C. I. Lewis intended his systems S1–S5 as contributions to the study of “strict implication”, but in his formulation, strict implication is so thoroughly intertwined with other notions, such as possibility and negation, that it remains a problem, to separate out the properties of strict implication itself. I shall solve this problem for S2–5 and von Wright's M. The results for S3–5 are given below, while the implicative parts of S2 and M, which are rather more complicated, are given in (...) §5.In this presentation, ‘⊃’ stands for strict implication, and missing brackets for ‘⊃’ are restored by associationtothe right. Astrictformula is one of the form A ⊃ B. Axiom schemes are used throughout. (shrink)

We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...) robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanRed Barns in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. (shrink)

The traditional possible-worlds model of belief describes agents as ‘logically omniscient’ in the sense that they believe all logical consequences of what they believe, including all logical truths. This is widely considered a problem if we want to reason about the epistemic lives of non-ideal agents who—much like ordinary human beings—are logically competent, but not logically omniscient. A popular strategy for avoiding logical omniscience centers around the use of impossible worlds: worlds that, in one way or another, violate the laws (...) of logic. In this paper, we argue that existing impossible-worlds models of belief fail to describe agents who are both logically non-omniscient and logically competent. To model such agents, we argue, we need to ‘dynamize’ the impossible-worlds framework in a way that allows us to capture not only what agents believe, but also what they are able to infer from what they believe. In light of this diagnosis, we go on to develop the formal details of a dynamic impossible-worlds framework, and show that it successfully models agents who are both logically non-omniscient and logically competent. (shrink)

En cet article nous montrons en premier lieu que la théorie de l'hexagone logique de Blanché n'est pas, comme il le pense, le résultat d'une réflexion philosophique, mais qu'elle relève véritablement de la logique scientifique, puisqu'elle s'insère tout naturellement dans la structure d'ensemble des liaisons uninaires de la logique trivalente des propositions. Cette démonstration nous conduit, en second lieu, à renverser le jugement défavorable que E. J. Lemmon avait porté sur la toute première ébauche de cette théorie, et ainsi à (...) déVelopper la logique modale dans le sens de Blanché plutôt que dans celui de von Wright. En troisième lieu, nous complétons l'application que fait Blanché de cette théorie de l'hexagone aux liaisons binaires de la logique bivalente des propositions, en intégrant en une seule structure tétrahexaédrique l'ensemble des seize liaisons binaires, lui-même s'étant contenté d'en grouper seulement dix en une espèce d'anneau bihexagonal. (shrink)

As anyone who is familiar with the literature knows, there is a great deal of controversy concerning which, if any, of the extant theories of propositional modal logic correctly formalizes the logic of certain logical concepts such as analyticity and logical necessity. Most of the controversy concerns certain principles that involve iterated modalities (where one modal operator occurs within the scope of another). For example, there is considerable disagreement about whether the principle(□p⊃□□p)should be considered valid. However, when philosophers and logiciansapplymodal (...) logic to concrete problems, they rarely need principles which involve iterated modalities. For most practical purposes, principles involving only one layer of modalities are all that are needed. This suggests that if we try to construct a theory of modal logic in which there are no iterated modalities, we can avoid most of the controversy and still have a theory that is strong enough for all of the normal uses to which modal logic is put. (shrink)