Epistemic Logic for AI and Computer Science
Epistemic logic has grown from its philosophical beginnings to find diverse applications in computer science as a means of reasoning about the knowledge and belief of agents. This book, based on courses taught at universities and summer schools, provides a broad introduction to the subject; many exercises are included together with their solutions. The authors begin by presenting the necessary apparatus from mathematics and logic, including Kripke semantics and the well-known modal logics K, T, S4 and S5. Then they turn to applications in the contexts of distributed systems and artificial intelligence: topics that are addressed include the notions of common knowledge, distributed knowledge, explicit and implicit belief, the interplays between knowledge and time, and knowledge and action, as well as a graded (or numerical) variant of the epistemic operators. The problem of logical omniscience is also discussed extensively. Halpern and Moses' theory of honest formulae is covered, and a digression is made into the realm of non-monotonic reasoning and preferential entailment. Moore's autoepistemic logic is discussed, together with Levesque's related logic of 'all I know'. Furthermore, it is shown how one can base default and counterfactual reasoning on epistemic logic.
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accessibility action AE-extension agent alive already apply approach arbitrary assertion assume assumption axiom belief called Check closed cluster common complete conclude condition consequence consider consistent contains COROLLARY counterfactual default define definition denoted derive epistemic epistemic formulas epistemic logic equivalent example Exercise express extension fact finite fire formula frame Furthermore give given Halpern hence holds honest immediately implies induction instance interpretation knowledge known Kripke model language Lemma loaded logic maximal means modal Moreover non-monotonic normal Note notion observe obtain operator particular possible preferred problem PROOF properties propositional prove reasoning reflexive relation represent respect result rule satisfiable semantics simple situation sound stable set structure Suppose Theorem theory transitive true truth valid
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