in polynomial time.

Inductive step. Suppose n > 1 and that the claim holds for all m < n. Then we have several options for φ.

1. φ = ¬ψ. Then by inductive hypothesis we can determine in polynomial time if H ⊨ ψ and thus if H ⊨ φ. 2. φ = ψ ∧ χ. Then we can determine in time P if H ⊨ ψ and H ⊨ χ. 3. φ = Xψ. Then we can determine (in polynomial time) if H 1 ⊨ ψ. 4. φ = ψ U χ. Then for 0 < j < k we can determine if H 0 , H 1 , ..., H j-1 ⊨ ψ and H j ⊨ χ in polynomial time. Therefore this whole process can be done in polynomial time.

To conclude, suppose we have an ethical planning domain ∆ = (γ, s 0 , Ω) and k-plans π 1 and π 2 . By the previous steps we can generate H π1 and H π2 , and for each ω ∈ Ω we can determine whether H π1 and H π2 ⊨ ω in polynomial time. Therefore evaluating for every possible value can be done in polynomial time. Determining ⪯ qual ∆ involves checking every value a maximum of once, so we can conclude that Comparison is in P .

Proof of Theorem 4

Proof. To show that Non-Dominance is PSPACE-hard, we show a reduction from the classical planning problem PLANMIN for propositional STRIPS planning [START_REF] Bylander | The computational complexity of propositional STRIPS planning[END_REF]. In this problem we have a set of conditions (propositions) that can be true of false, a set of operators (actions) that have preconditions and postconditions as sets of satisfiable conjunctions of positive and negative conditions, and a single goal which is a satisfiable conjunction of positive and negative conditions. We then attempt to find a sequence of k or less operators that acheives the goal from the starting state. For a more complete description and complexity results, see [START_REF] Bylander | The computational complexity of propositional STRIPS planning[END_REF].

To perform the reduction, set Ω = Ω 1 where Ω 1 = {ω} where ω is our goal. Creating an action theory from the set of operators can be done in polynomial time. Then, generate a random k-plan π and check if H π ⊨ ω, if it does then we are done. If it does not then non-dominance applied to π is equivalent to PLANMIN.

To show that Non-Dominance is PSPACE-complete we provide a basic algorithm that uses polynomial space. Given ∆ = (γ, s 0 , Ω) and k-plan π, check every possible plan π ′ for γ and s 0 and check Comparison against π. Terminate once a plan is found that dominates π or once all plans have been checked. This algorithm only needs two plans in memory at any one time (π and the plan being compared to π), and therefore it only requires polynomial space.

  |= φ 1 U φ 2 ⇐⇒ ∃t ′ ≥ t : t ′ ≤ k and H, t ′ |= φ 2 and ∀t ′′ ≥ t : if t ′′ < t ′ then H, t ′′ |= φ 1 .

	|= p	⇐⇒ p ∈ H st (t),
	H, t |= Xφ	⇐⇒ t < k and H, t + 1 |= φ,
	H, t

See Copp[START_REF] Copp | The Oxford Handbook of Ethical Theory[END_REF] for a philosophical introduction, and Jenkins et al.[START_REF] Jenkins | When robots should do the wrong thing[END_REF], Powers[START_REF] Powers | Deontological machine ethics[END_REF], and Vallor[START_REF] Vallor | Technology and the Virtues: A Philosophical Guide to a Future Worth Wanting[END_REF] for a discussion of these three theories in robotics.

Acknowledgements This work is supported by the CNRS project LEXIA ("The Logic of Explanation: From Explainable to Explaining Legal Knowledgebased Systems").


Eugénie Mortessagne

Dalila Bovet

Camille Nozières

Emmanuelle Pouydebat

Fabien Pifferi
email: fabien.pifferi@mnhn.fr

Learning performance of grey mouse lemurs (Microcebus murinus) during a visual discrimination task: effect of the stimuli's emotional value

Keywords: Cognition, emotion, learning, avoidance, lemurs, evolutionary origins

While the interaction between emotions and cognition is relatively well known in humans, it remains to be explored in non-human primates, whose dedicated studies are carried out on a limited diversity of species, preventing us from discussing the evolutionary origin of this interaction. Here, we explored this cognitionemotion interaction in the grey mouse lemur (Microcebus murinus), often described as possessing ancestral characteristics, allowing us to better comprehend if this link appears soon in the phylogeny of primate.

We tested whether emotions could modify the learning performance of 60 mouse lemurs during a visual discrimination task. In this task, individuals had to learn to discriminate between two platforms using emotionally valued visual stimuli and to jump on the target platform. Our results showed that individuals learning performance improved when distractors had an emotional valence compared to when they were neutral. Opposite, individuals had impaired learning performance when targets had an emotional valence compared to when they were neutral. These results are consistent with the cognitive avoidance pattern for negative stimuli reported in other studies. This study is the rst to explore emotion in mouse lemurs and to demonstrate that the emotion-cognition interaction is already present in a lemur's species.

Introduction

In humans, an important interaction exists between cognitive abilities and emotions. Indeed, several studies have shown that emotions can affect most cognitive processes such as judgments, attention, memory, reasoning, decision making, learning (de Houwer & Hermans, 2010; [START_REF] Lemaire | Emotion and Cognition: An Introduction[END_REF]Robinson et al., 2013). For example, performance in a working memory task is better when images to memorize have an emotional value (positive or negative) than when they are neutral [START_REF] Lindström | Emotion processing facilitates working memory performance[END_REF]. The emotional Stroop Task is commonly used in human psychology to assess attentional biases induced by emotion. In this task, human participants are instructed to name the colors in which emotionally loaded words are written. Participant's attention tends to be drawn to emotionally relevant stimuli (see Williams et al., 1994 for review) resulting in slower and less accurate responses when the words are negative, such as death or accident [START_REF] Bar-Haim | Threatrelated attentional bias in anxious and nonanxious individuals: a meta-analytic study[END_REF][START_REF] Mckenna | Reversing the Emotional Stroop Effect Reveals That It Is Not What It Seems: The Role of Fast and Slow[END_REF]). Thus, while the links between emotion and cognition are relatively well known in humans, they remain to be explored in other primates in order to understand when this link appears in the phylogeny of primates.

For non-human primates, an increasing number of dedicated studies show that in some haplorrhine's species (Guinea baboons, chimpanzees, bonobo, Japanese macaques, rhesus macaques, capuchins, gorilla), cognitive processes can be modulated by the emotional value of stimuli. For example, in a visual search task, Japanese macaques (Macaca fuscata) are faster to detect threatening stimuli (snakes) than neutral stimuli ( owers) [START_REF] Shibasaki | Rapid Detection of Snakes by Japanese Monkeys (Macaca fuscata): An Evolutionarily Predisposed Visual System[END_REF] and show preferential engagement of attention to snakes [START_REF] Masataka | Preferential attentional engagement drives attentional bias to snakes in Japanese macaques (Macaca fuscata) and humans (Homo sapiens)[END_REF]. This attentional prioritization of threatening stimuli (snake in this study) may be explained from an evolutionary perspective: individuals prone to detect threats would have a survival advantage [START_REF] Lacreuse | Attentional biases and memory for emotional stimuli in men and male rhesus monkeys[END_REF]. In a dot-probe task (a dot appears at the same location as one of the stimuli, the distribution of attention is measured by the time taken to respond to the dot), rhesus macaques (Macaca mulatta) detect targets presented in the same locations as social stimuli more quickly when the faces of conspeci cs are threatening rather than neutral [START_REF] Lacreuse | Attentional biases and memory for emotional stimuli in men and male rhesus monkeys[END_REF]. Several studied also use a modi ed version of the emotional Stroop task uses in humans. Developed by [START_REF] Allritz | How chimpanzees (Pan troglodytes) perform in a modi ed emotional Stroop task[END_REF], this task has only recently been used in chimpanzees, gorillas, Japanese macaques and bonobos [START_REF] Allritz | How chimpanzees (Pan troglodytes) perform in a modi ed emotional Stroop task[END_REF][START_REF] Hopper | A Comparative Perspective on Three Primate Species' Responses to a Pictorial Emotional Stroop Task[END_REF][START_REF] Laméris | Social and nonsocial stimuli alter the performance of bonobos during a pictorial emotional Stroop task[END_REF][START_REF] Vonk | Testing for the 'Blues': Using the Modi ed Emotional Stroop Task to Assess the Emotional Response of Gorillas[END_REF]. This emotional Stroop task explores whether emotionally valent stimuli (images) would interfere with the performance (accuracy and response time) of individuals in a color discrimination task (i.e., emotionally loaded pictures were presented with different colored borders, one of which gave a reward. The response time and accuracy to select the right color was measured). These studies show tendencies of longer response time for emotionassociated stimuli [START_REF] Allritz | How chimpanzees (Pan troglodytes) perform in a modi ed emotional Stroop task[END_REF][START_REF] Laméris | Social and nonsocial stimuli alter the performance of bonobos during a pictorial emotional Stroop task[END_REF][START_REF] Vonk | Testing for the 'Blues': Using the Modi ed Emotional Stroop Task to Assess the Emotional Response of Gorillas[END_REF] or decreased accuracy (i.e. proportion of correct response) [START_REF] Hopper | A Comparative Perspective on Three Primate Species' Responses to a Pictorial Emotional Stroop Task[END_REF]. These effects can be attributed to the fact that participants' attention is drawn to emotionally relevant stimuli. In addition, a study on Guinea baboons (Papio papio) demonstrated that the emotional value of mental representations, in the absence of physical stimuli, can also impact individuals' cognitive abilities [START_REF] Blanchette | Emotion-Cognition Interaction in Nonhuman Primates: Cognitive Avoidance of Negative Stimuli in Baboons (Papio papio)[END_REF]. In this study, baboons were asked to memorize the location of two targets of the same color, presented with a distractor of a different color, in a short-term memory task. As a result of long-term conditioning in the group of baboons involved in this study, one of the colors (green) was associated by individuals with a negative emotion (the green color is used as a signal of an incorrect response during their routine touch screen tests). The results showed that individuals were slower and less accurate when the targets were negative compared to when they were neutral. In contrast, subjects were faster and more accurate when the distractors were negative than when they were neutral. These results support the hypothesis of the cognitive equivalent to the phenomenon of avoidance of negative stimuli, showed in several studies (e.g., chimpanzee, rhesus macaques) (e.g., [START_REF] Hopkins | Handedness and Approach-Avoidance Behavior in Chimpanzees (Pan)[END_REF][START_REF] Lacreuse | Short-term testosterone manipulations modulate visual recognition memory and some aspects of emotional reactivity in male rhesus monkeys[END_REF][START_REF] Machado | Impact of Amygdala, Orbital Frontal, or Hippocampal Lesions on Threat Avoidance and Emotional Reactivity in Nonhuman Primates[END_REF][START_REF] Murray | Prefrontal cortex interactions with the amygdala in primates[END_REF][START_REF] Nelson | Individual Differences in the Responses of Naïve Rhesus Monkeys to Snakes[END_REF][START_REF] Sinnott | Perception of Scary Halloween Masks by Zoo Animals and Humans[END_REF][START_REF] Thompson | Approach versus avoidance in an ambiguous-cue discrimination problem in chimpanzees[END_REF]. For example, an eye-tracking study documented sustained avoidance of negative images (threatening picture of conspeci cs) in stressed rhesus macaques [START_REF] Bethell | Evidence That Emotion Mediates Social Attention in Rhesus Macaques[END_REF]. Finally, none of these studies, exploring the relationship between emotion and cognition, have focused on primates more distant from humans from a phylogenic point of view, such as strepsirrhines. In particular, to our knowledge, no studies explored the relationship between emotion and cognition in Malagasy lemurs, which belong to the most ancient extant primate radiation [START_REF] Yoder | Divergence dates for Malagasy lemurs estimated from multiple gene loci: geological and evolutionary context[END_REF]) and show the largest variation in body sizes, activity, feeding patterns, locomotion styles, and sociality patterns among the strepsirrhine [START_REF] Scheumann | Predation, Communication, and Cognition in Lemurs[END_REF]. They provide important models to explore the origin of primate behavior [START_REF] Scheumann | Predation, Communication, and Cognition in Lemurs[END_REF]. Thus, the aim of the present study is to evaluate the interaction between emotion and cognition in a small nocturnal Strepsirrhini, the grey mouse lemur (Microcebus murinus). This will be, to our knowledge, the rst study to evaluate this relation in a lemur species and will allow us to learn more about the evolutionary origin of this interaction, of which little is known. Grey mouse lemurs are often described as primates who have retained several primitive features (e.g. small size, arboreal and nocturnal lifestyle, omnivorous diet) characteristic of the primate ancestors (Charles-Dominique & Martin, 1970; [START_REF] Ho | The gray mouse lemur (Microcebus murinus) as a model for early primate brain evolution[END_REF][START_REF] Radespiel | Female dominance in captive gray mouse lemurs (Microcebus murinus)[END_REF]. Weighing between 60 and 120 g and with an average height of 25 cm from head to tail [START_REF] Languille | The grey mouse lemur: A non-human primate model for ageing studies[END_REF], it is one of the smallest primates in the world. During the day, the mouse lemur sleeps in holes on tree that he covers with leaves to build a nest. These nests are important resources for this nocturnal primate since they allow it to increase its chances of survival against predators (e.g. raptors, snakes, fossas) and to have a better thermoregulation by insulating them and creating a favorable microclimate [START_REF] Radespiel | Sex-Speci c Usage Patterns of Sleeping Sites in Grey Mouse Lemurs (Microcebus murinus) in Northwestern Madagascar[END_REF][START_REF] Schmid | Tree holes used for resting by gray mouse lemurs (Microcebus murinus) in Madagascar: Insulation capacities and energetic consequences[END_REF]. Efforts of eld biologists provided detailed analyses of many aspects of their behavior and ecology [START_REF] Radespiel | Sociality in the gray mouse lemur (Microcebus murinus) in northwestern Madagascar[END_REF][START_REF] Radespiel | Sex-Speci c Usage Patterns of Sleeping Sites in Grey Mouse Lemurs (Microcebus murinus) in Northwestern Madagascar[END_REF] study to date has been conducted on their emotions, which therefore remains unexplored. Thus, the present study has a twofold objective: to advance on the understanding of the evolutionary origin of the interaction between emotion and cognition by studying it in a primate close to the common ancestor, and to improve the knowledge of mouse lemurs' emotions, which could allow in the longer term to improve and optimize their well-being in captivity.

We conducted a learning test in which individuals have to discriminate two platforms (only one giving access to a reward) using visual cues. Visual stimulus can be used since vision has been identi ed as a key modality for prey detection in captive born mouse lemurs [START_REF] Piep | The sensory basis of prey detection in captive-born grey mouse lemurs, Microcebus murinus[END_REF]. The visual discrimination task has already been used as a classic cognitive task (with emotionally neutral stimuli) in various cognitive studies on mouse lemurs [START_REF] Gary | Encephalopathy induced by Alzheimer brain inoculation in a non-human primate[END_REF][START_REF] Hozer | Physiological and cognitive consequences of a daily 26 h photoperiod in a primate: exploring the underlying mechanisms of the circadian resonance theory[END_REF][START_REF] Picq | Jumping Stand Apparatus Reveals Rapidly Speci c Age-Related Cognitive Impairments in Mouse Lemur Primates[END_REF][START_REF] Royo | Effects of n-3 polyunsaturated fatty acid supplementation on cognitive functions, electrocortical activity and neurogenesis in a non-human primate, the grey mouse lemur (Microcebus murinus)[END_REF]. This task has several advantages such as a fast habituation time and understanding of the apparatus, a possibility to easily manipulate the stimuli and to repeat the learning endlessly, provided stimuli are changed. Moreover, this task is adapted to the arboreal nature of mouse lemurs since it requires them to jump to make a choice. The present study will be the rst to develop such an ecological task for the study of cognition and emotion interaction, adapted to small arboreal primate species and to species for which the use of a touchscreen requires too much training time and/or is not accessible. In our task, mouse lemurs had to discriminate two platforms, using visual stimuli with supposed emotional or neutral value, and to jump on one of the platforms.

We hypothesized that the emotional nature of the stimuli, depending on whether they are target (associated with the correct platform) or distractor (associated with the incorrect platform), would modify the learning performance of grey mouse lemurs in this visual discrimination task. Speci cally, we hypothesized that individuals would exhibit cognitive avoidance, characterized by the inhibition of processing threatening information [START_REF] Blanchette | Emotion-Cognition Interaction in Nonhuman Primates: Cognitive Avoidance of Negative Stimuli in Baboons (Papio papio)[END_REF][START_REF] Günther | Coping With Anxiety: Brain Structural Correlates of Vigilance and Cognitive Avoidance[END_REF]). This will result in better performance when the negative stimulus is the distractor and poorer performance when it is the target. We expected the contrary for the positive stimuli, with an approach tendency. Finally, we also expected differences between individuals. Indeed, in humans, highly anxious individuals show an attentional bias for threatening stimuli [START_REF] Bar-Haim | Threatrelated attentional bias in anxious and nonanxious individuals: a meta-analytic study[END_REF]. Anxious humans are also more likely to have their attention captured by negative stimuli and to have di culty to disengaging attention from the threat [START_REF] Yiend | Anxiety and Attention to Threatening Pictures[END_REF]. In non-humans' animals, "shy" individuals (generally slow explorer, non-aggressive, anxious) tend to take longer time to make choices but are more accurate (Sih & del Giudice, 2012) which could result in better learning compared to "bold" individuals (generally fast explorer, aggressive). To test these individuals' differences, we conducted two behavioral tests that have been previously validated as variables re ecting personality in grey mouse lemurs [START_REF] Verdolin | Are shy individuals less behaviorally variable? Insights from a captive population of mouse lemurs[END_REF]; Zablocki-Thomas et al., 2018).

Methods

Subjects

Sixty adult male (28) and female (32) grey mouse lemurs (Microcebus murinus) aged 2-5 years, born and raised in the laboratory colony of UMR 7179 (CNRS/MNHN, Brunoy, France), were involved in this study.

The animals were kept alone or in groups in their usual cages of variable size, provided with branches, leaves, various enrichments and a wooden nestbox, at constant temperature (24-26 °C) and relative humidity (55%), mimicking the conditions of Madagascar. The mouse lemurs were exposed to a seasonal alternation of the light/dark cycle consisting of summer-like long day length (14:10 light:dark) and winterlike short day length (10:14 light:dark). In this study, all individuals involved were in summer. The mouse lemurs were fed ad libitum with fresh fruits and vegetables and a mixture of cereals, gingerbread, yogurt, egg, milk and water prepared daily in the laboratory.

To ensure that all animals tested were in a suitable physical condition to perform the task, we also performed a motor coordination and endurance test using an accelerating rotating cylinder (Rotarod test). This allowed us to exclude the possibility that the results were due to impaired motor skills and/or physical condition. The animal's eyes were also checked by a veterinary ophthalmologist.

All experimental procedures were non-invasive and approved by the ethical committee "Comité d'éthique Cuvier n°68" under the authorization n°12992-2018011613568518 v4.

Cognitive task 2.2.1 Apparatus

The experiments were conducted in an isolated cognition room containing the apparatus. The apparatus was a handmade rectangular parallelepiped (height = 150 cm) composed of plywood walls (Figure 1). The apparatus was completely closed to prevent, as much as possible, the animal from being disturbed by our presence. The interior of the apparatus was illuminated by a light bulb attached to the ceiling of the cage, in the right corner. To observe the animal, a camera was placed in the center of the ceiling, allowing us to have an overall view of the apparatus. The lemur was placed inside the apparatus via a trapdoor opening from the outside. This trapdoor opened onto the starting platform, connected to the outside by a wire. In each trial, the animal had to jump from the starting platform onto one of the two landing platforms (15 cm x 30 cm). If the animal did not jump within 30 seconds, starting stand was progressively tilted downward using the wire and slow back and forth movements were performed to increase the motivation to jump. If the animal jumped onto the incorrect platform, the platform swung down and the mouse lemur fell into the bottom of the apparatus on a wide soft pillow to avoid any risk of injury. One side of the device could open to allow the experimenter to take back the mouse lemur and put it back on the starting platform, passing again through the trapdoor, for another trial.

If the animal jumped onto the correct platform, it could pass through one of the 3 openings of an opaque Plexiglas screen to access its nestbox. The opaque screen prevented mouse lemur from jumping directly to the opening of the nestbox. The reward consisted in allowing the mouse lemur to reach its nest and then to be "home safe" for 2 minutes. This reward (to enter and stay in the wooden nest) is particularly effective in mouse lemurs as they are very keen to nd their nestbox, due to their habit in their natural environment to make use of tree holes as vital means to evade predation and ensure thermoregulation. The placement of the correct platform was chosen randomly, trial by trial, with the condition that the same side could not be chosen for more than three consecutive trials. If the animal jumped on the same side 3 times in a row, the random alternation of location was temporarily suspended, and the correct platform was placed on the opposite side until the individual jumped there. This avoids reinforcing a side bias.

Stimuli

The aim was to test whether learning performance of mouse lemur in this discrimination task could be altered by emotions. Visual stimuli with supposed emotional values were chosen to discriminate the platforms. A glove was chosen as a negative stimulus. Grey mouse lemur involved in this study are regularly handled with gloves that causes them stress. For the positive stimulus, laurel leaves, with which our mouse lemurs make their nests, were chosen. Supposedly neutral stimuli (cardboard stars, which are not part of the mouse lemurs' daily life) were also used as controls. To avoid bias, stimuli were created to have the same surface area as possible. Each stimulus could either be associated with the correct platform or with the incorrect platform. In the rst case, the stimulus was referred to as the target and in the second as the distractor, the goal of the task being to learn the location of the correct platform. By combining the three types of stimuli with the two types of platforms, six experimental groups were created (Figure 2 -see legend for a description of the groups). A seventh group with target and neutral distractors is used as a control.

General procedure

This visual discrimination test was conducted over 3 days. The rst day was for the habituation phase and the other two days to the learning phase. The learning phase was conducted on two days to allow the animal to consolidate its learning during the night.

Habituation phase

The habituation phase was designed to familiarize the mouse lemur with the apparatus and to teach it to jump on the landing platforms. The habituation was composed of seven phases of eight trials each.

During phases n°1 and n°2, a central landing platform was attached between the two landing platforms, just below the nestbox opening. On phases n°3 and n°4, an opaque Plexiglas screen was added above the middle of the landing platform masking the nestbox opening. The mouse lemur had to jump onto the central landing platform then to pass through one of the 3 openings of the screen to access its nestbox.

For the last three phases, the central landing platform was removed and a single landing platform was placed alternately to the left or to the right of the nestbox opening, which was still masked by the opaque screen. For each phase, 8 trials were possible. A failed trial was recorded if the animal jumped elsewhere than on the platforms or did not jump after 5 minutes. If the animal failed all 8 trials in a phase, the habituation was stopped and repeated the next day.

Learning phase

During the learning phase, the mouse lemurs were given each day a session of a maximum of 30 trials. On each trial, the animal had to choose between one of two platforms on which were placed the positive, negative or neutral emotionally valent stimuli. A trial was considered successful when the animal jumped onto the correct platform. A trial was considered unsuccessful when the animal jumped onto the incorrect platform. Also, a trial was marked as a refusal if the animal jumped elsewhere than on the platforms or did not jump after 5 minutes. After 5 consecutive refusals, the test session was interrupted. The session could also be interrupted if the animal reached the success criterion, i.e., if it successfully completed 8 out of 10 consecutive trials. Each stimulus was associated with a platform at the beginning of the session, depending on which group the individual belonged to, and remained associated with it until the end of the two sessions. The goal was for the mouse lemur to learn the location of the correct platform using the visual stimulus.

Behavioral coding

The behavior of individuals was considered through two tests described below: agitation score and emergence time. Only 52 individuals out of 60 were tested because 8 animals died before testing or colony constraints prevented testing them. In this study, these tests could only be performed once but have already been validated as variables re ecting personality in mouse lemurs [START_REF] Verdolin | Are shy individuals less behaviorally variable? Insights from a captive population of mouse lemurs[END_REF] Zablocki-Thomas et al., 2018).

Agitation score

The rst test consisted of assigning an agitation score to each mouse lemurs based on their behavior during a manipulation. We followed the same protocol as described in [START_REF] Verdolin | Are shy individuals less behaviorally variable? Insights from a captive population of mouse lemurs[END_REF]. In brief, the test consisted in grabbing the animal and scoring its reaction: urinating (1 point), defecating (1 point), screaming (1 point), struggling (2 points), and biting (3 points). According to this protocol, animals could score a minimum of 0 (no agitation) and a maximum of 8 (high agitation). The scoring started directly after extraction of the animal from its nestbox and lasted 45 seconds.

Emergence time

The second test was to measure the emergence time of individuals according to the protocol used in Zablocki-Thomas et al. (2018). We caught animals directly in their cage and placed a single individual in the wooden nestbox. We placed the wooden nestbox at the entrance of the home cage of the individual.

We then waited at least 2 min so that the animal could habituate and calm down from the manipulation. The test consisted in opening the trap door and recording the latency for the animal to escape from the nestbox and return to its home cage. The test lasted 5 min maximum. Individuals that never left the nestbox within this 5 min were given a score of 300s.

Statistical analysis

All statistical analyses were performed using R software (version 4.2.1). For all analyses, we considered an effect to be statistically signi cant when P < 0.05.

To test our hypotheses, we examined three measures obtained during the cognitive tests: the percentage of success corresponding to the number of successful trials (trials during which the individual jumped on the correct platform) divided by the total number of trials; the percentage of errors corresponding to the number of failed trials (trials during which the individual jumped on the incorrect platform) divided by the total number of trials; and nally, the refusal rate corresponding to the number of refusals (the individual did not jump or jumped anywhere other than on the platforms) divided by the total number of trials. Our aim was to nd out whether the emotional valence of the target and distractor stimuli (i.e. the group) in uenced these performance parameters. We performed analysis of covariance (ANCOVA) with the performance variables (success, error and refusal rate) as independent variables and with age, sex, group and behavioral data as dependent variables. These ANCOVA were performed with the Anova() function of the "car" package (cran.r-project.org/web/packages/car). In order to select the best model for our data, we used the AIC (Akaike Information Criterion) index by using the stepAIC() function of the "MASS" package (https://cran.r-project.org/web/packages/MASS/index.html). The application requirements were met for the success and error percentages. For the percentage of refusals, we had to transform our data with a LOG transformation. In case of signi cant effects, post-hoc tests were performed (adjustment method: Bonferroni) via the tukeyhsd() function of the "rstatix" package (https://cran.rproject.org/web/packages/rstatix/index.html).

Results

We hypothesized that performance in the learning task would be modi ed by the nature of the target and distractor stimuli. As the age of the animals was consistent between the groups (Kruskal-Wallis's test: P = 0.133), we did not take it into account in the models. This also applies to the weight of individuals.

Success rate

Analysis of covariance (ANCOVA) showed signi cant effects of group on success rate (P < 0.001; Table 1). 3a). For the other explanatory variables tested (gender, behavior), the ANOVA did not show a signi cant in uence on the percentage of success.

Post-hoc tests comparing

3.2 Non-success rate (errors and refusals)

Errors rate

ANCOVA also showed signi cant effects of group on error rate (P < 0.001, Table 1). Post-hoc tests show a signi cant difference in error rate between group + TND (60.5%) and group NT + D (26.37%) (p.adj = 7.38e-03) ; between groups + TND and NT-D (19.38%) (p.adj = 6.45e-04) ; between groups NT + D and -TND (62%) (p.adj = 4.48e-03) ; between groups NT + D and NTND (59.8%) (p.adj = 5.11e-03) ; between groups -TND and NT-D (p.adj = 3.71e-04) ; between groups NT-D and NTND (p.adj = 3.73e-04) (Fig. 3b). Error rate for groups + T-D and -T + D were 31.86% and 43.11%, respectively.

Refusals rate

Finally, ANCOVA showed signi cant group effects on the refusals rate (P < 0.001, Table 1). Post-hoc tests show a signi cant difference in the refusal rate between group -T + D (38%) et group + TND (3.75%) (p.adj = 1.59e-02) ; between groups -T + D and NT + D (4.12%) (p.adj = 1.18e-02) ; between groups -T + D and -TND (6.75%) (p.adj = 0.05) ; between groups -T + D and NT-D (2.87%) (p.adj = 1.02e-03) ; between groups -T + D and + T-D (1.87%) (p.adj = 4.32e-03) et between groups -T + D and NTND (8.3%) (p.adj = 1.92e-02) (Fig. 3c). Finally, the analysis revealed an effect of the agitation score, attributed to each individual, on the refusals rate during the learning task (P = 0.02).

Discussion

While the interaction between emotions and cognition is relatively well known in humans, it remains to be explored in non-human primates, whose dedicated studies are carried out on a limited diversity of species, mostly haplorrhines, preventing us from discussing the evolutionary origin of this interaction. Our goal was to explore this interaction between emotion and cognition in a lemur species, the grey mouse lemur (Microcebus murinus), a strepsirrhine often described as possessing ancestral characteristics. We tested whether emotions could modify the learning performance of mouse lemurs in a visual discrimination task.

In this task, individuals had to learn, by trial-and-error, to discriminate between two platforms using emotionally valent visual stimuli (supposedly positive, negative, or neutral) and to jump onto the correct platform giving access to their nestbox.

Our results showed that the learning performance of mouse lemurs are modi ed by the emotional value of stimuli. In line with our prediction, mouse lemurs were less successful (low success rate and high error rate) on the learning task when the targets were negative and the distractors neutral (group -TND). In contrast, subjects were more successful (high success rate and low error rate) when the distractors were negative and the targets neutral (group NT-D). In short, relative to neutral stimuli, negative targets impaired performance and negative distractors improved performance, resulting in a more e cient learning. These results are consistent with previous study on the effect of negative stimuli on short term memory [START_REF] Blanchette | Emotion-Cognition Interaction in Nonhuman Primates: Cognitive Avoidance of Negative Stimuli in Baboons (Papio papio)[END_REF] or on the effect of negative stimuli on an emotional stroop task [START_REF] Hopper | A Comparative Perspective on Three Primate Species' Responses to a Pictorial Emotional Stroop Task[END_REF]. They can be explained by the phenomenon of cognitive avoidance, where the individual will avoid processing threatening information [START_REF] Blanchette | Emotion-Cognition Interaction in Nonhuman Primates: Cognitive Avoidance of Negative Stimuli in Baboons (Papio papio)[END_REF][START_REF] Günther | Coping With Anxiety: Brain Structural Correlates of Vigilance and Cognitive Avoidance[END_REF]. This effect is analogous to the basic behavioral avoidance of negative stimuli [START_REF] Blanchette | Emotion-Cognition Interaction in Nonhuman Primates: Cognitive Avoidance of Negative Stimuli in Baboons (Papio papio)[END_REF]. This avoidance led to impaired performance when the negative stimuli is the target. In contrary, avoidance of the negative stimuli, when it is the distractor, can result in less interference with the target processing and thus improve learning performance. Our result added to the existing literature on the effect of negative stimuli on primates' cognition (Allritz et In contrast to our prediction, positive target stimuli did not improve mouse lemurs' performance. Indeed, the same pattern observed with negative stimuli was also observed with positive stimuli: positive targets and neutral distractors (group + TND) impaired performance and positive distractors and neutral targets (group NT + D) improved performance. In short, relative to neutral stimulus, positive targets impaired learning performance and positive distractors improved learning performance. These results could be explained by the fact that what we assumed to be positive (laurel leaves) is not perceived as positive for the mouse lemur. Indeed, while it is rather easy to generate negative emotions, it is more challenging to generate positive emotions in mouse lemurs and in nonhuman species in general which is highlighted by the lack of study on positive emotions [START_REF] Webster | The Effects of Positive and Negative Experiences on Subsequent Behavior and Cognitive Performance in Capuchin Monkeys (Sapajus [Cebus] apella)[END_REF]. However, we know that the glove and the laurel leaves generate different types of reactions in individuals. Indeed, when the emotional stimuli were opposed to each other's, performance were better when the positive stimulus was the target, and the negative stimulus was the distractor (group + T-D) than the other way around (negative target and positive distractors (group -T + D). This shows a gradient in the stimuli used, with stronger effect for the negative stimulus (glove). Our results with positive stimuli can also be explained by the fact that positive stimuli, compared to neutral stimuli, do not necessarily improve the cognitive performance of individuals. A study on capuchins monkey nds that, in a working memory task, positive experience did not facilitate performance compared to control condition (Webster & Brosnan, 2021), though the positive condition (i.e., familiar puzzle apparatus with access to a preferred food reward) was most likely not perceived as positive by the individuals, or nulli ed by subjects' frustration when the apparatus was removed.

This shows, once again the challenge of evaluating positive emotion. Another study using the modi ed emotional Stroop task for non-humans' primates [START_REF] Hopper | A Comparative Perspective on Three Primate Species' Responses to a Pictorial Emotional Stroop Task[END_REF] nd that the individuals made more errors in selecting the correct square when it contained positive or negative photographs compared to neutral images, indicating that their cognitive ability was disrupted by emotional stimuli compared to neutral.

Moreover, when the two emotion-related stimuli were presented together (group + T-D & -T + D), we observed signi cant difference in success rate but not in error rate. This is because in the group where the target is negative and distractor positive, individuals refused a lot to jump on the platforms. It's in fact the only group with a high rate of refusal. One explanation is that individuals avoid the glove, as observed in other groups. However, individuals also tend to avoid laurel leaves, as also observed in the other groups.

Here, the leaves are additionally associated with the negative platform resulting in a double negative effect. This combination of negative effects leads to a total stop of the learning, the animals not wanting to perform the task anymore and either staying on the departure platforms or jumping on the side walls of the apparatus.

Our results did not reveal individual differences, regarding behavioral traits, in success and error rates.

They did highlight individual differences with a signi cant effect of agitation score on the refusal rate.

However, these results should be taken with great caution. Indeed, even though the tests we used have been validated as re ecting personality traits in mouse lemurs in different studies [START_REF] Verdolin | Are shy individuals less behaviorally variable? Insights from a captive population of mouse lemurs[END_REF]; Zablocki-Thomas et al., 2018), we did not perform the tests several times. Moreover, due to deaths or other constraints, we could not perform these tests on all the animals (only 52 out of 60 were tested).

Additionally, refusal rate was high for only one group, which leads to di culties in interpreting the results

showing an effect of agitation scores on refusal rates. Still, the individuals with the higher agitations score are the ones with the lowest refusal rates. In previous studies, agitation score was considered to re ect shyness or anxiety in mouse lemurs [START_REF] Verdolin | Are shy individuals less behaviorally variable? Insights from a captive population of mouse lemurs[END_REF] with greater agitation re ecting a shy personality and thus lower agitation a bold one. Therefore, the individuals with the lowest refusal rates are potentially the individual with a shy personality, which could be explained by a greater motivation to join their nest. Future research will have to further test the mouse lemurs' personality in order to draw conclusions on the effect of personality on the emotion-cognition relation.

To further interpret these results, it would be interesting for future research to conduct a new learning test with several stimuli per group. Indeed, multiplying the stimuli for each category can ensure that the observed results are due to emotions and not to an object-speci c effect. Also, to further improve our study, modi cations of the apparatus could be necessary. Indeed, it would be interesting to consider the reaction time of individuals (in our study it would be the time to jump) to determine if the attention of mouse lemur in this task was drawn by emotional stimuli, as observed in other studies [START_REF] Allritz | How chimpanzees (Pan troglodytes) perform in a modi ed emotional Stroop task[END_REF][START_REF] Lacreuse | Attentional biases and memory for emotional stimuli in men and male rhesus monkeys[END_REF][START_REF] Masataka | Preferential attentional engagement drives attentional bias to snakes in Japanese macaques (Macaca fuscata) and humans (Homo sapiens)[END_REF][START_REF] Shibasaki | Rapid Detection of Snakes by Japanese Monkeys (Macaca fuscata): An Evolutionarily Predisposed Visual System[END_REF]). This will require automation of the starting platform, as the way it is moved is experimenter dependent. We could also observe the direction of the gaze of individuals to allow us to see the attention paid by individuals to different stimuli. It would be necessary to place a camera in front of the individuals. The positioning of the body of the individual may also give an indication, as mouse lemurs tended to approach the edge of the side from which they were jumping and to bend over several times before jumping. Another ideal, but time-consuming modi cation, would be for individuals to perform this learning task completely independently. We could for example imagine placing a device inside the home cage of the individuals. This would remove entirely the bias due to our presence. Indeed, even if we tried to reduce the effect of the experimenter as much as possible, the mouse lemurs are very sensitive to the human presence. A study from our team (DiFrancesco et al., 2023) showed extremely high ECG values as soon as a human was present in a room near the lemurs. This consistently high level of stress may have caused bias in our test and masked potentially signi cant individual differences on performance parameters (e.g., success and error rate, learning e ciency).

To our knowledge, this preliminary study is the rst to demonstrate that the interaction between emotion and cognition is already present in a lemur species: we showed that the emotional value of target or distractors modi ed learning performance of mouse lemurs, suggesting a cognitive avoidance of emotional stimuli [START_REF] Blanchette | Emotion-Cognition Interaction in Nonhuman Primates: Cognitive Avoidance of Negative Stimuli in Baboons (Papio papio)[END_REF][START_REF] Günther | Coping With Anxiety: Brain Structural Correlates of Vigilance and Cognitive Avoidance[END_REF]. The implication for this study is double.

First, this allow us to develop our knowledge on the emotions of the grey mouse lemur, since no study to Figures

  the success rate of each group show a signi cant difference between group + TND (35.87%) and group NT + D (69.5%) (p.adj = 2.06e-02) ; between groups + TND and NT-D (77.75%) (p.adj = 1.68e-03) ; between groups NT + D and -TND (31.12%) (p.adj = 5.08e-03) ; between groups NT + D and -T + D (18.89%) (p.adj = 5.10e-05) ; between groups NT + D and NTND (31.9%) (p.adj = 3.43e-03) ; between groups -TND and NT-D (p.adj = 3.44e-04) ; between groups -TND and + T-D (62.75%) (p.adj = 4.40e-02) ; between groups NT-D and -T + D (p.adj = 2.32e-06) ; between groups NT-D and NTND (p.adj = 1.91e-04) ; between groups + T-D and -T + D (p.adj = 6.54e-04) ; between groups + T-D and NTND (p.adj = 3.45e-02) (Fig.

Table 1

 1 Summary table of ANCOVA results testing which variables (age, sex, groups, agitation score, exploration time) affect performance parameters (success, error, and refusal rates). Models represented in this table are best t models according to the AIC index. Variables in bold signi cantly in uence performance (α = 0.05).

	Dependent variables Independent variables Df	F	P
	Success rate	Group	6	12.7579	2.746e-08
		Emergence time	1	1.0672	0.3071
	Errors rate	Group	6	5.9828	1.237e-04
		Emergence time	1	0.5069	0.4802576
	Refusals rate (log)	Group	6	9.0148	1.972e-06
		Agitation score	1	5.1148	0.02872

  al., 2016; Blanchette et al., 2017; Lacreuse et al., 2013; Masataka et al., 2018; Shibasaki & Kawai, 2009) and demonstrated that this effect is present in a lemur species with ancestral characteristics (Charles-Dominique & Martin, 1970; Ho et al., 2021; Radespiel & Zimmerman, 2001).

Acknowledgments

We thank Martine Perret and Aude Anzeraey for logistic support and the animal keepers Isabelle Hiron-Hazé, Laurianne Dezaire and Sandrine Gondor. We also thank the Biodiversity, Evolution, Ecology, Society Initiative (IBEES) for the funding of this project.

date has been conducted on this subject. The grey mouse lemur being an emerging model, it is necessary to develop our knowledge on their emotions and to develop tools to assess their well-being. Second, this brings some new data concerning the evolutionary origins of the emotion-cognition interaction which remains poorly known. In the future, comparative studies exploring the interaction between emotion and cognition in different primate species, representative of the phylogeny, will be needed to learn more about the evolution of this interaction. Letters represent signi cant differences between groups (Tukey test, Bonferroni correction).

Declarations


senior moment Full article -2,130 words In a nutshell -40 words

A typical example of how older people are othered, and how stereotypes of all kinds are utilised to trivialise, essentialise, and denigrate. This expression "jocularly" connotes that being older is tantamount to being forgetful or to have impaired brain function.

Article abstract -250 words

Ageism is prevalent, usually perpetrated with impunity, and has deleterious mental and physical effects on those targeted. In addition to promoting inequality and exclusion, ageism disregards human dignity. Ageism can be positive, benevolent, or hostile. Hostile ageism includes being ignored or avoided on account of older age, using insulting age-related monikers, and being told they have senior moments. Senior moment is a derogatory, essentialising, and trivialising expression that incorrectly correlates advancing age with diminishing mental capacity. To those "humorously" utilising this phrase, any instance of confusion or forgetfulness by an older person is understood to be biologically determined on account of the deleterious effects ageing has on the brain. The persistent exposure to ageist stereotypes along with constantly being reminded that they are having senior moments can also be internalised by older adults, resulting in a deteriorated self-image and a stereotype threat. When faced with such a stereotype threat, many older adults might fear to ask for something to be repeated or explained, since this would "confirm" that they indeed have reduced mental abilities. An insensitive, inaccurate, unflattering, and insipid expression such as senior moment arises out of the need to employ euphemisms to placate the discomfort with older age and ageing. However, using senior moment to trivialise, essentialise, and denigrate older people, along with the ageing process, affects how they are perceived, which in turn influences how they are treated. All biased conceptions set the stage for shoddier treatment. All stereotypes other, and senior moment does this as well.

Body of the article -1,840 words

The prevalence of Ageism, some of its harmful effects, and the role senior moment plays:

Ageism is othering based on age, particularly older age. This involves stereotypes, prejudices, exclusion, and discrimination which work to trivialise, essentialise, and denigrate older adults, as well as the ageing process.

Gullette (2019:xiii) declares that: "ageism is the least censured, the most acceptable and unnoticed of the cruel prejudices," and suggests fighting ageism and not ageing. [START_REF] Zharovska | Explorations of Contemporary Age Discrimination: A Global View[END_REF] assert that discrimination based on age is a major global issue, and similarly to any form of discrimination is a violation of human rights. They also maintain that these prejudices are based on factors that can hardly be helped, such as those of a biological or cultural nature. They go on to say that ageism has any number of manifestations which cause many harmful consequences, affecting how older people are treated in the medical, sociocultural, socio-political, and financial spheres, all of which lead to exclusion, social inequality, poorer health, and violations of human dignity.

Based on a review of the literature, Barber (2017:88) quotes some ageism statistics, as follows:

• "84% of older Americans and 91% of older Canadians reported having experienced at least one incident of overt ageism1 , and over half of respondents reported experiencing multiple incidents."

• "The European Social Survey found that ageism was the most commonly experienced form of prejudice within their sample."

It could be reasonably surmised that the actual numbers are even higher, on account of a) some targets of ageism not realising they were being victimised by overt acts of discrimination, and b) a given proportion of respondents would not acknowledge such incidences on account of being embarrassed, for fear of further abuse, and so on [START_REF] Barber | An examination of age-based stereotype threat about cognitive decline: Implications for stereotype-threat research and theory development[END_REF] also points out that some ageist stereotypes may also be positive (such as being good-natured or warm), which when combined by the "overall perception" that older people are lower in mental competence, result in a pitying stereotype in which older people are then patronised. In this manner, they may be thought of as lovable but "not quite there," which can be quite demeaning to those who are more than sufficiently competent. Another significant point is made: if a younger person has a mental lapse, it is assumed that it was a fleeting thing, such as being in a hurry. If an older person were to have a similar mental slip, however, then it is a senior moment, which is understood to be of a more recurrent nature.

In the USA, based on their cross-sectional study involving over 2,000 participants between 50 and 80, [START_REF] Allen | Experiences of everyday ageism and the health of older US adults[END_REF] concluded that ageism is a prevalent and socially condoned phenomenon which they directly correlated with poorer health and reduced well being. Chronic physical health ailments included increased incidences of hypertension, heart disease, diabetes, cancer, and ongoing pain. The higher probability of mental health issues included depressive symptoms, and a diminished sense of well being.

The most common instances of what they refer to as everyday ageism include "brief verbal, nonverbal, and environmental indignities that convey hostility, a lack of value, or narrow stereotypes of older adults" (Allen, 2022:2). They specifically mention the onslaught of antiaging commercials, and being told that they are having senior moments as a part of the stereotypical manner in which they are seen. [START_REF] Davenport | You Look So Good for Your Age: First Steps of Creating a Measure of Daily Experiences of Ageism. Sexuality, Minoritized Identities and Lifespan Experiences (SMILES) Lab[END_REF] divide ageism into three manifestations:

• In benevolent ageism, they include being addressed using a term of endearment such as sweetie or dear (when hardly knowing the person), or people needlessly repeating things with the assumption that since the listeners were older they were not capable of understanding the first time.

• In positive ageism, they include people making reference to the wisdom acquired with age, or behaving with an added measure of respect on account of age.

• In hostile ageism, they refer to instances such as being ignored or avoided on account of older age, using insulting age-related monikers, and being told they had a senior moment.

Senior moment as one of the euphemisms that try to mask the societal distaste for ageing:

van den Hoonaard (2022) points out that one of the manifestations of the societal discomfort with the concept of ageing is the use of euphemisms. For example, to use senior or senior ager instead of old or older adult, or to refer to old age as the "golden years." She goes on to affirm that euphemisms might momentarily reduce the prejudice, but unless the societal conditions that gave rise to the prejudice in the first place are eliminated, the euphemisms themselves will soon also have similar negative connotations. By then, new, less stigmatised euphemisms will likely crop up, but the general discomfort with ageing and the othering of older people will nonetheless remain unchanged. She goes on to assert that humorous euphemisms serve to further embed ageism. Citing senior moment as an example, she that it helps to neutralise the embarrassment of a momentary lapse of memory, but that the main reason that this expression is "funny" is that being old is already associated with weakened mental function. In this manner, the victims of this othering stereotype are again victimised by being the brunt of these jokes.

As an othering expression, senior moment quickly gained momentum:

Bonnesen and Burgess ( 2004) go into great detail on senior moment, basing an entire scholarly article on the use of this ageist expression, published just a few years after it first appeared. They conclude that the increasing popularity of this expression is indicative that such stereotypes remain as a socially acceptable norm. Here are some highlights:

• They state that senior moment is just one out of many negative stereotypes related to ageing.

• They point out that the first appearance in a newspaper they could find was in 1997, and that its use increased exponentially over the next three years, which was indicative of its acceptance by the [US] American culture.

• They underscore the important role the media plays in the propagation of such negative attitudes. The media reflects social attitudes, and the media shapes them.

Othering in the library:

Katopol (2016) tells about how such stereotypes adversely affect the in-library experience of older patrons. The author states that our society has so many negative stereotypes associated with older individuals, that people barely realise that they are spreading them through what they say and do. An important message here is that people recurrently judge others based on misconceptions, and simply propagate these incorrect notions without giving the matter any further thought. That is an insidious manner in which bias and exclusion work, and a part of how effective they are in othering. In the case of "forgetful seniors," older patrons are concerned that if they ask to have something written down, or need an explanation repeated, that they will be "proving" that they indeed have diminished mental ability. This is all very ironic, since libraries are supposed to be a place where anyone and everyone should be able to acquire new knowledge in a safe and nurturing environment.

Othering on the job:

Griffiths, Thinnes, and Byers-Connon (2017) tell us how certain false beliefs and myths regarding older people can negatively affect how they are treated by those who work with them. Manifestations of this ageism may include incorrect assumptions regarding their mental and physical abilities, and such rigid preconceptions do not help matters. The negative stereotyping that older people are subjected to may promote them to also believe such nonsense, which can deteriorate their self-image and enjoyment of life in general.

They also point out that use of the expression senior moment encourages people to believe that older people have frequent memory lapses. The authors cite an example of an older man who was brusquely explained a new and complicated procedure to obtain health benefits. When this person asked for explanations, the impatient younger person just repeated himself loudly, and when the older person moved on, the younger one muttered "these senile old guys."

Perhaps if there wasn't such a prevalence of linguistically-based dividers of peoples, the younger man may have had a little more empathy.

The othered internalising the othering: [START_REF] Bai | Images of ageing in society: A literature review[END_REF] explains how younger people tend to negatively typecast older people, and how this continued exposure to negative stereotypes is then internalised by the targeted group.

The detrimental effects that these demeaning prejudices have on older people include a deteriorated self-perception, harm to their mental and physical well-being, and impairment of their social functioning.

Ageing stereotypes do not harm only the targeted group:

In "Believing what you hear: The impact of aging stereotypes upon the old," [START_REF] Bennett | Believing what you hear: The impact of aging stereotypes upon the old[END_REF] there is a journal article whose title says it like it is for all stereotypes, not just those that are ageist. The authors explain how the expression senior moment not only impacts older people, but also younger people "on the way there:"

• the younger people hear it and use it

• they adopt negative stereotypes pertaining to older people, including that they themselves may eventually have memory problems

• they then perceive these problems as inevitable

• when they later have a momentary lapse, the prophecy is already considered on its way to becoming fulfilled

• they then believe themselves to be on track to mental incompetence and finally dementia This cycle is kept going by the continued mindless use of this expression. So, in excluding others with this ageist expression, those being "witty and clever" are also harming themselves.

Final thoughts:

Why should older age be equated with forgetfulness or to having impaired brain function? It must not, of course, but ageist expressions such as senior moment makes it appear to be so.

Othering is usually perpetrated against people and groups that are perceived as vulnerable, and in the case of senior moment might also serve as a way to deal with their fears of ageing, and to feel better about themselves at the expense of others in the meantime. For example, some younger people might tell themselves that "we younger people can hear fine, remember things, and have 'normal' use of our brain, while they older people do not."

The use of senior moment also presents a stereotype threat that can seriously diminish the quality of life of the targeted group. In this manner, the harm is being done at all times, not just when someone endures insulting age-related monikers or hears (or even self-deprecatingly articulates) an expression such as senior moment. It is very unpleasant to be in the position of not being able to ask something to be repeated or explained in order to not risk "confirming" these negative preconceived conceptions.

Why not exchange fearing and othering older adults and the ageing process for appreciation and respect? In this fashion, the fears and stereotypes could be eliminated, which in turn would obviate the need for expressions such as senior moment. An immediate solution to ending the sociocultural and sociolinguistic othering senior moment promotes is to simply stop using this insensitive, inaccurate, unflattering, and insipid expression.

Steven M Kaplan. senior moment -a typical example of how older people are othered. 2023. hal-

For instance, to be insulted or ignored.