## Epistemic Logic for AI and Computer ScienceEpistemic 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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### Contents

II | 1 |

III | 7 |

IV | 8 |

V | 13 |

VI | 23 |

VII | 25 |

VIII | 28 |

IX | 35 |

XXXVII | 104 |

XXXVIII | 109 |

XXXIX | 113 |

XL | 114 |

XLI | 126 |

XLII | 129 |

XLIII | 139 |

XLIV | 141 |

X | 38 |

XI | 39 |

XII | 45 |

XIV | 47 |

XV | 51 |

XVI | 56 |

XVII | 59 |

XVIII | 64 |

XIX | 65 |

XX | 68 |

XXI | 71 |

XXII | 73 |

XXIII | 74 |

XXIV | 77 |

XXV | 79 |

XXVI | 83 |

XXVII | 84 |

XXVIII | 87 |

XXIX | 89 |

XXX | 90 |

XXXI | 91 |

XXXII | 92 |

XXXIII | 93 |

XXXIV | 94 |

XXXV | 96 |

XXXVI | 103 |

### Other editions - View all

Epistemic Logic for AI and Computer Science John-Jules Ch Meyer,Wiebe van der Hoek No preview available - 1995 |

### Common terms and phrases

accessibility relations AE-extension agent apply approach arbitrary assertion assume assumption atoms autoepistemic logic axiom Bj<p canonical model cluster consider COROLLARY counterfactual default logic default reasoning default theory define definition denoted derive dynamic logic epistemic formulas epistemic logic equivalence relation example finite fk(i formula 9 frame Furthermore Halpern & Moses hence holds honest ig_ass implies Kj<p knowledge structure Kripke model Kripke structure Lemma load logical omniscience maximal consistent set modal logic modal operators Moreover non-monotonic non-monotonic logic normal Note notion objective formula obtain possible primitive propositions problem PROOF properties propositional logic propositionally prove reflexive Reiter's Rjst S5-model satisfiable Section semantics set of formulas situation stable set Suppose Theorem truth assignment truth definition valid X A KP