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Epistemic logic and logical omniscience: A survey. (English) Zbl 0890.03006

Reasoning about knowledge and belief has been investigated from the points of view of philosophy, game theory, distributed systems, and artificial intelligence. A formal framework for an investigation of reasoning about knowledge and belief is provided by epistemic logic.
In artificial intelligence, research on reasoning about knowledge and belief focuses on designing intelligent agents that can reason about the current state of the world, beliefs of other agent’s beliefs and its own beliefs. The paper provides a survey of epistemic logics, mainly those relevant from the artificial intelligence point of view.
First, classical epistemic logic, its possible-worlds semantics and the classic axiom systems for knowledge and belief are introduced. The logical omniscience problem – the main drawback of the classical approach – is characterized. Logical omniscience requires an agent to know all logic consequences of its beliefs and all valid sentences. The property is too strong from several points of view.
The core part of the paper is devoted to epistemic logics in artificial intelligence and it is focused on the known approaches used to mitigate the logical omniscience phenomenon.
The discussed approaches are: Levesque’s logic of implicit and explicit belief, Lakemeyer’s logic of nested implicit and explicit belief, logic of awareness of Fagin and Halpern, Cadoli-Shaerf’s epistemic model, nonstandard epistemic logic of Fagin, Halpern and Vardi, Vardi’s epistemic structures, logic of local reasoning of Fagin and Halpern, Vardi’s fusion epistemic models, Delgrande’s logic of explicit propositions.
Levesque’s approach is one of the first attempts to solve the logical omniscience problem. The approaches discussed in the paper are based on Levesque’s model and their goal is to improve some aspects of it.

MSC:

03B45 Modal logic (including the logic of norms)
68T27 Logic in artificial intelligence
03B60 Other nonclassical logic
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