Didier Dubois
email: dubois@irit.fr

Francis Faux
email: faux@irit.fr

Henri Prade
email: prade@irit.fr

Prejudiced Information Fusion Using Belief Functions

Shafer views belief functions as the result of the fusion of elementary partially reliable testimonies from different sources. But any belief function cannot be seen as the combination of simple support functions representing such testimonies. Indeed the result of such a combination only yields a special kind of belief functions called separable. In 1995, Ph. Smets has indicated that any belief function can be seen as the combination of so-called generalized simple support functions. We propose a new interpretation of this result in terms of a pair of separable belief functions, one of them modelling testimonies while the other represents the idea of prejudice. The role of the latter is to weaken the weights of the focal sets of the former separable belief function. This bipolar view accounts for a form of resistance to accept the information supplied by the sources, which differs from the discounting of sources.

Introduction

G. Shafer [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF] has presented his theory of belief functions essentially as an approach to the fusion of unreliable elementary testimonies, each being represented by simple support functions. However many belief functions prove to be not separable, i.e., not the orthogonal sum of simple support functions. Ph. Smets [START_REF] Smets | The canonical decomposition of a weighted belief[END_REF] tries to remedy this difficulty by generalizing simple support functions, showing that any belief function is the conjunctive combination of such generalized elementary belief functions (where some masses can be negative). Using a retraction operation, he shows that any belief function can be decomposed into two separable belief functions. One represents the fusion of elementary testimonies (expressing confidence), and the other (expressing doubt) plays the role of a moderator that can annihilate, via retraction, some information supplied by the former, possibly resulting in ignorance. This pair of belief functions is called "Latent Belief Structure" by Smets. In this paper, we present a bipolar belief function model which pushes the notion of "Latent Belief Structure" further. In a belief function, the doubt component is assumed to reflect a cognitive bias interpreted as a prejudice, pertaining to the information supplied by the confidence component. This cognitive bias leads to weaken the strength attached to the combination of some elementary testimonies appearing in the confidence part, thus expressing a lack of trust in the information obtained by merging these testimonies.

The organization of the rest paper is as follows. In Sect. 2, some necessary background on belief functions is introduced. In Sect. 3, we propose new results about the decomposition of belief functions, providing new insights in the weight function introduced by Smets [START_REF] Smets | The canonical decomposition of a weighted belief[END_REF], as well as conditions for separability in a simple case. Section 4 presents a generalized setting for the merging of elementary testimonies in the presence of prejudices, focusing on the process of belief attenuation by means of the retraction operation. This framework is illustrated on the Linda example [START_REF] Tversky | Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment[END_REF], highlighting the difference between belief retraction and source discounting.

Separable Belief Functions

In Shafer evidence theory, the uncertainty concerning an agent's state of belief on a finite set of possible situations, called the frame of discernment Ω is represented by a basic belief assignment (BBA) or mass function m defined as a mapping

m : 2 Ω to [0, 1] verifying A⊆Ω m(A) = 1. Each subset A ⊆ Ω such as m(A) > 0 is called a focal set of m. A BBA m is called normal if ∅ is not a focal set (subnormal otherwise), vacuous if Ω is the only focal element, non-dogmatic if Ω is a focal set, categorical if m has only one focal set different from Ω.
An elementary testimony T with strength 1-x in favor of a non-contradictory proposition A ∈ 2 Ω is represented by a simple BBA (SBBA) m : 2 Ω -→ [0, 1] such that m(A) = 1x, for A = Ω and m(Ω) = x, with x ∈ [0, 1] and is denoted by m = A x . The value x, we call diffidence weight, evaluates the lack of reliability of the testimony (or the source of information). A vacuous BBA can thus be denoted by A 1 for any A ⊂ Ω, and a categorical BBA A = Ω can be denoted by A 0 .

A belief function Bel(A) is a non-additive set function which represents the total quantity of belief in the subset A of Ω and is defined by Bel(A) = ∅ =B⊆A m(B). A BBA m can be equivalently represented by its associated plausibility and commonality functions respectively defined for all A ⊆ Ω by

P l(A) = A∩B =∅ m(B) = 1 -Bel(A) and Q(A) = B⊇A m(B).
The conjunctive combination of BBA's m j derived from k distinct sources,

denoted by m ∩ is expressed by m ∩ (A) = A 1 ∩...∩A k =A k j=1 m j (A j ) .
Note that m ∩ is not always normal. Dempster's rule, denoted by ⊕, is a normalized version of the conjunctive combination rule and is defined such that:

m ⊕ (∅) = 0 and m ⊕ (A) = K • m ∩ for A = ∅. The normalization factor K is of the form (1 -c(m 1 , . . . m k )) -1 where c(m 1 , . . . m k ) = A 1 ∩...∩A k =∅ k j=1 m j (A j ) < 1
represents the amount of conflict between the sources. These two combination rules are commutative, associative, and generally used to combine BBAs from distinct sources. The Dempster rule is simply expressed using the commonality functions as:

Q 1 ⊕ . . . ⊕ Q k = K.Q 1 • Q 2 • • • Q k .
In Shafer's view [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF], a separable BBA is the result of Dempster's rule of combination of simple BBAs: m = ∅ =A⊂Ω A w(A) , w(A) ∈ [0, 1], ∀A ⊂ Ω, A = ∅. We call the mapping w : 2 Ω \ {Ω} → (0, 1] a diffidence function. If the BBA is non-dogmatic (m(Ω) > 0), this representation is unique, and w(A) > 0, ∀A ⊂ Ω. Denoeux [START_REF] Denoeux | Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence[END_REF] has extended this concept to the conjunctive combination of subnormal BBA's ∩ ∅ =A⊂Ω A w(A) , w(A) ∈ [0, 1] ∀A ⊂ Ω.

Shafer [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF] [Th. 7.2 p.143] shows that if Bel is a separable belief function, and A and B are two of its focal sets such as A∩B = ∅, then A∩B is a focal set of Bel. The condition A ∩ B = ∅ can be dropped if we allow for sub-normalized belief functions. But the converse is not true. This necessary condition clearly indicates that not all belief functions are separable. To overcome this difficulty, Smets [START_REF] Smets | The canonical decomposition of a weighted belief[END_REF] generalized the concept of simple support function, considering A x such that x ∈ (0, +∞). Smets has shown that any non dogmatic BBA can be decomposed into the conjunctive combination of generalized BBA's: m = ∩ ∅ =A⊂Ω A w(A) , extending the range of diffidence functions w to (0, +∞). For every A ⊂ Ω, the weights w(A) are obtained from the commonality function of m as:

w(A) = B⊇A Q(B) (-1) |B|-|A|+1 = C∩A=∅,|C|odd Q(A∪C) C∩A=∅,|C|even Q(A∪C) .

The Bipolar Decomposition of a Belief Function

We can write the decomposition of a non-dogmatic belief function as m = (

∩ A∈C A w + (A) ) ∩ ( ∩ B∈D B w -(B)
), where -w + and w -are standard diffidence functions in (0, 1) defined from the original one w associated to m, such that: w + (A) = min(1, w(A)), and w

-(A) = min(1, 1/w(A)), ∀A ⊂ Ω. -C and D ⊆ 2 Ω , w(A) < 1 if A ∈ C and w(B) > 1 if B ∈ D. -∩ defined by m 1 ∩ m 2 = ( ∩ ∅ =A⊂Ω A w 1 (A) ) ∩ ( ∩ ∅ =B⊂Ω B 1 w 2 (B)
) is the retraction operation, also obtained by the division of commonality functions:

Q 1 ∩ Q 2 (X) = Q 1 (X) Q 2 (X) , ∀X ⊆ Ω, called decombination [2]
or removal [START_REF] Shenoy | Conditional independence in valuation-based systems[END_REF]. Ginsberg [START_REF] Ginsberg | Non-monotonic reasoning using Dempster's rule[END_REF] and Kramosil [START_REF] Kramosil | Probabilistic Analysis of Belief Functions[END_REF] have exploited this division rule.

-Factors of the form A w(A) represent testimonies in favor of A if w(A) < 1, and will be called prejudices against believing A if w(A) > 1.

A belief function is separable if and only if w(A) ≤ 1, ∀A ⊂ Ω in the above decomposition. In that case, the set of focal sets of m contains Ω and is closed under conjunction [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF]. So a separable belief function will be of the unique form:

m = ∩ A∈C A w + (A) .
A mass function m can thus be decomposed in a unique irredundant way as a pair (m + , m -), of separable belief functions induced by BBAs m + and m -, such that m = m + ∩ m -. The confidence component denoted by m + is a BBA obtained from the merging of SBBAs, with focal sets in C, and the diffidence component denoted by m -is a BBA obtained likewise, with focal sets in D. By construction, C ∩ D = ∅. The pair (m + , m -) of separable BBAs is called a latent belief structure [START_REF] Smets | The canonical decomposition of a weighted belief[END_REF] more recently studied in [START_REF] Denoeux | Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence[END_REF][START_REF] Pichon | On Latent belief structures[END_REF]9]. The existence of positive and negative information is generally coined under the term bipolarity [START_REF] Dubois | An introduction to bipolar representations of information and preference[END_REF], an idea applied to latent belief structures in [START_REF] Dubois | Not impossible" vs. "guaranteed possible" in fusion and revision[END_REF]. A general study of the canonical conjunctive decomposition of a belief function was realised by Ke et al. [START_REF] Ke | Some notes on canonical decomposition and separability of a belief function[END_REF] and Pichon [START_REF] Pichon | Canonical decomposition of belief functions based on Teugels representation of the multivariate Bernoulli distribution[END_REF], albeit without focusing on its possible meaning.

In the following we are interested in retrieving the mass function m from its diffidence function w via the commonality function rather by the conjunctive combination. First, note that the expression B⊇A Q(B) (-1) |B|-|A|+1 makes sense for A = Ω, and we get w(Ω) = 1/Q(Ω). So function w can be extended to the whole of 2 S , even if only sets A ⊂ Ω appear in the decomposition formula. In previous studies, w(Ω) remained undefined. Of course, w(Ω) > 1 but this will be also the case for the diffidence weights of other subsets for non-separable belief functions.

Noticing that m(A) = A⊆B (-1) |B|-|A| Q(B), and moreover log

w(A) = A⊆B (-1) |B|-|A|+1 log Q(B), it is clear that m is to Q what -log w is to log Q. Since Q(A) = A⊆B m(B), we have log Q(A) = A⊆B log(1/w(B)) = log A⊆B 1 w(B) . Hence, Q(A) = 1 A⊆B w(B) (1)
Note that in (1), the weight w(Ω) appears explicitly in all the expressions of Q(A) for all subsets A. Hence we can retrieve the BBA m, from the diffidence function w computed from it, directly as

m(E) = E⊆A (-1) |B|-|A| ( 1 A⊆B w(B) ).
In particular we can have the following result:

Proposition 1. A diffidence function computed from m via (1) is such that A⊆Ω w(A) = 1.
Proof. We know that commonalities satisfy

Q(∅) = 1. Using (1) yields Q(∅) = 1 ∅⊆B w(B) = 1. So, A⊆Ω w(A) = 1.
It gives a general definition of a diffidence function as a mapping w : 2 Ω → (0, +∞), such that A⊆Ω w(A) = 1 and w(Ω) ≥ 1. Note that the mass function m w derived from any function w defined in this way is not always positive. Indeed, suppose that w

(A) = λ < 1, w(B) = µ > 1, w(C) = 1, C = Ω otherwise (so w(Ω) = 1/λµ > 1)
. By means of the conjunctive rule, one gets the BBA:

m(A ∩ B) = (1 -λ)(1 -µ), m(A) = λ(1 -µ), m(B) = (1 -λ)µ, m(Ω) = λµ. It is clear that m(A ∩ B), m (
A) are negative, in general. So the mapping m → w is injective, but it is not surjective. Namely, given a diffidence function w such that A⊆Ω w(A) = 1 and w(Ω) ≥ 1, Q w obtained by (1) is a decreasing set-function that ranges on [0, 1], but decreasingness is not sufficient to ensure that masses obtained from function Q w are all positive, i.e., Q w is not always a commonality function. On the other hand, diffidence functions such that w(A) ≤ 1, ∀A ⊂ Ω are in one to one correspondence with BBAs of separable belief functions.

+ β + γ < 1, (hence m(Ω) = 1 -(α + β + γ)). Note that Q(a) = 1, Q(ab) = 1 -α -γ, Q(ac) = 1 -α -β, Q(B) = 1 -α -β -γ for other non-empty sets B.
We can decompose m as a combination m = {ab} w(ab) ∩ {ac} w(ac) ∩ {a} w(a) . Its diffidence function is given in Table 1.

a α w(a) = (1-α-γ)(1-α-β) 1-α-β-γ 1 -(w(ab) + w(ac) - w(ab)w(ac))w(a) ab β w(ab) = 1-α-β-γ 1-α-γ (1 -w(ab))w(ac)w(a) ac γ w(ac) = 1-α-β-γ 1-α-β (1 -w(ac))w(ab)w(a) abcd 1 -α -β -γ w(Ω) = 1 1-α-β-γ w(ac)w(ac)w(a) other subsets 0 1 0
It is a separable belief function if the diffidence weights are ≤ 1. Note that

w(ab) = 1-α-β-γ 1-α-γ < 1 and w(bc) = 1-α-β-γ 1-α-β < 1 but it is not always the case for w(a) = (1-α-γ)(1-α-β) 1-α-β-γ
. The condition of separability of the belief function m is

α 2 + α(-1 + β + γ) + βγ 0. Fixing β, γ, this condition is of the form α 1 ≤ α ≤ α 2 , with α 1 = (1-β-γ)- √ (-1+β+γ) 2 -4βγ 2 and α 2 = (1-β-γ)+ √ (-1+β+γ) 2 -4βγ 2
, provided that (1-β -γ) 2 ≥ 4βγ. The latter condition is valid only if β and γ are small enough, that is if

√ β + √ γ ≤ 1. Besides note that 0 ≤ α 1 ≤ α 2 ≤ 1 -β -γ.
It is of interest to consider the special case when β = γ. It is easy to verify that α 1 = 1-2β- When m defined by parameters α, β, γ is separable, we get w(a) = 1, which leads to the condition (α + β)(α

+ γ) = α. Hence w(ab) = 1 -α -β and w(ac) = 1 -α -γ. So can define m b (ab) = α + β, m b (Ω) = 1 -α -β; and m c (ac) = α + γ, m c (Ω) = 1 -α -γ. Choosing α = α 1 or α 2 leads to respective pairs of SBBAs (m 1 b , m 1 c ) and (m 2 b , m 2 c
). We can check that indeed these pairs are related by the condition

m 1 b (ab) = 1 -m 2 c (ac), that is, α 1 + β + α 2 + γ = 1.
Finally, we can study the variation of the diffidence weights when α ranges from 0 to its maximum 1βγ. Note that w(a) is the mass of Ω for the SBBA m a focusing on a, when considering the decomposition of the BBA m. The less w(a) the stronger is the testimony pointing to a, the testimony is not present if w(a) = 1, and it becomes a prejudice against a when w(a) > 1. It can be checked (see Fig. 1 right) that:

-For α = 0, we get w(a)

= (1-β)(1-γ) 1-β-γ > 1.
-w(a) decreases with α until a value α = 1βγ -√ βγ where the derivative vanishes. The minimal value of w(a) is (β+

√ βγ)(γ+ √ βγ) √ βγ
and it is less than 1 only if

√ β + √ γ ≤ 1, as seen earlier. When α 1 and α 2 exist, α 1 ≤ α ≤ α 2 ,
and they coincide if and only if

√ β + √ γ = 1.
-w(a) increases with α ≥ α and lim α→1-β-γ w(a) = +∞.

Looking at the right part of Fig. 1, we note that when α = 0, w(a) > 1 and testimonies in favor of ab and ac are weak; so the prejudice against a is strong enough to erase the focal set a from m. When w(a) reaches its minimal value, the prejudice in favor of a is maximal. When α is close to its maximum value 1βγ, testimonies in favor of ab and ac are less and less challenged since their diffidence weights get close to 0, while the prejudice against a rapidly increases to infinity. At the limit, we get a dogmatic belief function with m(a) = 1βγ and the prejudice no longer compensates the elementary testimonies in favor of ab and ac.

Prejudiced Information Fusion

A generalized SBBA focused on a subset E with diffidence weight x represents the idea that "one has some reason to believe that the actual world is in E (and nothing more)" when x is small (x < 1), whereas, when x > 1, it expresses the idea that "one has some reason not to believe that the actual world is in E" [START_REF] Smets | The canonical decomposition of a weighted belief[END_REF], what we called prejudice. Note that the latter does not mean that we have a reason to believe the complement E of E (which would mean assigning a weight x < 1 to E). In this section, we try to provide an interpretation of non-separable belief functions in terms of merging elementary testimonies with prejudices that weaken the result of the former merging. The idea is that the agent possessing a prejudice of strength y > 1 against believing E is ready to doubt about the truth of E whenever receiving a testimony claiming that E is true. More generally, the combination A x ∩ B y of a simple BBA A x , x < 1 with a simple prejudice B y , y > 1 yields the diffidence function w(•) such that:

if B = A, w(E) =      x if E = A y if E = B 1 otherwise.
(

) 2
and w(A) = xy if A = B. So, it is a belief function if and only if A = B and xy < 1. It is equivalent to erode the testimony A x with another testimony A 1/y using retraction. In particular, A x ∩ A 1/x yields total ignorance. However, erosion cannot alter A x by retracting B = A.

We can compare the erosion with discounting an SSB A x : the discounting procedure reduces the mass 1x bearing on A with a factor δ ∈ [0, 1] and yields m δ (A) = A (1-δ)+δ.x , which is equal to

A xy provided that 0 < δ = 1-xy 1-x ≤ 1 since y > 1, that is 1 < y < 1/x.
More generally we can retract a focal set B from a separable mass function m. Consider m = ∩ k i=1 A w i i and its combination with a prejudice B x , x > 1. Focal sets of m are of the form E I = ∩ i∈I A i , I ⊆ {1, . . . k} with masses m(E I ) = i∈I (1w i ) i ∈I w i (where we allow that some E I 's may be identical). Combining this mass function with E x J yields a mass function m

′ such that m ′ (E J ) = xm(E J ) + (1 -x)( I⊆J m(E I ))= xm(E J ) + (1 -x)Bel(E J ) (where E ∅ = Ω). So E I is erased from the focal sets of m by E x J if and only if x = Bel(E J ) Bel(E J )-m(E J ) = I⊆J m(E I ) I⊂J m(E I ) = 1/(1 -i∈J (1 -w i ))
, which is clearly more than 1. Note that we can erode a single focal set via retraction, while discounting affects all focal sets to the same extent. Similarly, it can be checked that

if J ⊂ I, m ′ (E J ) = ( i ∈I w i ) i∈I\J (1 -w i )(1 -x + x i∈J (1 -w i )) = 0 if and only if x = 1/(1 -i∈J (1 -w i )) again, while if J ⊂ I, m ′ (E I ) = xm(E I ),
which is provably less than 1. In other words, retracting the focal set E J erases all focal sets E I ⊂ E J as well, namely all combinations between the merging of information from sources indexed in J, with information from other sources.

So we can consider that any belief function comes from merging unreliable elementary testimonies, with prejudices that weaken the weights pertaining to the conjunctions of information items coming from sources. It is indeed natural to consider that information we receive from the outside is challenged by our prior information taking the form of stereotypes, or prejudices that one is often unaware of. The receiver is reluctant to consider the result of such conjunction valid. For instance, consider a variant of the Linda problem [START_REF] Tversky | Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment[END_REF]. In this case, the bank teller Linda, depicted as a philanthropist, is found by participants to a psychological experiment, more likely to be a philanthropist bank teller than a bank teller, because the former looks more "representative" or typical of persons who might fit the description of Linda. Here we consider the case when we receive two testimonies, namely one (B v ) claiming that Linda is a banker and another one A w that she is a philanthropist. The fusion process leads us to allocate a belief degree (1v)(1w) to the fact that she is a philanthropist bank teller. However, a prejudiced individual would hardly believe that a bank teller can be philanthropist, and would like to erode, possibly erase, this belief by combining the result of the fusion with the generalized SSB (A ∩ B) u with 1 < u ≤ 1/(v + wvw), which leads to a belief degree equal to 1 -(u + vvw)u, that is all the lesser as the prejudice is strong.

Conclusion

This paper revisits the decomposition of a belief function into a combination of generalized simple support functions proposed by Smets [START_REF] Smets | The canonical decomposition of a weighted belief[END_REF] showing that it can be viewed as the merging of uncertain testimonies and of prejudices against the results of their partial conjunctions. We have laid bare new formal properties of the diffidence function w and shown how to reconstruct the BBA m from it via Moebius-like transforms. Our results strengthen the approach to belief function based on the merging of pieces of evidence, as opposed to the approach based on upper and lower probability. Future research can be a study of the information ordering based on diffidence functions, introduced by Denoeux [START_REF] Denoeux | Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence[END_REF], on which our results can shed more light.

  Example: Two Overlapping Focal Sets on a 4-Element Frame. Let Ω = {a, b, c, d}. We denote {a} by a, {a, b} by ab, etc. Consider m with m(ab) = β; m(ac) = γ; m(a) = α with α

2 .

 2 We must have β ≤ 0.25 otherwise the belief function cannot be decomposable (α 1 and α 2 are not defined). For β = 0.25 we have that α 1 = α 2 = 0.25. See the graph of the functions giving α 1 and α 2 in terms of β on Fig. 1. It indicates the zone of non-separability under the line 1 -2β and on the right-hand side of the curve for α 1 and α 2 .

Fig. 1 .

 1 Fig. 1. Left: m(a) in terms of β = γ if w(a) = 1. Right: diffidence weights in terms of α

Table 1 .

 1 Decomposition with focal sets: ab, ac, a and Ω

	A	m	w	Inverse solution


Marie Garnier
email: mgarnier@univ-tlse2.fr

Sarah Bourse
email: sarah.bourse@univ-tlse2.fr

Patrick Saint-Dizier

Investigating Argument Relatedness Based on Linguistic Knowledge

Keywords: Argument Mining, Linguistic Knowledge, Relatedness, Annotation

In this contribution, we explore the type of linguistic knowledge that is required to establish relatedness between a claim and a justification which may be distant or in different texts, within the framework of argument mining. We propose an original annotation method based on XML-Frames and a linguistic analysis of the main resources which are needed to establish relatedness on a linguistic basis.

I. AIMS AND MOTIVATIONS

One of the main challenges of argument mining is to correctly identify the statements that are justifications or that support a given claim across different types of online texts (for example, news articles, blogs, consumer reviews). This issue is called argument relatedness and it is a central point in information retrieval. It is also essential in argument mining [START_REF] Palau | Argumentation mining: the detection, classification and structure of arguments in text[END_REF]- [START_REF] Swanson | Argument mining: extracting arguments from online dialogue[END_REF]. The main objective of research on argument relatedness is to be able to mine statements which develop the same topic as the given claim and have an argumentative orientation. Broadly speaking, relatedness is a measure of the semantic and topical proximity of two text spans. These segments may differ lexically (via the use of synonyms, hyponyms or hypernyms, to name a few possibilities) or syntactically (for example, with alternations, such as active vs. passive structures). Previous research [START_REF] Saint-Dizier | Argument Mining: the bottleneck of knowledge and lexical resources[END_REF] has shown that establishing relatedness between an argument and a statement requires knowledge in 58% to 88% of situations, depending on the topic of the claim.

Since supports and attacks (elements that oppose a claim) of a claim mainly address the purposes, goals, functions or structure of the main concepts of the claim, previous studies have used the Qualia structure of the Generative Lexicon [START_REF] Pustejovsky | The Generative Lexicon[END_REF] as a knowledge representation system for relatedness. This approach pairs domain knowledge with lexical semantics in an efficient and principled way. However, this previous work also shows that Qualia structures are difficult to develop and must be defined for each topic. This makes knowledgebased argument mining an approach that, although effective, is difficult to reuse over different domains.

The current research project examines and evaluates the possibility of establishing relatedness solely on the basis of linguistic knowledge and lexical semantics. The development of general-purpose linguistic processes and resources that characterize relatedness would make the implementation of relatedness much simpler and much more reusable over domains. This contribution explores this hypothesis as well as the linguistic knowledge which is required, in particular lexical semantics.

The rest of the paper is structured as follows. The analysis protocol and the annotation system are presented in Section II, while Section III deals with the future steps that need to be taken to be able to establish relatedness on a linguistic basis.

II. ANALYSIS PROTOCOL

This research introduces two specificities. First, the analysis of relatedness is based on the topical content of the claim, as a claim-driven analysis allows the analysis to focus on the features of the claim and to integrate the new elements found in various statements related to that claim. In addition, the annotation is not based on standard linear text annotations but on the use of frames encoded in XML: the use of an XML-Frame approach is motivated by the fact that the elements found in statements and that are decisive for the analysis of the semantic elements of relatedness may not be adjacent, which makes text annotation, which is linear, almost intractable.

In this framework, relevant statements are extracted from the source text and fed into XML-Frames in which the features are filled in manually by annotators. Each statement found to be related to the claim and with an argumentative orientation originates an instance of the frame. The result is a set of frames which can be organized as a tree, where the root is the frame representing the claim and the children are those statements found in texts and that introduce additional constraints on the topic. These additional constraints on the claim topic characterize relatedness.

The relations of each statement with the claim are described in each frame instance through the use of features indicating the linguistic and conceptual links between the claim and the statement. Our corpus is based on texts about controversial social issues, addressing topics such as affirmative action or the gender pay gap. These are relatively complex issues, which guarantees that the need for linguistic and conceptual knowledge will be apparent. The goal is then to mine statements which are related to this claim in various texts. These statements must have a topic that is subsumed by the claim topic and an argumentative orientation which may support or attack the claim, depending on the content of the statement. The argumentative orientation is given by evaluative expressions such as scalar adjectives, possibly modified by an adverb of intensity. Those statements are also frequently associated with discourse structures which further develop them.

The frame template we have defined for the study of relatedness is very detailed. Inside the general frame <statement>, four sub-frames are embedded (<topic>, <evaluative>, <discourse>, <arg scheme>), with the first two subframes also including two additional subframes which allow for the identification of a main topic and a field of application for this topic.

As an illustration, let us consider the following claim: affirmative action in education is good for the economy. This claim is composed of a topic: affirmative action in education and an evaluative expression: is good for the economy. The topic is itself composed of a main concept, affirmative action and a field of application for this concept, in education. The evaluative expression is analyzed in the same way (is good and for the economy). The annotation scheme is presented below in more detail: To say it briefly, this frame allows the description of most features that characterize relatedness. The 'link' and 'concept op' features respectively specify the linguistic link (exact words, derivation, semantic field, etc.) and the conceptual operation taking place between the words of the claim and the words of the text (reformulation, summarization, definition, etc.). The same description is made for the evaluative expression with, in addition, the orientation and strength of the evaluation.

The <discourse> subframe describes elements such as elaborations, illustrations, comparisons, conditions or circumstances that are not directly argumentative but can be seen as being part of the argument. Finally, the annotator is invited to specify the kind of argument scheme(s) that has been used, from a standard list of arguments [6] [7].

III. TOWARD A LINGUISTIC CATEGORIZATION OF RELATEDNESS

The 'link' and 'concept op' features are specifically designed to allow for the linguistic categorization of relatedness. To describe the linguistic and conceptual links with the claim, the annotators can use predefined categories or natural language, until a stable list of categories can emerge through the collective observation and analysis of the corpus. Then, a categorization of the main linguistic operations can be carried out, and the associated resources can be developed and structured from existing resources. The aim of this categorization is to characterize the linguistic operations behind relatedness and to evaluate the efficiency and scope of a linguistic approach, i.e. how much of relatedness analysis can be resolved via linguistic processes.

The parameters which are under investigation, categorization and evaluation are as follows:

• the paradigmatic lexico-semantic transformations developed from the topic of the claim and its restrictions, in particular, forms of synonymy, partial reformulations (the lower representation of women in paid work), paraphrases, restrictions, opposites, forms of inchoativity (terms describing the result instead of the process) or vice-versa (for example: gender pay parity → gender pay gap).

• the functional transformations which are related to the nature of the topic, and may induce some domain dependent lexical data (for example: providing a better balance of job opportunities for all). These functional terms are derived from linguistic resources that develop the goals or purposes of entities. These may be found, for the simplest kinds, in WordNet (examples and data can be found in [START_REF]WordNet presentation and database access[END_REF]).

• the local syntactic transformations on the claim topic, (the gap in salary between genders),

• forms of discourse transformations such as: summarization (when the topic is long), illustration or instantiation, expression of consequence,

• the lexical data which is necessary, its structure according to lexical semantics principles [START_REF] Cruse | Lexical Semantics[END_REF], and its availability. A number of resources are already present in our <TextCoop> platform that realizes discourse analysis in English and French with high accuracy (about 90% accuracy in the case of the domains considered here). The version 5.1 of this platform is available at [START_REF][END_REF] while system foundations and examples can be found in [START_REF] Saint-Dizier | Challenges of Discourse Processing: the case of technical documents[END_REF].

ACKNOWLEDGMENTS

This research project is partly funded by a grant from the Maison des Sciences de l'Humain et de la Société, Université de Toulouse, France.


Mathilde Janier

Patrick Saint-Dizier

Evaluating the Strength of Arguments on the Basis of a Linguistic Analysis: A Synthesis

In this contribution, we present several layers of linguistic analysis, the aim of which is to provide indications on the strength of arguments in context. This contribution proposes a synthesis of existing resources to evaluate strength also used in opinion analysis, then it develops features which are proper to argument strength. Linguistic elements related to (1) the argument contents, (2) the discourse structures associated with this argument (which may introduce restrictions), (3) the nature of argument schemes used, and (4) some rhetoric elements are investigated.

INTRODUCTION

There are several ways to measure the strength of arguments. The strength can be measured from a logical and pragmatic perspective or it can be measured from a language point of view. Both approaches are not necessarily coherent but they must be combined to produce a relatively accurate measure of strength. Argument strength may be measured for each argument in isolation or for groups of related arguments, taking into account their relations and structure.

In this contribution, an argument is composed of a claim and of one or more propositions Pi which support or attack the claim. Claims and propositions Pi have their own strength. In this contribution, we first identify linguistic phenomena and their related cues which are a priori marks of strength on propositions Pi taken in isolation. We then integrate this analysis into a larger view where a proposition Pi is associated with discourse structures which may reinforce or weaken its strength. In a subsequent stage, sets of related propositions Pi are considered, so that their relative strength can be characterized on the basis of linguistic factors. Finally, the impact of argument schemes and rhetoric cues is explored to give an overall picture of how argument strength based on linguistic analysis can be measured. Priority is therefore given to linguistic analysis, in which results of lexical semantics are relatively stable and accurate, over a more pragmatic and intuitive analysis of argument strength.

This investigation and analysis is carried out within the framework of argument mining and analysis in which, given a controversial issue, arguments for or against this standpoint are mined in different types of texts (see for example [START_REF] Mochales | Argumentation mining: the detection, classification and structure of arguments in text[END_REF], [START_REF] Mochales | Argumentation mining[END_REF]). Besides supporting or attacking an issue, propositions Pi may also attack or support each other. The problem of the relatedness between a claim and propositions Pi has been addressed in [START_REF] Saint-Dizier | Knowledge-driven argument mining based on the qualia structure[END_REF], it will therefore not be discussed in this contribution which focuses on a crucial and difficult parameter: evaluating the potential strength of an argument. In our perspective, persuasion is a kind of contextual evaluation of the strength of an argument. This will not be addressed here, although it is clear that it should be the ultimate component of such an investigation.

Quite a large number of investigations, more or less successful and ad'hoc, have been developed within the framework of opinion analysis. This document reviews the main results and develops additional or more specific material proper to argument strength analysis. In opinion analysis, platforms and resources such as Sentistrength (http://sentistrength.wlv.ac.uk/) and the Stanford Sentiment Treebank. Major synthesis on opinion strength are developed in [START_REF] Taboada | Lexiconbased methodsfor sentiment analysis[END_REF] and [START_REF] Liu | Sentiment Analysis and Opinion Mining[END_REF]. However, if some features are shared with argument strength analysis, argument strength is more complex to characterize since an argument is a complex system composed of a claim, one or more justifications, and quite frequently some forms of evidence, backing and warrant and rebuttals. Qualifiers may also be stated. Finally, the nature of the argument scheme that has been used may be crucial. This contribution develops a synthesis of a number of these aspects.

Investigations on argument strength have focused on a few aspects such as [START_REF] Claude | L'argumentation dans la langue[END_REF] teaching how to organize written essays and how to organize arguments and give them an appropriate strength, (2) research on persuasion which is, in our view, an analysis of strength in contexts (domain and listeners are taken into account), and (3) in theoretical analysis of argumentation where graphs of attacks and supports are developed. Let us note for example [START_REF] Grasso | User models for motivational systems -the affective and the rational routes to persuasion[END_REF] that deals with an in-depth analysis of persuasion, [START_REF] Zhao | A measure of perceived argument strength: Reliability and validity[END_REF] which investigates the content of persuasive messages. Sensitivity to argument strength of various populations is developed in e.g. [START_REF] Corella | An affirmed self and an open mind: Self-affirmation and sensitivity to argument strength[END_REF].

The relation of strength with rhetorical questions has been addressed in e.g. [START_REF] Munch | Rhetorical question, summarization frequency, and argument strength effects on recall[END_REF]. A number of linguistic factors are analyzed in e.g. [START_REF] Claude | L'argumentation dans la langue[END_REF], and later in [START_REF] Van Eemeren | Argumentation, Communication and Fallacies[END_REF], [START_REF] Van Eemeren | Argumentation, Analysis, Evaluation[END_REF]. However, to the best of our knowledge little has been done to characterize argument strength from a linguistic point of view, within the perspective of argument mining. This article is a contribution to this perspective, it also outlines the high context sensitivity of linguistic factors.

This paper is organized as follows. In a first stage, the contribution to argument strength of individual lexical items found in propositions Pi is investigated. The hypothesis is that such propositions have an intrinsic strength independently of the claim. Lexical semantics structures to organize linguistic data are introduced. Then, the strength variations induced by the combination of several lexical items in a proposition and the support construction in which it may be embedded are explored and tested experimentally. Since it turns out that contextual effect in its broad sense is crucial to have an accurate estimate of the strength of an argument, several contextual parameters are discussed, in particular the impact of the discourse structures which are adjoined to the argument or to a proposition Pi and the kind of argument scheme on which the argument relies.

Several types of corpora are used to carry out this investigation. Documents are oral or written, they are essentially in English with a few of them in French. Our corpus is composed of the following elements:

• a corpus of debates extracted from the BBC Moral Maze, analyzed in conjunction with the university of Dundee, with about 2000 arguments [START_REF] Budzinska | A model for processing illocutionary structures and argumentation in debates[END_REF], available on their platform, • a corpus of consumer opinions in the hotel domain [START_REF] Garcia | Some facets of argument mining for opinion analysis[END_REF] and in relation with the services offered by the local French airline HOP! (French texts); this corpus is particularly rich in discourse structures which modify argument strength and scope, which includes about 250 arguments, • a corpus of short texts, that contains about 150 arguments, used to identify the relatedness problem [START_REF] Saint-Dizier | The bottleneck of knowledge and language resources[END_REF], [START_REF] Saint-Dizier | Knowledge-driven argument mining based on the qualia structure[END_REF] from the domains of vaccination, nuclear energy (in French), and women's condition in India.

These corpora are quite diverse in nature and linguistic characteristics, they allow an accurate identification of the linguistic elements at stake in the expression of strength. This corpus is used to identify and evaluate the importance of various linguistic constructions and linguistic resources in strength expression, it is therefore difficult to evaluate its relevance a priori. The main point is that it contains a large diversity of types of statements so that most linguistic phenomena can be observed, but probably not quantified, which is not our aim at this stage.

STRENGTH FACTORS WITHIN A PROPOSITION

Given a claim, propositions Pi for or against it are essentially evaluative statements. These may be direct evaluations or may require knowledge and inference to identify what is evaluated and how. The terms used in propositions Pi to provide an evaluation of a standpoint induce a polarity for the argument and strength indicators which say whether their attack or support is strong or weak. This section explores the linguistic phenomena and their related cues, within the propositions Pi, which may potentially be strength indicators. The hypothesis is that such propositions have an intrinsic strength independently of the claim, which is explored in this contribution. It is however clear that the strength of the argument is a combination of the strength of the claim and of the proposition that supports or attacks it.

Evaluating the strength entailed by linguistic cues is quite subjective. Our goal is to collect those marks and to structure them according to scales. Evaluating their real impact in context requires measures which go beyond this analysis, but this is a necessary step. Some simple elements are given in section 3.4. Each linguistic cue is investigated in isolation, then the correlation of several cues is investigated.

Two levels of the expression of strength are considered here: (1) the implicit strength conveyed by head terms used in propositions and (2) the strength conveyed by expressions, such as propositional attitudes expressions, of which a proposition Pi is the sentential complement. The propositions Pi considered in this investigation have a simple syntactic structure. They are composed of a main point called the kernel and adjuncts -in general discourse structures -which add e.g. restrictions, justifications, purposes or illustrations to the kernel. These discourse structures may scope either over the proposition or over the entire argument.

The linguistic resources which are used are those of our TextCoop platform, with which discourse analysis and argument mining is realized. Resources considered in this investigation come for a large part from general purpose and domain dependent lexical resources we developed for opinion analysis.

A categorization of the expression of strength

As also shown in the area of opinion analysis, there are many elements which may have an impact on the strength of a proposition Pi. Those with a higher impact are head elements such as verbs, and elements which are less prominent in the syntax such as evaluative adjectives and adverbs. These latter are analyzed as adjuncts to the noun for adjectives and to the VP or the sentence for adverbs. These linguistic elements are used to determine the orientation of the propositions Pi w.r.t. the claim (support, neutral, attack). In addition, their implicit semantics is an important factor to evaluate the overall strength of an argument.

The main categories of elements internal to a proposition Pi which may impact the strength are: The expression of strength is also mediated by a number of terms which introduce propositions Pi. These are called control constructions, they sub-categorize for a proposition or a sentential comple-ment which is here a proposition Pi. These constructions, although found in opinion analysis, are more developed in argumentation. They also appear in dialog analysis in general. The scope of these constructions is the entire argument, not the justification, as it would be the case in opinion expression. Control constructions can be organized according to the following linguistic categories:

1. Propositional attitude verbs and expressions: besides the expression of agreement or disagreement, which is their main aim, most of the elements of this category have an implicit weight. In this class fall verbs and expressions such as: think, believe, agree, deny, argue, refute, acknowledge, reckon, disagree, accept, reject.

The semantics of these verbs is investigated in depth in [START_REF] Wierzbicka | English Speech Act Verbs: A semantic dictionary[END_REF]. These elements have different weights which may depend on the context and personal interpretations, for example, believe may be weaker or stronger than think. Propositional attitude constructions do not have, a priori, an impact on the argument orientation. Propositional attitude constructions can be modified by a negation or by a modal such as would, could, have to as in: I would argue that, I have to acknowledge that. These may impact the strength. 2. Psychological expressions or expressions denoting a desire, a position or an experience. These expressions may be at the origin of the expression of a doubt or a weak support; they include verbs and expressions such as: I feel, I am worried about, I am intrigued by, dream of, be encouraged by, tend to. These terms are often in an initial position or in a final position for constructions such as worries me as in: the obligation of vaccination worries me, where the nominalized sentence is raised to play the role of the subject. 3. Report verbs and associated constructions. They introduce arguments and propositions Pi in a direct manner or as a reported speech from e.g. other participants in a debate or from external persons, frequently considered as experts (see also Section 4.2).

Similarly to the two above categories, these constructions can be modified by a negation or a modal. In this category fall expressions such as: report, say, mention, stated, announced, discuss, claim and their morphological variants. Identifying the strength of these terms is difficult: while report, say, announced are rather neutral, terms such as claim, stated are much stronger. For example, given the claim: Ebola is a dangerous disease, a strong attack may be: the authorities of Guinea claimed that there is no risk of proliferation of Ebola. 4. Epistemic constructions. These also occur quite frequently, they include expressions such as: know, my understanding is that, I am convinced that, I suppose, I realize, it is reasonable to assume, infer, implies, I can see.

While some introduce doubts or uncertainty, others are clear affirmations of a certain knowledge that may contradict or support a standpoint. 5. Modal expressions. These behave as left adjuncts and modify some of the expressions described above or may be adjoined to the head verb of the argument. Most of them either weaken the statement or introduce forms of hypothesis: might, would, must, have to, could be, should be possible, it is reasonable to, can mean, may mean. For example, for the claim on vaccination against Ebola, a weak support could be:

a systematic vaccination could define sanitary belts to avoid the proliferation of the disease. 6. Adverbials related to the expression of opinion. In our corpora, they frequently increase the strength of the arguments. They include: probably, necessarily, most definitely, definitely, surely, usually, frequently, often, certainly, of course, obviously, generally speaking, of course, indeed.

Structuring expressions of strength by semantic category

It is obviously impossible to a priori assign strength values to the terms given in the different categories given above, nor is it possible to assign weights to their combinations. A option is to structure these terms along scales [START_REF] Cruse | Lexical semantics[END_REF], as for scalar adjectives in opinion analysis. In this experiment, it turns out that the polarity of about 75% of the adjectives are domain independent. While the adjectives used in opinion expression lend themselves relatively easily to an evaluation of their positive or negative character, this is more complex for verbs, modals or the expressions categorized above. To organize the elements in the different categories, an experiment is made using non-branching proportional series (Cruse 86) which allow to define partial orders over groups of terms w.r.t. a given measurable property. These scales organize terms of a category from those with a strong negative orientation to those with a strong positive orientation. A neutral point is mentioned: it is a term when such a term exists or an abstract point. The partial order introduces some flexibility by allowing several terms to be at a given point on the scale when it is not relevant to make strength distinctions between them. Our approach is (1) to classify the terms of each category in a dedicated scale following their standard semantics, (2) to evaluate the results and to possibly revise the classification according to the results obtained from the experiment reported in 3.4.

For example, the negatively and positively oriented verbs given above (3.1, items 1 and 2) are structured as follows:

[[ruin] -[break, demolish] -[affect, alter, lessen, undermine, damage] -[hurt] -Neutral -[preserve, guarantee] -[benefit] -[improve, consolidate, strengthen] - [optimize]].
Terms which are considered to have almost the same strength appear in the same set, represented between square brackets. The neutral point is represented by the constant 'Neutral', the two sets around it have a moderate strength while the extremes sets are the strongest ones.

Adjectives are more difficult to structure because they do not modify in an homogeneous way the same property, for example, resistant and optimal may not operate on the same concepts, where optimal is rather higher-order. A global scale such as the following can however be developed:

[[dangerous, harmful] -[risky, polluted] -[weak] -Neutral -[useful, capable, consistent, beneficial] -[resistant] - [optimal]].
In this example, a certain number of adjectives is in the same set since these have a relatively similar impact on strength.

Finally, a scale for propositional attitude verbs is the following:

[[deny -refute -reject] -[disagree] - Neutral -[believe, think, accept] -[agree, acknowledge, reckon] -[argue]].
The verbs to the extreme of the scale are more crucial in the acceptance or rejection of the claim than those close to the Neutral point. Adverbials modify these verbs or the VP they head by adding or reducing the strength. These can be classified as follows by increasing strength: is not trivial, even for human experts.

[[probably] -[indeed,
To have an accurate analysis of the strength of propositions Pi, a semantic representation of the elements which contribute to strength expression is developed. It is based on the categories of the elements found in the proposition and on a rough estimate of their strength, as reflected by the non-branching proportional series presented in section 3.2. For example, the proposition: Nuclear plants should be banished. has the following semantic representation w.r.t. its strength: [argument verb(strong negative) ∧ modal(weaken)]. where banished is among the strongest negative verbs on the corresponding scale while the modal should weakens the strength of this verb. Then, the whole proposition: I am definitely convinced that nuclear plants should be banished, which includes an epistemic construction, is represented as follows:

[ control verb(epistemic, strong positive) ∧ adverbial(reinforce)]([argument verb(strong negative) ∧ modal(weaken)]).
Let us call this expression the signature of the strength of the proposition. Considering the different elements of this representation, the resulting strength is strong with a negative orientation.

A simple way to identify the strength of an proposition is to develop composition equations:

• in the proposition: the head terms are the verbs or the adjectives.

They a priori have a polarity and a strength level which is lexically induced. A standard scale with 5 values: [null, weak, average, high, maximal] is used in this first experiment. These lexical structures may be combined with intensifiers which are modals for verbs and adverbs for adjectives. Intensifiers weaken or reinforce the strength of the element they modify. For example, if banished has the strength 'high' with a negative orientation, then should lower it to 'average' while preserving its orientation.

• The same strategy holds for the structure in which the proposition is embedded. For example, I am definitely convinced is composed of a head verb with strength 'high', and the adverbial definitely increases its strength to 'maximal'. • The strength and orientation of a proposition are combined with the control structure in which it is embedded. The resulting strength is a function of the strength of each structure, for example the average. In our example, 'maximal' must be combined with 'average', leading to 'high'.

This model takes into account the different linguistic parameters of an proposition, it is however very simple: it is based only on linguistic considerations and on an a priori strength evaluation of each lexical element. It does not take into account other crucial factors such as the context of the utterance, the argument schemes used, the domain and its style, the intonation and the preceding claims and propositions Pi.

An experimental evaluation of strength based on annotations

It is difficult to ask annotators to evaluate the strength of propositions Pi without any analytical support. The model provided in the previous section, although quite simple, can be used as a support for annotators who can concentrate on each element separately and then make a global evaluation of the strength. In this section, a new protocol for strength analysis is introduced.

The idea is to automatically annotate propositions Pi with the values described in 3.3, and then to ask human annotators to indicate their own evaluation for (1) a proposition, (2) the embedding structure when it exists, and (3) and the combination of the two. In a subsequent stage, discourse structures will also be annotated using our TextCoop platform. The manual annotations can then be compared to the annotations produced by the system as described in section 3.3. A more accurate model of strength analysis can then be developed from these two evaluations.

Let us now illustrate the annotation structure that the annotator uses. The annotator must specify the strength and possibly the orientation for each of the uninstantiated attributes (strength, orientation, intensity). The above example is annotated by the system, based on a lexical and surface syntactic analysis; values are left open so that annotators can filled them in: <proposition strength= , orientation = > <support strength= , orientation = > I am definitely convinced that </support> <kernel strength= , orientation = > nuclear plants <modal intensity = > should </modal> <verb strength= , orientation = > be banished </verb> </kernel> </proposition> with strength ∈ [null, weak, average, high, maximal] orientation ∈ [positive, neutral, negative] intensity ∈ [lower, increase].

A first, preliminary experiment aims at identifying the strength differences as postulated a priori by the linguistic description and as perceived by humans. Contextual effects, such as the style or the strength of other arguments, are not taken into account in this first experiment in order to concentrate on propositions and arguments strength taken in isolation. The contextual dimension will be considered in a second stage (see section 3).

In this initial experiment, a set of two hundred propositions have been annotated. These are constructed via lexical variation, to ac-curately evaluate the impact of each lexical item, from 15 original claims. In these propositions, the lexical items which originate the strength are substituted by others, e.g. convinced becomes feel and then believe. Substitutions are the identical, as much as possible to preserve relevance, over the 15 claims to preserve the homogeneity of the results. A total of 38 lexical items are tested in various linguistic realizations. The goal is to validate the protocol and have preliminary results before starting a larger experiment.

The strength values are transformed into numbers to allow numerical computations. The following parameters are investigated:

• the strength S1 associated with each lexical term: the different values associated with each lexical item are averaged, to produce their average individual strength estimate. Then, a partial ordering similar to the linguistic ordering presented in section 3. • the strength S3 of the support construction is elaborated in a similar way when it exists, it is equal to 1 when there is none, • the global strength S4 of the proposition including the support construction when it exists. For this level, the following vector is considered:

[support strength S3, proposition strength R, global strength G].
The results of this experiment are not very surprising:

• the individual strength of lexical items taken in isolation is very similar to the series developed independently of any context from a linguistic point of view, only 2 elements are classified differently, • the proposition strength shows a variation of 15% compared to the linguistic estimate of section 3.3. It is lower in 80% of the cases. Most of the modals are interpreted as lowering the strength and a gradation is expected: moderate lowering and strong lowering, which would decrease the initial strength by 2 instead of just 1.

The prominent role played by modals in the strength expression is an important result of this task, • the support construction strength shows a variation of a maximum of 25% either above or below the linguistic estimate. This can be explained by the difficulty to interpret the strength of terms such as believe compared to think. These terms are in fact context and speaker dependent, • the combination of the proposition and its support shows a variation of about 30% around the linguistic estimate, which is relatively large and questions the validity of the linguistic classification taken in isolation.

This simple and preliminary experiment shows that while there is a relative stability on the strength of terms such as verbs and adjective, the strength evaluation is less stable for modals, and needs some important adaptations for support constructions and their combination with or influence on the claim and vice-versa. This motivates the second step of our investigation: taking into account various forms of context, which should allow to have a more reliable estimate of the strength of support constructions and modals.

OTHER FACTORS OF STRENGTH

Several other factors, which are essentially contextual, have a major influence on the strength of propositions Pi and on arguments more generally. Their influence is however difficult to accurately analyze. These factors are explored in this section. The results of the previous section (3.4) indeed show that the strength induced by some lexical items depends on the context of the utterance.

The first factor are the discourse structures which may be adjoined to a proposition or an argument that describe e.g. circumstances, conditions, restrictions, etc. This factor has been investigated within the RST framework (http://www.sfu.ca/rst/). The second factor is the argument scheme that has been used. Some have a higher strength or reliability than others. The third factor is the context of the proposition: it may be uttered in isolation or it may be part of a series of propositions Pi and of arguments. As developed in e.g. [START_REF] Van Eemeren | Argumentation, Communication and Fallacies[END_REF], propositions associated with a claim may be structured as series or in parallel. In the first case, the strength is the strength of the weaker one, and in the second case it is the strength of the strongest one. This type of factor is not found in opinion analysis where statements are in general treated in isolation. The fourth factor is the syntactic structure of the premise-conclusion pair where focus shifts can be observed via for example left-extraposition. The last factor is the linguistic context of the utterance. For example some debates may only use soft arguments in order to remain polite and to avoid strong attacks, whereas others use extremely strong terms even for arguments which are not crucial.

In this section, the impact on argument strength of the first two factors is discussed. The remaining ones require additional investigations.

Influence of discourse structures on argument strength

As in any form of elaborated discourse, arguments are quite frequently associated with elements such as comments, elaborations, comparisons, illustrations, etc. which can be considered as either forms of explanation or secondary or subordinated arguments. These discourse structures are borrowed from the RST ( [START_REF] William | Rhetorical structure theory : Toward a functional theory of text organization[END_REF], see also http://www.sfu.ca/rst/) considered within the perspective of argument strength analysis. These structures frequently implement argument schemes [START_REF] Walton | Argumentation Schemes[END_REF] and applied to opinion analysis [START_REF] Garcia | Some facets of argument mining for opinion analysis[END_REF], as developed in section 4.2 below. In our view, explanation is not a basic rhetorical relation as introduced in RST, but a very generic construction, a 'proto-relation', which covers a large number of communication and argumentative situations. For the claim: Ebola vaccination is necessary, the statement: the Ebola vaccine is easy to use for emerging countries (cheap, can be transported without any need for refrigeration, active for a long time) is argumentative where the expression : '(cheap, can be transported without any need for refrigeration, active for a long time)' can be analyzed [START_REF] Claude | L'argumentation dans la langue[END_REF] either as an elaboration or as an illustration of the head expression ' easy to use for emerging countries' (2) or as a secondary or subordinate proposition which supports the main one. In RST theory, the head expression is a nucleus while the elaboration or illustra-tion is its satellite. The explanation or secondary proposition which supports the main one increases the strength of 'easy to use'.

However, the role of illustrations w.r.t. to argument strength is not easy to determine. Given the claim: I do not recommend this hotel, in a proposition such as: The bathrooms were in a bad condition: [ILLUST RAT ION the showers leaked, and the plug mechanism in the bath jammed ...], the illustrations given to support the diagnosis ('bad condition') do not seem to reinforce or weaken its strength. They are interpreted as reformulations which are another way to say something without altering the initial content. The difference between these two examples is the contribution of the illustration: in the first example 'easy to use' is rather vague and is reinforced by the example, whereas in the second example 'bad condition' is more precise and remains at the same strength level.

Let us consider other types of discourse relations such as the circumstance and justification relations. For example, given the standpoint: Ebola is a dangerous disease, a justification may weaken a strong proposition, instead of supporting it: [JUST IF ICAT ION in order to avoid any form of panic or, worse, of bio-terrorism], the authorities of Guinea claimed that there is no risk of proliferation of Ebola. In the following example, possibly with a form of irony, the strength and polarity of 'breakfast is excellent' is largely affected -if not reversed -by the contrast: The breakfast is excellent [P RECISION with very imaginative exotic fruit salads ] [CONT RAST but most of the products are not fresh and most have passed their sell-by date ].

More complex -yet realistic -arguments associated with restrictions of various sorts make the identification of the overall strength quite challenging: [CONT EXT We stayed here for a one day conference off-season], and the hotel was OK [CONCESSION -although the room I had was kind of weird.] I think it was the sitting room to the suite on the top floor [P RECISION -the bed was a fold-out bed, not comfortable, [CONCESSION (slept okay though)], and the coffee table was small, dirty and pushed to the side.] [CONCESSION It did have a lovely terrace though] -shame it was raining cats and dogs.

[RECOMMENDAT ION Not a great experience.] Depending on customers' preferences, this opinion can be judged to be slightly positive or negative, in spite of the negative polarity of the recommendation, which turns out to be the main argument. Therefore, this opinion may either support of attack the standpoint I do not recommend this hotel.

Evaluating the impact of discourse structures is therefore a very challenging task. Even if the polarity and strength of each individual structure can be evaluated, their combination with the main argument and their interactions when there are several structures is complex and highly domain dependent. We are now exploring various types of experimental protocols which could contribute to this analysis. The discourse structures shown in the examples are recognized by our TextCoop platform with an accuracy of about 90% [START_REF] Saint-Dizier | Processing natural language arguments with the textcoop platform[END_REF]. The challenge is now to go into the semantics of each structure.

The impact of argument schemes on argument strength

Another component to follow is to explore the inner structure of an argument and the underlying scheme that has been used. [START_REF] Walton | Argumentation Schemes[END_REF], [START_REF] Parsons | Argument schemes for reasoning about trust[END_REF],

have identified and structured a large number of schemes which are used in everyday argumentation. Some of them can be detected via a linguistic analysis [START_REF] Vw Feng | Classifying arguments by scheme[END_REF], [START_REF] Green | Manual identification of arguments with implicit conclusions using semantic rules for argument mining[END_REF]. These can provide information on the strength of arguments. A number of schemes among the most frequently encountered are reviewed in this section.

Argument from analogy

The typical form of arguments from analogy is as follows: Premise 1: Generally, case C1 is similar to case C2. Premise 2: A is true (false) in case C1. Conclusion: A is true (false) in case C2. For example: It has been shown that vaccinating against malaria can be useless in some cases; similarly, the vaccine against Ebola is not recommended. This sentence makes an analogy between two serious diseases and tries to show that if the vaccine against one of these diseases is useless then the vaccine against the other is useless too. Some linguistic cues marking analogy are: similarly, x is like y, doing x is as [adjective useful, dangerous, crucial] as doing y.

Metaphors can also mark analogy. For instance, Ebola is a war which has to be fought. An analogy is made between Ebola and war. This type of construction has often been used in literature, some metaphors are now well-known and used in everyday conversations, which proves that its rhetorical effect is high; as a consequence, arguments from analogy may have a strong impact.

Argument from expert opinion

The typical structure of arguments from expert opinion is: Premise 1: E is a reliable authority in the domain S. Premise 2: A is a proposition contained in S. Premise 3: E asserts that A. Conclusion: Therefore, A.

An example of argument from expert opinion is : Depression and anxiety should be taken seriously. The London School of Economy reports that half of all illnesses in the under 65s is mental. In this example, the conclusions of a group of people who has expertise in the domain of health are used to support the claim that mental illnesses have to be taken seriously.

Arguments from expert opinion are marked by two linguistic cues; first, nouns which name the expert, e.g. expert, doctor, economist, politician etc.; second, constructions such as reported speech which allow indicating the expert's opinion, e.g. claim, warn, explain, indicate, etc. The strength of these report verbs (as suggested in section 3.2) must be taken into account in the scheme. When there is no explicit cue, additional knowledge may be necessary to determine whether a person is an expert. For instance, Stephen Hawking warned against risks linked to the development of AI can only be understood as being an expert opinion if one knows that Stephen Hawking has long been working on Artificial Intelligence.

The opinion of experts is used in many cases to support a claim since it is hard to contradict an expertise. As a consequence, arguments from expert opinion have a strong impact. However, the strength of the argument can be critiqued by questioning the knowledge of the experts. For instance, in the above example, one may wonder whether the London School of Economy definitely has expertise in the health domain (see also Section 4.2.8).

Argument from negative consequences

This scheme has the following form: Premise 1: If an action leads to bad consequences, all else being equal, it should not be brought about. Premise 2: If action A is brought about, bad consequences will occur. Conclusion: Therefore A should not be brought about.

Vaccinating people against Ebola has reduced their immune system. This vaccine must not be used anymore. is an argument from negative consequences.

Negative adjectives and nouns are usually found in the premise(s) (here, reduce), while action verbs used in the negative form are used in the conclusion (here, must not be used). However, these cues are extremely domain dependent. Warning against negative consequences can have a strong impact, but the nouns and adjectives used can help determining how strong the argument is.

Arguments from examples

This scheme has the following form: Premise 1: Example 1 is an example that supports claim P. Premise 2: Example n is an example that supports claim P. Conclusion: Claim P is true.

For example: It has been shown that the vaccine is not the right solution. For example, two weeks after the injection, an old man died and the foetus of a pregnant woman shown malformations.

Linguistic cues typical of the illustration discourse relation such as for example, for instance, in the same manner can contribute to detect the arguments from example. However, these cues are not always linguistically realized, for instance, the same argument could be presented as follows: Two weeks after the injection, an old man died and the foetus of a pregnant woman presented malformations. The vaccine is not the right solution.

Evaluating how this form of strength interacts with the others, presented above, requires some experimentation. It is not clear, for example, if they all operate at the same level, or if some have a higher weight.

The strength of the argument can be measured with the number of examples used. The above argument has two premises (two examples) supporting the claim. The conclusion could be supported by many other examples of people who badly reacted to the vaccine, which would reinforce the claim that the vaccine is not the right solution.

Arguments from position to know

This scheme has the following form: Premise 1: Source a is in a position to know about things in a certain subject domain S containing proposition A. Premise 2: a asserts that A (in Domain S) is true (false). Conclusion: A is true (false).

For instance: A British politic visiting Western Africa has revealed that the number of deaths due to Ebola has dropped since the vaccination began. Vaccinating populations must therefore continue. In this example, the claim that vaccinating against Ebola must continue is supported by the opinion of a British political person. This type of argument is close to arguments from expert opinion. However, arguments from position to know are weaker that arguments from expert opinion because it is easier to question whether the person who is being quoted has the right information.Similarly to arguments from expert opinion, reported speech can help detecting arguments from position to know.

Argument from popular opinion

Arguments from popular opinion take the following form: Premise 1: Everybody is doing X. Premise 2: X is a good thing to do. Conclusions: Therefore, X must be the right thing to do.

As an example: vaccination in general is a cheap and efficient way to get rid of major diseases, therefore all populations exposed to Ebola must systematically undergo vaccination.

Linguistic cues referring to populations and group of people can help detect arguments from popular opinion, e.g. the population, people, individuals, everyone, all the persons, etc. The use of numbers or percentages can also mark the strength of the argument. Similarly to arguments from position to know, arguments from popular opinion have less strength than the ones from expert opinion since the action (or opinions) of groups of people can be discussed.

Arguments from cause to effect

This scheme has the following form: Premise 1: Doing X will cause Y to occur or If X occurs then Y will occur, Premise 2: X is done or X occurs, Conclusion: Y will occur.

The statement: A new vaccine has been developed which will lower the number of deaths. The first vaccinations have begun last week. Less farmers in the vaccinated area will die after its injection. is an example of argument from cause to effect. This type of argument can be seen as an anticipation: future effects are foreseen; as a consequence, linguistic cues to detect such arguments are uses of future tenses or conditional. Anticipation has however little credibility in many cases, as a consequence, arguments from cause to effect are weak arguments.

Organizing schemes w.r.t. their strength

From the observations above, a tentative classification of argument strength induced by argument schemes can be made. In our case, no domain knowledge is considered, which could affect this classification: Strong: analogy, expert opinion Moderate: negative consequences, from examples Weak: position to know, popular opinion, cause to effect.

In Walton, each scheme is associated with a number of critical questions which allow testing the soundness of the argument; these can be used to attack the argument.For instance, the argument from analogy has the following critical questions: CQ1: Are there respects in which C1 and C2 are different that would tend to undermine the force of the similarity cited? CQ2: Is A the right conclusion to be drawn in C1? CQ3: Is there some other case C3 that is also similar to C1, but in which some conclusion other than A should be drawn?

Here are the critical questions for arguments from position to know: CQ1: Is a in a position to know whether A is true (false)? CQ2: Is a an honest (trustworthy, reliable) source? CQ3: Did a assert that A is true (false)?

The critical questions for arguments from expert opinion are: C1: Is E a genuine authority? C2: Did E really assert A? C3: Is E an authority in the right field?

Evaluating the overall strength of critical questions per scheme can be used to determine the strength of the scheme w.r.t. an argument. An argument which has stronger critical questions could be a weak argument (it can be easily attacked), or, on the contrary, it can be a strong one (it is difficult to defeat it).

Finally, the problem of fallacious arguments can interfere with the strength evaluation. For example, analogy is sometimes classified as fallacious. As [START_REF] Walton | Argumentation Schemes[END_REF], p 49) note: 'the problems seems to be that argument from analogy is a plausible form of argument only when it is used for guessing; it is not good enough to be used to prove a claim.' Evaluating fallacious arguments is a major concern in argumentation, however, in practical situations like ours, this means considering domain and general purpose knowledge and inferences.

CONCLUSION

In this contribution, we have surveyed a number of linguistic factors which contribute to the expression of argument strength. We proposed a categorization and a model to structure lexical items which may convey strength. We have outlined the elements which are proper to argument strength analysis and those which may be shared with opinion analysis. We have outlined, via a short experiment their sensitivity to context, taken in its broader sense: including the utterer, the listeners or readers, the domain and context of the arguments. In a second part, we have explored the impact of discourse structures and argument schemes on the expression of strength.

These different features show that it is difficult to evaluate a priori the strength of a a proposition that supports or attacks an argument. The weight of the different components of strength need a careful experimental analysis, and their interactions with context require the development of a model that includes language aspects as well as knowledge and specific forms of reasoning.

  It is frequent to have propositions Pi that include terms from the two levels presented in section 3.1: a first level of strength is expressed within the proposition and then the proposition is embedded into a variety of constructions from the second set of categories. For example, given the claim: Nuclear plants are useful since they pollute less than coal or oil.

	usually, of course]
	-[often, frequently, generally speaking] -
	[definitely, surely, obviously, necessarily]
	-[most definitely]].
	3.3 Strength representation when combining
	categories: a basic model

a proposition such as: I am definitely convinced that nuclear plants should be banished. includes the strong negative term banished in its statement, which is somewhat soften by the modal should. This proposition is included into an epistemic construction with a strong connotation: a strong verb convinced modified by the intensifier adverbial definitely. Evaluating the strength of such a proposition compared to e.g.: I am convinced that nuclear plants must be banished.

CNRS-IRIT email: mathildejanier@hotmail.com, stdizier@irit.fr