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)

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)

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is important that the (...) participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models. (shrink)

Epistemic logic begins with the recognition that our everyday talk about knowing and believing has some systematic features that we can track and re‡ect upon. Epistemic logicians have studied and extended these glints of systematic structure in fascinating and important ways since the early 1960s. However, for one reason or another, mainstream epistemologists have shown little interest. It is striking to contrast the marginal role of epistemic logic in contemporary epistemology with the centrality of modal logic for metaphysicians. This article (...) is intended to help in correcting this oversight by presenting some important developments in epistemic logic and suggesting ways to understand their applicability to traditional epistemological problems. Obviously, by itself, tweaking the formal apparatus of epistemic logic does not solve traditional epistemological problems. Epistemic logic can help us to navigate through problems in a systematic fashion by unpacking the logic of the problematic concepts, it can also lead us to recognize problems that we had not anticipated. This is basically analogous to the role that modal logic has played in contemporary metaphysics. (shrink)

Dynamic epistemic logic describes the possible information-changing actions available to individual agents, and their knowledge pre-and post conditions. For example, public announcement logic describes actions in the form of public, truthful announcements. However, little research so far has considered describing and analysing rational choice between such actions, i.e., predicting what rational self-interested agents actually will or should do. Since the outcome of information exchange ultimately depends on the actions chosen by all the agents in the system, and assuming that agents (...) have preferences over such outcomes, this is a game theoretic scenario. This is, in our opinion, an interesting general research direction, combining logic and game theory in the study of rational information exchange. In this article we take some first steps in this direction: we consider the case where available actions are public announcements, and where each agent has a (typically epistemic) goal formula that she would like to become true. What will each agent announce? The truth of the goal formula also depends on the announcements made by other agents. We analyse such public announcement games. (shrink)

We formalize what it means to have permission to say something. We adapt the dynamic logic of permission by van der Meyden (J Log Comput 6(3):465–479, 1996 ) to the case where atomic actions are public truthful announcements. We also add a notion of obligation. Our logic is an extension of the logic of public announcements introduced by Plaza ( 1989 ) with dynamic modal operators for permission and for obligation. We axiomatize the logic and show that it is decidable.

Truth of x (independently of any description of x) that it is f. A property f which holds of x but is not per se of x is said to hold per accidens of x. The essence of an individual is the sum of its per se properties. We can formulate the following: doctrine a: concrete individuals do not have essences though abstract entities do. Doctrine b: concrete individuals have essences but they do not individuate, whereas abstract entities have essences (...) which do individuate. Assumption i: we shall say that a thing exists insofar as it has an essence. Assumption ii: we shall say that we know a thing when we know what its per se properties are. We argue that plato held doctrine a and aristotle doctrine b (with assumptions i and ii). (edited). (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)

The author moves from the consideration of law as a set of rules serving as a means of socially regulating human conduct. He focuses on the fact that in order to fulfil its function, the law must be seen as a type of information. In this perspective law is a particular language and therefore gives rise to linguistic problems, linked to the technical character of juristic discourse. The author deals with some of the linguistic and sociological aspects of legal language (...) and attempts to pinpoint some trends of interlingual development. (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)

De re modality is eliminable if there is an effective translation of all wffs into non-de re equivalents. We cannot have logical equivalence unless 'logic' has odd theses, but we can have material equivalence by banning all essences, something the nonde re facts let us do, or by giving everything such humdrum essences as self-identity and banning the more interesting ones. Eliminability cannot be got from weaker assumptions, nor independent ones of even modest generality. The net philosophical import is that, (...) quite apart from the merits of essentialism, de re language has scant utility. (shrink)

Strictly speaking, intuitionistic logic is not a modal logic. There are, after all, no modal operators in the language. It is a subsystem of classical logic, not [like modal logic] an extension of it. But... (thus Fitting, p. 437, trying to justify inclusion of a large chapter on intuitionist logic in a book that is largely about modal logics).