Salem Benferhat
email: benferhat@cril.univ-artois.fr

Zied Bouraoui
email: bouraouiz@cardiff.ac.uk

Mohd Huma Chadhry

Shafry Bin

Mohd Rahim

Karim Tabia
email: tabia@cril.univ-artois.fr

Abdelmoutia Telli
email: telli@cril.univ-artois.fr

Mohd Shafry
email: shafry@utm.my

Bin Mohd

Rahim Fc

How to reason from inconsistent ontologies with prioritized assertional bases?

Keywords: Inconsistency, Prioritized knowledge bases, Lightweight Ontologies

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I. INTRODUCTION

Description Logics (DLs) are formal frameworks for representing and reasoning with ontologies. A DL knowledge base is built upon two distinct components: a terminological base (called TBox) representing generic knowledge, and an assertional base (called ABox) containing facts or assertions.

Recently, a particular interest was given to Ontology Based Data Access (OBDA), in which the ontological view (i.e. the TBox) is used to offer a better exploitation of assertions (i.e. the ABox) when querying them (e.g. [START_REF] Lenzerini | Ontology-based data management[END_REF], [START_REF] Poggi | Linking data to ontologies[END_REF]). A crucially important problem that arises in OBDA is how to manage conflicting information. In such a setting, an ontology is usually verified and validated while the assertions can be provided in large quantities by various and unreliable sources that may be inconsistent with respect to the ontology. Moreover, it is often too expensive to manually check and validate all the assertions. This is why it is very important in OBDA to reason in the presence of inconsistency. Many works (e.g. [START_REF] Bienvenu | On the complexity of consistent query answering in the presence of simple ontologies[END_REF], [START_REF] Bienvenu | Tractable approximations of consistent query answering for robust ontology-based data access[END_REF], [START_REF] Lembo | Inconsistency-tolerant query answering in ontologybased data access[END_REF], [START_REF] Lukasiewicz | From classical to consistent query answering under existential rules[END_REF], [START_REF] Lukasiewicz | Inconsistency handling in datalog+/-ontologies[END_REF]), basically inspired by the ones in the database area (e.g. [START_REF] Arenas | Consistent query answers in inconsistent databases[END_REF], [START_REF] Bertossi | Database Repairing and Consistent Query Answering[END_REF], [START_REF] Chomicki | Consistent query answering: Five easy pieces[END_REF]) and propositional logic approaches (e.g. [START_REF] Benferhat | Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study part 1: The flat case[END_REF]), deal with inconsistency in DLs by proposing several inconsistency-tolerant inferences, called semantics. These semantics are based on the notion of a maximally assertional (or ABox) repair which is closely related to the notion of a database repair [START_REF] Lembo | Inconsistency-tolerant semantics for description logics[END_REF] or a maximally consistent subbase used in the propositional logic setting (e.g. [START_REF] Nicholas | On inference from inconsistent premisses[END_REF]). An ABox repair is simply an assertional subbase which is consistent with an ontology.

In many applications, assertions are often provided by several and potentially conflicting sources having different reliability levels. Moreover, a given source may provide different sets of uncertain assertions with different confidence levels. Gathering such sets of assertions gives a prioritized or a stratified assertional base (i.e. ABox). The role of priorities in handling inconsistency is very important and it is largely studied in the literature within the propositional logic setting (e.g. [START_REF] Benferhat | Some syntactic approaches to the handling of inconsistent knowledge bases : A comparative study. Part 2 : the prioritized case[END_REF]). Several works have also studied the notion of priority when querying inconsistent databases (e.g. [START_REF] Martinez | Inconsistency management policies[END_REF], [START_REF] Staworko | Prioritized repairing and consistent query answering in relational databases[END_REF]) or DLs knowledge bases (e.g. [START_REF] Benferhat | How to select one preferred assertional-based repair from inconsistent and prioritized DL-Lite knowledge bases?[END_REF], [START_REF] Bienvenu | Querying inconsistent description logic knowledge bases under preferred repair semantics[END_REF], [START_REF] Du | Weight-based consistent query answering over inconsistent SHIQ knowledge bases[END_REF]).

The context of this paper is the one of handling inconsistency in lightweight ontologies when the ABox is prioritized. We use DL-Lite [START_REF] Artale | The DL-Lite family and relations[END_REF], an important tractable fragment of DLs, as an example of lightweight ontologies which is well-suited for OBDA [START_REF] Lembo | Inconsistency-tolerant query answering in ontologybased data access[END_REF].

In the presence of conflicting information, there is always a compromise that one needs to reach between the expressiveness and computational issues. Having multiple repairs often allows to derive more conclusions than if one repair is only used. However, query answering from multiple repairs is generally more expensive than query answering from a single repair. In fact, reasoning from a single repair can be viewed as an approximation of reasoning from multiple repairs. Recently, a so-called nondefeated repair has been proposed in [START_REF] Benferhat | How to select one preferred assertional-based repair from inconsistent and prioritized DL-Lite knowledge bases?[END_REF]. This paper proposes a characterization of the non-defeated repair using the concept of accepted assertions. This leads to select a unique preferred repair from initial inconsistent knowledge base. Selecting only one preferred repair is important since, once computed, it allows an efficient query answering.

The rest of this paper is organized as follows: Section II-A provides the needed background on DL-Lite. Section III presents some elementary concepts on inconsistency handling such as the concepts of conflicts, repairs and free assertions. Section IV presents the so-called nondefeated repair and its characterization using the concept of accepted assertions. Section V introduces the notion of a prioritized deductive closure and its use in non-defeated repair. The last section provides a potential application of our approach to video data.

II. DL-Lite AND PRIORITIZED ASSERTIONAL BASE

A. DL-Lite: A Brief Refresher

This section briefly recalls DL-Lite logics. For the sake of simplicity, we only consider DL-Lite R language [START_REF] Calvanese | Tractable reasoning and efficient query answering in description logics: The DL-Lite family[END_REF] and we will simply use DL-Lite instead of DL-Lite R . Note that the results of this paper can be extended in a straightforward way to any tractable DL-Lite as far as computing ABox conflicts is done in polynomial time. This is true for DL-Lite core (a particular case of DL-Lite R ) and DL-Lite F . The DL-Lite language is defined as follows:

R -→ P | P - E -→ R | ¬R B -→ A | ∃R C -→ B | ¬B
where A is an atomic concept, P is an atomic role and P -is the inverse of P . B (resp. C) is called basic (resp. complex) concept and role R (resp. E) is called basic (resp. complex) role. A knowledge base (KB) is a couple K= T , A where T is a TBox and A is an ABox.

A TBox includes a finite set of inclusion axioms on concepts and on roles respectively of the form: B C and R E. The ABox contains a finite set of atomic concepts and role assertions respectively of the form A(a) and P (a, b) where a and b are two individuals. The semantics of a DL-Lite knowledge base is given in terms of interpretations. An interpretation I=(∆ I , . I ) consists of a non-empty domain ∆ I and an interpretation function . I that maps each individual a to a I ∈ ∆ I , each A to A I ⊆ ∆ I and each role P to P I ⊆ ∆ I × ∆ I . Furthermore, the interpretation function . I is extended in a straightforward way for concepts and roles as follows: A knowledge base K is called consistent if it admits at least one model, otherwise K is said to be inconsistent. A TBox T is said to be incoherent if there exists at least a concept C such that for each interpretation I which is a model of T , we have C I =∅.

A I ⊆ ∆ I P I ⊆ ∆ I × ∆ I (P -) I = {(y, x) ∈ ∆ I × ∆ I |(x, y) ∈ P I } (∃R) I = {x ∈ ∆ I |∃y ∈ ∆ I such that (x, y) ∈ R I } (¬B) I = ∆ I \ B I (¬R) I = ∆ I × ∆ I \ R I

B. Prioritized Assertional Bases

A prioritized assertional base (or a prioritized ABox), simply denoted by A=(S 1 , • • • , S n ), is a tuple of sets assertions. The sets S i 's are called layers or strata. Each layer S i contains the set of assertions having the same level of priority i and they are considered as more reliable than the ones present in a layer S j when j > i. Hence, S 1 contains the most important assertions while S n contains the least important assertions.

Throughout this paper and when there is no ambiguity we simply use 'prioritized DL-Lite KB K= T , A ' to refer to a DL-Lite KB with a prioritized ABox of the form

A=(S 1 , • • • , S n ).
This paper proposes methods to deal with inconsistent DL-Lite KB. The input of our method is a prioritized DL-Lite knowledge base K= T , A with A=(S 1 , • • • , S n ). The output of our approaches is a standard DL-Lite knowledge base K = T , R , where R is not prioritized (namely, just a set of assertions). K and K have the same terminological base. R will be called a preferred repair. Then a query q is said to follow from K if it can be derived, using the standard DL-Lite inference, from K . Let us first recall important concepts for handling inconsistency when no priority is available between assertions.

III. INCONSISTENCY-TOLERANT REASONING FOR

PRIORITIZED DL-Lite ASSERTIONAL BASES.

A. The concept of repairs

Within the OBDA setting, we assume that T is coherent and hence its elements are not questionable in the presence of conflicts. Coping with inconsistency can be done by first computing the set of consistent subsets of assertions (not necessarily maximal), called repairs, then using them to perform inference (i.e. query answering). More formally a repair is defined as follows:

Definition 1: Let K= T , A be a flat (not prioritized) DL-Lite KB. A subbase R ⊆ A is said to be a repair if T , R is consistent. And R is said to be a maximally inclusion-based repair of K, denoted by MAR, if T , R is consistent and ∀R : R R , T , R is inconsistent.

In the rest of this paper, we will use the term 'flat' to express the fact that there is no priority between different assertions of an ABox. According to the definition of MAR, adding any assertion f from A \ R to R entails the inconsistency of T , R ∪ {f } . Moreover, the maximality in MAR is used in the sense of set inclusion. We denote by MAR(A) the set of MAR of A with respect to T . The definition of MAR coincides with the definition of ABox repair proposed in [START_REF] Lembo | Inconsistency-tolerant semantics for description logics[END_REF].

Using the notion of repair, coping with inconsistency in flat DL-Lite knowledge bases can be done by applying standard query answering either using the whole set of repairs (universal entailment or AR-entailment [START_REF] Lembo | Inconsistency-tolerant semantics for description logics[END_REF]) or only using one repair.

B. Free Assertions and Conflict Sets

We now introduce the notion of a conflict. It is a minimal subset C of assertions of A such that K= T , C is inconsistent.

Definition 2: Let K= T , A be a DL-Lite KB. A sub- base C ⊆ A is said to be an assertional conflict of K iff T , C is inconsistent and ∀ f ∈ C, T , C \ {f } is consistent.
From Definition 2, removing any fact f from C restores the consistency of T , C . In DL-Lite, when the TBox is coherent, a conflict involves exactly two assertions [START_REF] Calvanese | Evolution of DL-Lite knowledge bases[END_REF]. We denote by C(A) the set of conflicts in A.

A nice feature of DL-Lite is that computing the set of conflicts is done in polynomial time [START_REF] Benferhat | A prioritized assertional-based revision for DL-Lite knowledge bases[END_REF], namely Conf is in P. We now introduce the notion of non-conflicting or free elements.

Definition 3: Let K= T , A be DL-Lite KB. An assertion f ∈ A is said to be free if and only if ∀c ∈ C(A) : f / ∈ c. Intuitively, free assertions correspond to elements that are not involved in any conflict. We denote by free(A) the set of free assertions in A. The notion of free elements is originally proposed in [START_REF] Benferhat | Representing default rules in possibilistic logic[END_REF] in a propositional logic setting. Within a DL-Lite setting, f ree(A) is computed in polynomial time thanks to the fact that computing conflicts is done in polynomial time.

The folowing Lemma 1 rephrases the set of free elements using the set of maximally inclusion-based repairs: Lemma 1: Let K= T , A be a DL-Lite KB. Then: free(A) = X∈MAR(A) X. For flat DL-Lite knowledge bases, the f ree-entailment (entailment based on free assertions) is equivalent to the IAR-entailment proposed in [START_REF] Lembo | Inconsistency-tolerant semantics for description logics[END_REF]. In fact, in the context of propositional logic the concept of a maximal consistent subset has been introduced before the concept of repairs [START_REF] Nicholas | On inference from inconsistent premisses[END_REF]. Besides, the concept of f ree entailment have been introduced in [START_REF] Benferhat | Representing default rules in possibilistic logic[END_REF]. In the rest of this paper, we will only use the notaion f ree(A) to describe the set of assertions that are not responssible of conflict in T , A .

IV. ACCEPED PRIORITIZED ASSERTIONS

The f ree entailment repair can be viewed as a safe way to deal with inconsistency. The term safe is used by opposition to the term risky or adventurous with respect to the derived conclusions. This section provides an extension of f ree entailment repair when assertional bases are prioritized. We first need to introduce the concept of defeated assertion.

Definition 4: Let K= T , A be a prioritized DL-Lite KB. Let f be an assertion of A. Then the assertion f ∈ S i is said to be defeated if:

• K= T , {f } is

inconsistent, or

• There exists an assertion g ∈ S j such that T , {f, g} is inconsistent and j ∈ i.

Basically, an assertion f is said to be defeated if it is contradicted by some priority assertion. In the case where an assertion is not defeated, it is called accepted. More precisely:

Definition 5: Let K= T , A be a prioritized DL-Lite KB. Let f be an assertion of A. Then the assertion f ∈ S i is said to be accepted if and only if it is not defeated.

It turns out that the set of accepted assertions is exactly equal to the so-called no-defeated repair introduced in [START_REF] Benferhat | How to select one preferred assertional-based repair from inconsistent and prioritized DL-Lite knowledge bases?[END_REF]. The idea in the construction of no-defeated repair is to iteratively retrieve, layer per layer, the set of f ree elements. More precisely: Definition 6: Let K= T , A be a prioritized DL-Lite KB. We define the non-defeated repair, denoted by nd(A)=S 1 ∪ . . . ∪ S n , as follows: ∀i = 1, .., n : S i = f ree(S 1 ∪ . . . ∪ S i ).

Namely, nd(

A) = f ree(S 1 ) ∪ f ree(S 1 ∪ S 2 ) ∪ . . . ∪ f ree(S 1 ∪ . . . ∪ S n ).
Hence an important result of this paper is to provide a characterization of the so-called non-defeated repair using the concept of accepted beliefs. The definition of non-defeated subbase is an adaptation of the definition proposed in [START_REF] Benferhat | Some syntactic approaches to the handling of inconsistent knowledge bases : A comparative study. Part 2 : the prioritized case[END_REF] within a propositional logic setting. However, contrarily to the propositional setting, as we will see later, the non-defeated repair can be applied on A or its deductive closure cl(A) which leads to two different ways to select a single preferred repair. Besides the non-defeated repair is computed in polynomial time in a DL-Lite setting while its computation is hard in a propositional logic setting. Algorithm 1 gives the computation of the non-defeated repair. Algorithm 1 first computes the set of conflicts (step 1). Step 2 simply initializes nd(A) to an empty set. The expression:

{f : f ∈ S 1 ∪ . . . ∪ S i and ∃ g ∈ S 1 ∪ . . . ∪ S i such that {f, g} ∈ C }
represents the set of conflicting elements in S 1 ∪ . . . ∪ S i . Hence, Step 4 computes the set of free elements in S 1 ∪ . . . ∪ S i .

Step 5 adds this result to nd(A). Clearly, Algorithm 1 straightforwardly implements Definition ??. In Algorithm 1 the set of conflicts is computed once. Hence, the compexity of Algorithm 1 is Conf (step 1) plus O(n) (step 2-6), where n is the number of strata in the DL-Lite knowledge base K.

The first nice feature of non-defeated repair is that it is consistent. Indeed, Recall that:

nd(A) = f ree(S 1 )∪f ree(S 1 ∪S 2 )∪. . .∪f ree(S 1 ∪. . .∪S n ).
Recall also that if C is a conflict then either C is singleton or C is a doubleton. Now, assume that nd(A) is inconsistent. Then this means that there exists a conflict C of T , A such that C ⊆ nd(A).

Assume that C = {f } is a singleton and S i is the first layer where f ∈ S i (namely, ∀j < i, f / ∈ S j ). This means that:

• ∀ j < i, f / ∈ f ree(S 1 ∪ • • • ∪ f ree(S 1 ∪ • • • ∪ S j ) (since f / ∈ S 1 ∪ • • • ∪ S i-1 ), • ∀j ≥ i, f / ∈ f ree(S 1 , • • • , S j ) (since f ree only contains non-conflicting information). Hence, f / ∈ f ree(S 1 ) ∪ • • • ∪ f ree(S 1 ∪ • • • ∪ S n ). Namely, f / ∈ nd(A).
Now, assume that C = {f, g} is a doubleton. Let S i (resp. S j ) be the first layer containing f (resp. g).

Let us assume that i ≤ j. Then clearl

C f ree(S 1 ) ∪ • • • ∪ f ree(S 1 ∪ • • • ∪ S j-1 ) since f S 1 ∪• • •∪S 1 ∪• • •∪S j-1 .
Besides, for all k ≥ j, we have:

f ree(S 1 ∪ • • • ∪ S k ) ∩ C = ∅.
Hence, using the definition of f ree assertion, we get:

C f ree(S 1 ) ∪ • • • ∪ f ree(S 1 ∪ • • • ∪ S n ).
Hence nd(A) contains no conflict and it is consistent. The second nice feature when using the set of accepted belief is that the complexity of computing nd(A) is in P. Indeed, recall the computing conflicts is done in a polynomial time. Since the set of free assertions can be obtained in a linear time with respect to the set of conflicts, then the whole computation of nd(A) is also done in polynomial time.

F i = (S 1 ∪ . . . ∪ S i ) -{f : f ∈ S 1 ∪ . . . ∪ S i and ∃ g ∈ S 1 ∪ . . . ∪ S i such that {f, g} ∈ C } 5: nd(A) ← nd(A) ∪ F i 6: return nd(A)

V. ACCEPTED ASSERTIONS ON A PRIORITIZED CLOSURE

We now introduce the concept of a prioritized closure. In fact, the three preferred repairs given in the previous sections can be either defined on T , A or on T , cl(A) where cl(A) denotes the deductive closure of a set of assertions A and is defined as follows.

S i = cl(S 1 ∪ . . . ∪ S i-1 ∪ S i ).
The first motivation of Definition 8 is that if an assertion f is derived from K, S 1 ∪ • • • ∪ S n then f should belong to cl(A). The second motivation is that if an assertion f is believed to some rank i then it should also be believed to all ranks that are higher than i.

Namely, if f is derived from K, S 1 ∪ • • • ∪ S i then ∀j i, f ∈ S j .
One way to get a larger set of accepted assertions is to use cl(A) instead of A. Namely, we define a closed nondefeated repair, denoted by clnd(A), as S 1 ∪. . .∪S n , such that:

∀i = 1, .., n : S i = f ree(c (S 1 ∪ . . . ∪ S i )). (1)
Clearly, nd(A) ⊆ clnd(A) and cl(nd(A)) ⊆ clnd(A).

The converse is false.

VI. EXAMPLE

This section contains a brief description of a potential application of our approach to classifying and solving conflicts in a collection of dance videos issued from different sources. Motion in video carries important information which is of a multi-fold nature. Motion sometimes need to be interpreted for understanding or anticipating any immediate reaction to the motion. Hence, the significance of motion perception in a video is seen in several of the present systems and it remains to be active research area. Movements in dances encompass different types of information; sacred rituals, social dialogue or cultural expressions and more. This calls for the need to completely and precisely describe and process motion information and make it digitally available for further processing. Several applications can be reached by dance video automatic annotations, such as dance video retrieval, classification of video databases or animation of dances using modeling of stored information.

A video is a sequence of frames which extend over time. A set of frames can be referred to as a dance segment once a human completes a dance step in a composed dance. Sequence of actions that display a motion which is isolated and makes up a dancing vocabulary can be referred to as a dance step. Improvisation in a dance refers to simultaneous dance moves, which are not previously composed.

Dance moves need to categorized as expressions such as Time Steps in Cha-Cha-Cha or Passo Basico in Samba dance 2 . Our aime is to explore how different dance steps in a Malaysian dance video can be categorized and described to extract knowledge from the video. For instance, in the dance video Inang, we can describe the step Side Bend as a position in which the upper body and the raised arms arch in left or right direction and the feet tap toe in the opposite direction, creating the form of an arch on right and then left side. The dance step with the name Side Bend are segmented from the entire video and this segment of dance movement is labeled as Side Bend.

In the presence of a collection of dance segments issued from different sources (cameras for instance), the problem of conflict may arise. To illustrate this situation, let us consider an example where we assume that we only have the following concepts:

• Forwardmove, We also assume that we only have one relation:

• DanceSegment: gives for each of dance video the list of dance segments

The terminological base is expressed by the following TBox: This assertional base is assumed to be provided by different sources (different cameras for example) having different reliability levels. This knowledge base is clearly inconsistent. Indeed, using the assertion StartF orwardmove(s1) and the positive inclusion axiom P axiom3 one can derive F orwardmove(s1). This derived fact together with the assertion Backgroundmove(s1) contradict the negative axiom N axiom1. Without the use of priorities, the free entailment will simple lead to:

F ree(A) = {DanceSegment(v1, s1), DanceSegment(v1, s2), F astBackgroundmove(s2)} Namely, only assertions that are not conserved by the conflict are preserved. When there is a priority relation between assertional facts, one can go one step further in solving conflicts. In our example, Backgroundmove(s1) is assumed to be issued from a source more reliable than the one that delivers the assertion StartF orwardmove(s1). Hence, using the non-defeated entailment, we get : nd(A) = {Backgroundmove(s1), SlowBackgroundmove(s1), DanceSegment(v1, s1), DanceSegment(v1, s2), F astBackgroundmove(s2)}.

Clearly, nd(A) is clearly larger than F ree(A). The nice feature of our approach is once nd(A) is computed, query the initial inconsistent knowledge base can be done efficiently.

VII. CONCLUSION

This paper focused on how to select a single preferred repair from a prioritized inconsistent DL-Lite knowledge base. Selecting only one repair is important since it allows efficient querying answering once the preferred repair is computed. A future work is to apply our approach to query Malaysian dance videos in presence of possible conflicts.

  An interpretation I is said to be a model of a concept (resp. role) inclusion axiom, denoted by I |= B C (resp. I |= R E), if and only if B I ⊆ C I (resp. R I ⊆ E I ). Similarly, we say that an interpretation I is a model of a membership assertion A(a) (resp. P (a, b)), denoted by I |= A(a) (resp. I |= P (a, b)), if and only if a I ∈ A I (resp. (a I , b I ) ∈ P I ).

Algorithm 1

 1 Non-Defeated Repair Input: K = T , A where A = S 1 ∪ . . . ∪ S n Output: A flat assertional base nd(A) 1: C ← C(A) {List of conflicts} 2: nd(A) ← ∅ 3: for i = 1 to n do 4:

Definition 7 :Definition 8 :

 78 Let K= T , A be a flat DL-Lite KB. Let T p be the set of all positive inclusion axioms of T 1 . We define the deductive closure of A with respect to T as follows: cl(A)={B(a): T p , A |= B(a) where, B is a concept of T and a is an individual of A} ∪ {R(a, b): T p , A |= R(a, b), where R is a role of T and a,b are individuals of A}. The use of a deductive closure of an ABox fully makes sense in DL languages. The following definition extends Definition 7 to the prioritized case. Let K= T , A be a prioritized DL-Lite KB. We define a prioritized closure of A with respect to T , simply denoted by cl(A), as follows: cl(A) = (S 1 , . . . , S n ) where: ∀i = 1, .., n :

Example 1 :

 1 Let us the following knowledge base where: T = {A ¬B, B C, A C} and A = S 1 = {A(a), B(a)}. One can check that nd(A) = ∅, cl(nd(A)) = ∅ while nd(cl(A)) = clnd(A) = {C(a)}.

  DanceSegment - Paxiom 10: backgrounddmove ∃ DanceSegment - Naxiom1: Forwardmove ¬ Backgroundmove Assume that we have four individuals: i) two dances segments s1 and s2, and ii) two videos v1 and v2. Assume that we only have four assertions facts given by the ABox A = (S1, S2) with S1 = {Backgroundmove(s1), DanceSegment(v1, s1)}, S2 = {StartF orwardmove(s1), DanceSegment(v1, s2)}, and S3 = {SlowBackgroundmove(s1), F astBackgroundmove(s2)}.

  StartForwardmove, and • StartBackgroundmove. These concepts concern dances segment that represent direct moves. The concept Forwardmove (resp. SlowForwardmove and FastForwardmove) lists the set of dance segments that represent a forward move (resp. a slow and fast forward move). Similarly, The concept Backgroundmove (resp. Slowbackgroundmove and Fastbackgroundmove) lists the set of dance segments that represent a background move (resp. a slow and fast background move). The concept StartForwardmove (resp. StartBackgroundmove) lists the set of dance segments that represent a starting forward (resp. background) move in a video.

• Backgroundmove, • FastForwardmove, 2 http://www.dancadesalao.com/agenda/ingles.php • SlowForwardmove, • FastBackgroundmove, • SlowBackgroundmove, •

Positive inclusion axioms are of the form B 1 B

.

Acknowledgments

This work is supported by Research and Innovation Staff Exchange (RISE) H2020-MSCA-RISE-2015 project called High Dimensional Heterogeneous Data based Animation Techniques for Southeast Asian Intangible Cultural Heritage Digital Content or AniAge Project [EU H2020 project-AniAge (691215)].


Malgorzata Kloc
email: mkloc@houstonmethodist.org

Rafik M Ghobrial

Jacek Z Kubiak
email: jacek.kubiak@univ-rennes1.fr

The role of genetic sex and mitochondria in response to COVID-19 infection

Keywords: COVID-19, SARS-CoV-2, macrophages, Y chromosome, X chromosome, immunity, melatonin

The difference between the female and male immune response to COVID-19 infection, and infections in general, is multifactorial. The well-known determiners of the immune response such as X and Y chromosomes, sex hormones and microbiota, are functionally interconnected and influence each other in shaping the organism's immunity. We focus our commentary on the interplay between the genetic sex and mitochondria, and how this may affect a sex-dependent immune response in COVID-19 infection.

Introduction

Research and clinical studies indicate that the genetic sex of patients influences the immune response, and the course, and prognosis of many common noninfectious and infectious diseases. A similar correlation has also been observed recently in COVID-19 infected patients; the world-wide statistical analyses of COVID-19 cases indicate that the rate of infection and the direness of the outcome are much higher and sever in males than in females. The most popular explanation for this phenomenon is "the immunocompetence handicap model" proposing that in males, the testosterone-dependent secondary male sex traits develop at the expense of the immune response. Sex hormones are known to affect the innate and adaptive immunological response with the androgens being anti-proinflammatory, and the estrogens pro-inflammatory [START_REF] Klein | Sex differences in immune responses[END_REF][START_REF] Vemuri | The microgenderome revealed: sex differences in bidirectional interactions between the microbiota, hormones, immunity and disease susceptibilitySemin[END_REF]. However, the mechanisms of these sex-related differences are multifactorial and depend on very complex reciprocal interactions between sex chromosome-encoded and regulatory factors, hormones, and microbiota inhabiting the human body. In the last decade, it became clear that the microorganisms inhabiting the human gastrointestinal tract differ, in the type and abundance of species, between the sexes. This sex-dependent microbiome, called the microgenderome develops after puberty when the sex hormones kick in, and regulates local and systemic inflammation, and response to infection (Fig. 1); [START_REF] Klein | Sex differences in immune responses[END_REF][START_REF] Vemuri | The microgenderome revealed: sex differences in bidirectional interactions between the microbiota, hormones, immunity and disease susceptibilitySemin[END_REF][START_REF] Steegenga | Sexually dimorphic characteristics of the small intestine and colon of prepubescent C57BL/6 mice[END_REF]. Recent studies also indicate that the sex-related difference in the immune response may depend on the sexually dimorphic populations of mitochondria. Below we give a short summary of how these different elements pitch in and shape the immune response to COVID-19 and other diseases.

X and Y chromosome regulation of immunity

Although some differences between the female and male immune response are directly related to the number of X chromosomes (two X in females versus one X in males), and the effect of sex hormones on the functions of immune cells, the studies of last decade indicate that both Y and X chromosomes regulate immune cell transcription and translation (transcriptome and proteome) profiles.

X chromosome

The Archive.ensabl.org 2017: http://mar2017.archive.ensembl.org/Homo_sapiens/Location/Chromosome?r=X [START_REF]1-1 -Chromosome summary -Homo sapiens[END_REF] indicate that the human chromosome X consists of over 150 million DNA base pairs and contains more than 800 protein-coding genes, which include the highest number of the innate and adaptive immunityrelated genes of the whole human genome, and several hundred non-coding genes. The immune response genes include fraktaline receptor CXCR3 (C-X-C motif chemokine receptor 3) that directs immune cells, A c c e p t e d m a n u s c r i p t including macrophages, movement into inflamed tissues and organs; the gene for CD80 ligand that binds to the CD40 receptor on antigen-presenting cells, B cells, monocytes/macrophages and dendritic cells, and through interaction with CD154 transduces signals for T-dependent B-cell activation; and the Interleukin-1 receptor-associated kinase 1 (IRAK1) gene. The X chromosome also contains 10 % of all genomic microRNAs (miRNAs) genes that regulate expression and degradation of autosomal gene products [START_REF] Bianchi | The X chromosome and immune associated genes[END_REF][START_REF] Schurz | The X chromosome and sexspecific effects in infectious disease susceptibility[END_REF].

Studies showed that the absence of, or extensive deletions in one of the X chromosomes lead to a variety of autoimmune diseases) (Fig. 2); [START_REF] Bianchi | The X chromosome and immune associated genes[END_REF][START_REF] Schurz | The X chromosome and sexspecific effects in infectious disease susceptibility[END_REF].

A higher rate of COVID-19 infection in males may be, in part, influenced by the X chromosome mosaicism in the female cells, due to the stochastic X chromosome inactivation [START_REF] Lyon | Gene action in the X-chromosome of the mouse (Mus musculus L.)[END_REF]. For example, the angiotensin-converting enzyme 2, (ACE2), the receptor for β-type coronaviruses SARS-CoV-1 and SARS-CoV-2, is encoded by the ACE2 gene located on the X chromosome. It is possible that some alleles of this gene may code for the receptors with different efficiency of recognizing and binding the virus. Male cells always express a single ACE2 allele because all cells contain an identical X chromosome. In contrast, a female has a heterogenic ACE2 allele because of the mosaicism of X chromosomes, which are stochastically distributed between the cells. Thus, in the female, a potentially more efficient form of ACE2 receptor would be present in only half of all cells. This may limit infectability with SARS-CoV-1 and -2 viruses and, to some extent, give females a relative resistance to the infection (Fig. 2). It has also been debated if such ACE2 polymorphism may have an impact on hypertension and other diseases [START_REF] Benjafield | No association of angiotensin-converting enzyme 2 gene (ACE2) polymorphisms with essential hypertension[END_REF][START_REF] Pan | Association of ACE2 polymorphisms with susceptibility to essential hypertension and dyslipidemia in Xinjiang, China[END_REF].

Y chromosome

The human Y chromosome is much smaller than the X chromosome, consist of around 60 million DNA base pairs, and, in the majority of animals, its large portion is transcriptionally silent (heterochromatic).

The Y chromosome is mainly composed of transposable elements, repeat sequences (comprising over 50% of its content), multicopy genes such as the polymorphic variants of the ribosomal genes, and a low number of protein-encoding genes, which mainly are male-specific and regulate sexual development, spermatogenesis, sex ratio, and fertility, and often evolved through the transposition/translocation from the autosomes. This male-specific region of the Y chromosome (MSY) does not recombine and thus remains unchanged between the consecutive male generations [START_REF] Case | The Y chromosome as a regulatory element shaping immune cell transcriptomes and susceptibility to autoimmune disease[END_REF][START_REF] Koerich | Low conservation of gene content in the Drosophila Y chromosome[END_REF][START_REF] Quintana-Murci | The human Y chromosome: The biological role of a "Functional Wasteland[END_REF][START_REF] Skaletsky | The male-specific region of the human Y chromosome is a mosaic of discrete sequence classes[END_REF]. Studies showed that Y chromosome, can regulate the heterochromatin/euchromatin status of the autosomes and X chromosomes and thus affects silencing/expression of various genes, including the immune response genes, and regulate the tissue/cell-specific alternative gene splicing [START_REF] Case | The Y chromosome as a regulatory element shaping immune cell transcriptomes and susceptibility to autoimmune disease[END_REF][START_REF] Lemos | Polymorphic Y chromosomes harbor cryptic variation with manifold functional consequences[END_REF][START_REF] Lemos | Epigenetic effects of polymorphic Y chromosomes modulate chromatin components, immune response, and sexual conflict[END_REF][START_REF] Paredes | Ribosomal DNA deletions modulate genome-wide gene expression: ''rDNA-sensitive''genes and natural variation[END_REF][START_REF] Piergentili | Multiple roles of the Y chromosome in the biology of Drosophila melanogaster[END_REF][START_REF] Zhou | Y chromosome mediates ribosomal DNA silencing and modulates the chromatin state in Drosophila[END_REF]. Although the mechanism by which the Y chromosome influences heterochromatin/euchromatin content and thus the transcription of the other genes A c c e p t e d m a n u s c r i p t is largely unknown, one of the hypotheses postulates that the Y chromosome sequesters heterochromatinization factors and another that it affects the architecture of cell nucleus, which makes specific genes inaccessible to the transcription factors [START_REF] Francisco | How do Y-chromosomes modulate genome-wide epigenetic states: genome folding, chromatin sinks, and gene expression[END_REF][START_REF] Silkaitis | Sex-biased chromatin and regulatory cross-talk between sex chromosomes, autosomes, and mitochondria[END_REF][START_REF] Taddei | The function of nuclear architecture: a genetic approach[END_REF][START_REF] Ye | Interaction between an integral protein of the nuclear envelope inner membrane and human chromodomain proteins homologous to Drosophila HP1[END_REF]. Phylogenetic studies showed that the males with the haplogroup I, which is one of the most popular European lineages of the Y chromosome, have upregulated inflammatory response, downregulated adaptive immunity, and a higher risk of coronary diseases [START_REF] Charchar | Inheritance of coronary artery disease in men: An analysis of the role ofthe Y chromosome[END_REF][START_REF] Khan | Y Chromosome, Hypertension and Cardiovascular Disease: Is Inflammation the Answer?[END_REF][START_REF] Maan | The Y chromosome: a blueprint for men's health?[END_REF]. In the murine models, Y chromosomes influence the number of natural killer T cells, the gene expression pattern in CD4 + T cells, the immune response of macrophages, and mortality rate following the infection with coxsackievirus [START_REF] Case | Chromosome Y regulates survival following murine coxsackievirus B3 infection. G3[END_REF][START_REF] Teuscher | Evidence that the Y chromosome influences autoimmune disease in male and female mice[END_REF][START_REF] Spach | Cutting edge: The Y chromosome controls the age dependent experimental allergic encephalomyelitis sexual dimorphism in SJL/J mice[END_REF], which argues for the strong impact of the Y chromosome on a large variety of immune cells and immune processes. Studies of Case et al. [START_REF] Case | The Y chromosome as a regulatory element shaping immune cell transcriptomes and susceptibility to autoimmune disease[END_REF] showed that the copy number of the Y chromosome gene Sly and RNA-binding motif gene Rbmy inversely regulates the susceptibility to autoimmune disease. Studies in mouse influenza model [START_REF] Krementsov | Genetic variation in chromosome Y regulates susceptibility to influenza A virus infection[END_REF] showed that certain genetic variants of chromosome Y result in higher susceptibility to influenza A infection, activate proinflammatory cytokine expression in T cells, and increase pathogenic immune response in the lungs (Fig. 2).

Mitochondria

Studies of the past decades [START_REF] Angajala | Diverse Roles of Mitochondria in Immune Responses: Novel Insights Into Immuno-Metabolism[END_REF][START_REF] Weinberg | Mitochondria in the regulation of innate and adaptive immunity. Immunity. Author manuscript[END_REF] showed that mitochondria are not only the bioenergetic (they generate ATP) and biosynthetic (they generate components for the synthesis of various macromolecules) hubs but are also indispensable regulators of the innate and adaptive immune response, development and maintenance/survival and activation of the specific phenotypes of immune cells. Mitochondria can also affect various signaling pathways and transcription in immune cells by changing the ATP level, alternating their metabolic pathways, and releasing the reactive oxygen species (ROS) and mitochondrial DNA (mtDNA) signals. By changing the type of respiration from the broken TCA cycle to β-oxidation, the mitochondria can switch macrophage phenotype from the pro-inflammatory (M1) to the antiinflammatory (M2). In addition, the localization of mitochondria in the proximity of endoplasmic reticulum (ER) membranes of the immune cells directly affects their metabolism and immune-related functions [START_REF] Angajala | Diverse Roles of Mitochondria in Immune Responses: Novel Insights Into Immuno-Metabolism[END_REF][START_REF] Weinberg | Mitochondria in the regulation of innate and adaptive immunity. Immunity. Author manuscript[END_REF]. Also, the outer membrane of mitochondria contains the mitochondrial antiviral signaling (MAVS) protein that is activated by the viral RNA sensor, the retinoic acid-inducible gene I (RIG-I) that senses the presence of viral RNA. MAVS can also act as an antiviral defense mechanism. In the macrophages infected with RNA viruses MAVS interacts with the antiviral protein viperin, affecting the level of antiviral compound interferon (Fig. 3); [START_REF] Angajala | Diverse Roles of Mitochondria in Immune Responses: Novel Insights Into Immuno-Metabolism[END_REF][START_REF] Hee | Viperin interaction with mitochondrial antiviral signaling protein (MAVS) limits viperin-mediated inhibition of the interferon response in macrophages[END_REF]. Proper functioning of mitochondrial MAVS response can be especially relevant and significant for COVID-19 infection where the SARS-CoV-2 virus directly infects alveolar macrophages inducing them to switch on the cytokine storm in the lungs [START_REF] Wang | Alveolar Macrophage Activation and Cytokine Storm in the Pathogenesis of Severe COVID-19[END_REF].

A c c e p t e d m a n u s c r i p t

Moreover, because the survival and replication of the virus depend on energy produced by the host mitochondria, which in turn, are affected by the virus (Fig. 3), the novel antiviral strategies may include compounds that modulate mitochondrial bioenergetic functions [START_REF] El-Bacha | Virus-induced changes in mitochondrial bioenergetics as potential targets for therapy[END_REF].

All these data indicate that the healthy and properly functioning mitochondria are indispensable for the adequacy of the immune response. Thus, it is not surprising that one of the theories explaining the higher infection rate and severity of infections, such as COVID-19, in males, relates to the maternal transmission of mitochondria, and substandard quality of mitochondria in the males. In mammals, including humans, mitochondria are maternally transmitted in the egg cytoplasm. Following fertilization, during early embryogenesis, maternal mitochondria replicate and enter the prospective somatic and germ cells [START_REF] Silkaitis | Sex-biased chromatin and regulatory cross-talk between sex chromosomes, autosomes, and mitochondria[END_REF].

Although there are some, very rare, examples of paternal transmission of mitochondria in humans [START_REF] Shiyu | Biparental Inheritance of Mitochondrial DNA in Humans[END_REF], the concept of maternal inheritance of mitochondrial DNA in humans remains valid. During the formation and maturation of the mammalian egg, the mitochondria undergo the quality control [START_REF] Lieber | Mitochondrial fragmentation drives selective removal of deleterious mtDNA in the germline[END_REF] and those which are defective, or contain, harmful for the female, mutations, are eliminated. Because this mitochondrial culling is female-biased, the mitochondria remaining in the egg cytoplasm may contain mutations harmful for the male. This so-called "mother curse" [START_REF] Silkaitis | Sex-biased chromatin and regulatory cross-talk between sex chromosomes, autosomes, and mitochondria[END_REF] may also influence the quality and caliber of a male immune response.

Recently, the melatonin was suggested as a potential adjuvant for COVID-19 treatment [START_REF] Zhang | COVID-19: Melatonin as a potential adjuvant treatment[END_REF]. Melatonin has positive effects on mitochondrial homeostasis by scavenging toxic oxygen species, nitrogen-based reactants, enhancing antioxidative enzymes, facilitating the electron transport chain, limiting electron leakage, free radical generation, and stimulating ATP synthesis [START_REF] Leon | Melatonin and mitochondrial function[END_REF]. In light of our hypothesis that the quality of mitochondria may influence COVID-19 infection, the melatonin treatment of COVID-19 patients may be more beneficial for men than women.

Although, at present, there is no proven effective remedy for the sex-biased outcome of COVID-19 and other microbial infections, the detailed knowledge of all mechanisms underlying the differences between female and male immune response should facilitate the development of new treatments and therapeutic approaches.

Statement of Ethics

Not applicable

Disclosure Statement

Authors do not have conflict of interest and have nothing to disclose A c c e p t e d m a n u s c r i p t The microorganisms acquired during birth, and from the environment (air and food) colonize the human body, especially the digestive system. After puberty, the sex hormones influence the abundance and variety of species inhabiting the male and female body; less variety in males than in females. The

XX XY

INNATE and ADAPTIVE IMMUNUNITY

Reciprocal interactions between brain and microgenderome

Establishment of sex-specific microbiome after puberty

Female sex hormones

Male sex hormones microorganisms Fig. 1 A c c e p t e d m a n u s c r i p t compounds produced by the microgendorome reciprocally influence the function of innate and adaptive immunity, and brain (adapted from Vemuri et al. [START_REF] Vemuri | The microgenderome revealed: sex differences in bidirectional interactions between the microbiota, hormones, immunity and disease susceptibilitySemin[END_REF]).

Fig. 2. Effect of sex chromosomes on the immune-related functions

The X chromosome contains many immune response-related genes and 10% of all genomic miRNAs that regulate transcription, splicing, and degradation of many genes. It also, through the specification of female identity, directs maternal purging and transmission of mitochondria. Because in the female cells, the inactivation of one of the X chromosomes is random, the female body may contain different alleles of

Fig. 1 .

 1 Fig. 1. Microgenderome effect on the immune system

  Fig.2

Fig. 3 .

 3 Fig. 3. Effect of mitochondria on the anti-viral immune response.The presence of the virus is sensed by the RIG-I that is a major sensor of viral RNA. This activates antiviral MAVS protein present in the mitochondrial membrane. Activated MAVS, through the interaction with the virus inhibitory protein, viperin, affects the level of interferon, which in turn regulates virus replication. In addition, viruses can directly affect mitochondrial functions such as aerobic or anaerobic respiration, which in turn affect immune cell phenotypes and responses.

A c c e p t e d m a n u s c r i p t

Acknowledgements

We acknowledge that some of the images used to make figures were from the Servier Medical ART: SMART, smart.servier.com.

We also acknowledge the support from the Polish Ministry of National Defense project "Kościuszko" # 5508/2017/DA to JZK.

Funding Sources

Support from the Polish Ministry of National Defense project "Kościuszko" # 5508/2017/DA to JZK.