We present a complete, decidable logic for reasoning about a notion of completely trustworthy evidence and its relations to justifiable belief and knowledge, as well as to their explicit justifications. This logic makes use of a number of evidence-related notions such as availability, admissibility, and “goodness” of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemovʼs Justification Logic designed to preempt Gettier-type counterexamples. We combine this with ideas from belief revision and awareness (...) logics to provide an account for explicitly justified knowledge based on conclusive evidence that addresses the problem of omniscience. (shrink)

We present Arrow Update Logic, a theory of epistemic access elimination that can be used to reason about multi-agent belief change. While the belief-changing of Arrow Update Logic can be transformed into equivalent belief-changing from the popular Dynamic Epistemic Logic approach, we prove that arrow updates are sometimes exponentially more succinct than action models. Further, since many examples of belief change are naturally thought of from Arrow Update Logicrelativized” common knowledge familiar from the Dynamic Epistemic Logic literature.

Barteld Kooi and Bryan Renne (2011). Generalized Arrow Update Logic. In K.R. Apt (editor). Theoretical Aspects of Rationality and Knowledge, Proceedings of the Thirteenth Conference (TARK 2011), pp. 205-211.

Is knowledge definable as justified true belief? We argue that one can legitimately answer positively or negatively, depending on whether or not one’s true belief is justified by what we call adequate reasons. To facilitate our argument we introduce a simple propositional logic of reason-based belief, and give an axiomatic characterization of the notion of adequacy for reasons. We show that this logic is sufficiently flexible to accommodate various useful features, including quantification over reasons. We use our framework to contrast (...) two notions of JTB: one internalist, the other externalist. We argue that Gettier cases essentially challenge the internalist notion but not the externalist one. Our approach commits us to a form of infallibilism about knowledge, but it also leaves us with a puzzle, namely whether knowledge involves the possession of only adequate reasons, or leaves room for some inadequate reasons. We favor the latter position, which reflects a milder and more realistic version of infallibilism. (shrink)

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known “action models” from Dynamic Epistemic Logic. Our “temporal action models” may be used to define a number of informational actions that can modify the “objective” temporal structure of a model along with the agents’ basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, (...) this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in DEL. (shrink)

Dynamic Epistemic Logic (DEL) is the study of how to reason about knowledge, belief, and communication. This paper studies the relative expressivity of certain fragments of the DEL language for public and private communication. It is shown that the language of public communication with common knowledge and the language of private communication with common knowledge are expressively incomparable for the class of all pointed Kripke models, which provides a formal proof that public and private communication are fundamentally different in the (...) presence of common knowledge. It is also shown that single-recipient private communication does not add expressive power to the language of modal logic with common knowledge for any class of transitive pointed Kripke models. The latter result provides a sense in which positive introspection—believing our own beliefs—induces a kind of self-dialog. (shrink)

This paper presents a logic combining Dynamic Epistemic Logic, a framework for reasoning about multi-agent communication, with a new multi-agent version of Justification Logic, a framework for reasoning about evidence and justification. This novel combination incorporates a new kind of multi-agent evidence elimination that cleanly meshes with the multi-agent communications from Dynamic Epistemic Logic, resulting in a system for reasoning about multi-agent communication and evidence elimination for groups of interacting rational agents.