| 1. |
- Egré, Paul, et al.
(author)
-
Characterizing logical consequence in many-valued logic
- 2017
-
In: Journal Of Logic And Computation. - : Oxford University Press (OUP). - 0955-792X .- 1465-363X. ; 27:7, s. 2193-2226
-
Journal article (peer-reviewed)abstract
- Several definitions of logical consequence have been proposed in many-valued logic, which coincide in the two-valued case, but come apart as soon as three truth values come into play. Those definitions include so-called pure consequence, order-theoretic consequence and mixed consequence. In this article, we examine whether those definitions together carve out a natural class of consequence relations. We respond positively by identifying a small set of properties that we see instantiated in those various consequence relations, namely truth-relationality, value-monotonicity, validity-coherence and a constraint of bivalence-compliance, provably replaceable by a structural requisite of nontriviality. Our main result is that the class of consequence relations satisfying those properties coincides exactly with the class of mixed consequence relations and their intersections, including pure consequence relations and order-theoretic consequence. We provide an enumeration of the set of those relations in finite many-valued logics of two extreme kinds: those in which truth values are well-ordered and those in which values between 0 and 1 are incomparable.
|
|
| 2. |
- Égré, Paul
(author)
-
Qu'est-ce que le vague?
- 2019
-
Book (other academic/artistic)abstract
- La plupart des termes du langage ordinaire sont vagues, au sens où les règles de leur usage ne permettent pas de leur assigner une limite d’application claire et déterminée. À partir de quelle taille peut-on dire d’un individu qu’il est grand? Quelle quantité d’une grandeur suffit à dire « beaucoup »? Il ne semble pas exister de réponse bien définie à ces questions. La frontière semble inévitablement floue et variable selon le contexte et le locuteur. Le vague a été mis en évidence dès l’Antiquité avec le paradoxe du tas de blé, ou sorite, qui demande combien de grains de blé sont requis pour faire un tas. Loin d’être un simple cas d’école, le vague est un problème courant qui affecte la signification des catégories juridiques (à quel moment un fœtus devient-il une personne?) mais aussi scientifiques (quelles propriétés font d’un corps céleste une planète?).L’objet de ce livre est d’expliquer la nature et l’origine du vague dans le langage. Il vise notamment à élucider la question de savoir si le vague est une forme d’ignorance de faits déterminés, ou s’il s’agit d’un phénomène distinct, inhérent à la constitution du sens linguistique.
|
|
| 3. |
- Egré, Paul, et al.
(author)
-
The Logic of Conditionals
- 2021
-
In: Stanford Encyclopedia of Philosophy. - : Stanford University.
-
Book chapter (peer-reviewed)abstract
- This article provides a survey of classic and recent work in conditional logic. We review the problems of a two-valued analysis and examine logics based on richer semantic frameworks that have been proposed to deal with conditional sentences of the form “if A, B,” including trivalent semantics, possible-world semantics, premise semantics, and probabilistic semantics. We go on to examine theories of conditionals involving belief revision, and highlight recent approaches based on the idea that a conditional is assertable provided the truth of its antecedent makes a relevant difference to that of its consequent. We close with a brief discussion of systems accounting for the interaction of conditionals with modalities and speech act operators.
|
|
