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In Praise of Belief Bases: Doing Epistemic Logic Without Possible Worlds

AAAI Conferences

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 a decidability result for our logic.


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.


Multi-Agent Only-Knowing Revisited

arXiv.org Artificial Intelligence

Levesque introduced the notion of only-knowing to precisely capture the beliefs of a knowledge base. He also showed how only-knowing can be used to formalize non-monotonic behavior within a monotonic logic. Despite its appeal, all attempts to extend only-knowing to the many agent case have undesirable properties. A belief model by Halpern and Lakemeyer, for instance, appeals to proof-theoretic constructs in the semantics and needs to axiomatize validity as part of the logic. It is also not clear how to generalize their ideas to a first-order case. In this paper, we propose a new account of multi-agent only-knowing which, for the first time, has a natural possible-world semantics for a quantified language with equality. We then provide, for the propositional fragment, a sound and complete axiomatization that faithfully lifts Levesque's proof theory to the many agent case. We also discuss comparisons to the earlier approach by Halpern and Lakemeyer.


Subjective Knowledge and Reasoning about Agents in Multi-Agent Systems

arXiv.org Artificial Intelligence

Though a lot of work in multi-agent systems is focused on reasoning about knowledge and beliefs of artificial agents, an explicit representation and reasoning about the presence/absence of agents, especially in the scenarios where agents may be unaware of other agents joining in or going offline in a multi-agent system, leading to partial knowledge/asymmetric knowledge of the agents is mostly overlooked by the MAS community. Such scenarios lay the foundations of cases where an agent can influence other agents' mental states by (mis)informing them about the presence/absence of collaborators or adversaries. In this paper, we investigate how Kripke structure-based epistemic models can be extended to express the above notion based on an agent's subjective knowledge and we discuss the challenges that come along.


A General Multi-agent Epistemic Planner Based on Higher-order Belief Change

arXiv.org Artificial Intelligence

In recent years, multi-agent epistemic planning has received attention from both dynamic logic and planning communities. Existing implementations of multi-agent epistemic planning are based on compilation into classical planning and suffer from various limitations, such as generating only linear plans, restriction to public actions, and incapability to handle disjunctive beliefs. In this paper, we propose a general representation language for multi-agent epistemic planning where the initial KB and the goal, the preconditions and effects of actions can be arbitrary multi-agent epistemic formulas, and the solution is an action tree branching on sensing results. To support efficient reasoning in the multi-agent KD45 logic, we make use of a normal form called alternating cover disjunctive formulas (ACDFs). We propose basic revision and update algorithms for ACDFs. We also handle static propositional common knowledge, which we call constraints. Based on our reasoning, revision and update algorithms, adapting the PrAO algorithm for contingent planning from the literature, we implemented a multi-agent epistemic planner called MEPK. Our experimental results show the viability of our approach.