Rethinking Epistemic Logic with Belief Bases

arXiv.org Artificial Intelligence

We introduce a new semantics for a logic of explicit and implicit beliefs based on the concept of multi-agent belief base. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and doxastic/epistemic alternative are primitive, in our semantics they are non-primitive but are defined from the concept of belief base. We provide a complete axiomatization and prove decidability for our logic via a finite model argument. We also provide a polynomial embedding of our logic into Fagin & Halpern's logic of general awareness and establish a complexity result for our logic via the embedding.


Justified Beliefs by Justified Arguments

AAAI Conferences

The paper addresses how the information state of an agent relates to the arguments that the agent endorses. Information states are modeled in doxastic logic and arguments by recasting abstract argumentation theory in a modal logic format. The two perspectives are combined by an application of the theory of product logics, delivering sound and complete systems in which the interaction of arguments and beliefs is investigated.


An Approach to Minimal Belief Via Objective Belief

AAAI Conferences

As a doxastic counterpart to epistemic logic based on S5 we study the modal logic KSD that can be viewed as an approach to modelling a kind of objective and fair belief. We apply KSD to the problem of minimal belief and develop an alterna- tive approach to nonmonotonic modal logic using a weaker concept of expansion. This corresponds to a certain minimal kind of KSD model and yields a new type of nonmonotonic doxastic reasonin


Thinking takes time: A modal active-logic for reasoning in time

AAAI Conferences

All agents, whether human or automated, that function in the real-world are subject to the fact that time is spent as their reasoning progresses. Most commonsense reasoning formalisms do not account for the passage of time as the reasoning occurs, and hence are inadequate from the point of view of modeling an agent's ongoing process of reasoning. There are numerous problems in AIplanning and commonsense reasoning where the capacity to reason and act in time is of paramount importance. Below is a list of few sample problems in which the passage of time (as the agent reasons) is crucial: 1. Nell Dudley and the railroad tracks: Nell is tied to the railroad tracks and the agent Dudley must figure out and enact a plan to save her in time before an oncoming train approaches.


Parametric Constructive Kripke-Semantics for Standard Multi-Agent Belief and Knowledge (Knowledge As Unbiased Belief)

arXiv.org Artificial Intelligence

We propose parametric constructive Kripke-semantics for multi-agent KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions of two basic functional building blocks, namely bias (or viewpoint) and visibility, functioning also as the parameters of the doxastic and epistemic accessibility relation. The doxastic accessibility relates two possible worlds whenever the application of the composition of bias with visibility to the first world is equal to the application of visibility to the second world. The epistemic accessibility is the transitive closure of the union of our doxastic accessibility and its converse. Therefrom, accessibility relations for common and distributed belief and knowledge can be constructed in a standard way. As a result, we obtain a general definition of knowledge in terms of belief that enables us to view S5-knowledge as accurate (unbiased and thus true) KD45-belief, negation-complete belief and knowledge as exact KD45-belief and S5-knowledge, respectively, and perfect S5-knowledge as precise (exact and accurate) KD45-belief, and all this generically for arbitrary functions of bias and visibility. Our results can be seen as a semantic complement to previous foundational results by Halpern et al. about the (un)definability and (non-)reducibility of knowledge in terms of and to belief, respectively.