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.


Exploiting Belief Bases for Building Rich Epistemic Structures

arXiv.org Artificial Intelligence

We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the proposed semantics they are non-primitive but are defined from the concept of belief base. We show that this semantics allows us to define the universal epistemic model in a simpler and more compact way than existing inductive constructions of it. We provide (i) a number of semantic equivalence results for both the basic epistemic language with "individual belief" operators and its extension by the notion of "only believing", and (ii) a lower bound complexity result for epistemic logic model checking relative to the universal epistemic model.


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.