Denis Bonnay

Hintikka makes a distinction between two kinds of games: truthconstituting games and truth-seeking games. His well-known game-theoretical semantics for first-order classical logic and its independence-friendly extension belongs to the first class of games. In order to ground Hintikka’s claim that truth-constituting games are genuine verification and falsification games that make explicit the language games underlying the use of logical constants, it would be desirable to establish a substantial link between these two kinds of games. Adapting a result from Thierry Coquand, we propose such a link, based on a slight modification of Hintikka’s games, in which we allow backward playing for ∃loïse. In this new setting, it can be proven that sequent rules for first-order logic, including the cut rule, are admissible, in the sense that for each rule, there exists an algorithm which turns winning strategies for the premisses into a winning strategy for the conclusion. Thus, proofs, as results of truth-seeking games, can be seen

Hintikka and Sandu have developed IF logic as a genuine alternative to classical first-order logic : liberalizing dependence schemas between quantifiers, IF would carry out all the ideas already underlying classical logic. But they are alternatives to Hintikka’s game-theoretic approach; one could use instead Henkin quantifiers. We will present here some arguments of both technical and philosophical nature in favor of IF. We will show that its notion of independence, once extended to connectives, can indeed claim to be fully general, and that IF logic provides an analysis of independence patterns. This last point will be argued for thanks to an explanation of the epistemic content of IF, through a partial translation into modal logic.

La logique est un compagnon naturel de la philosophie. Qu'est-ce qu'un raisonnement correct? Qu'est-ce qu'une preuve? Peut-on definir le concept de verite? Que faire face aux paradoxes? Ces questions sont debattues par les philosophes depuis l'Antiquite; et la logique moderne, usant de langages formels, developpe une analyse rigoureuse de ces concepts les plus fondamentaux. Les onze textes classiques reunis ici proposent un retour reflexif sur cette discipline et sur la signification philosophique de ses achevements. Ils s'adressent a quiconque souhaite prendre la mesure des enjeux conceptuels de la logique, et a tous les etudiants desireux de completer leur apprentissage de la discipline par une reflexion epistemologique sur ses fondements.

Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality.

In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system we call Centered semantics. We then propose a semantics of degrees of clarity, inspired from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the unclarity of unclarity.