## Mathematical Problems from Applied Logic I: Logics for the XXIst CenturyDov M. Gabbay, Sergey Goncharov, Michael Zakharyaschev Mathematical Problems from Applied Logic I presents chapters from selected, world renowned, logicians. Important topics of logic are discussed from the point of view of their further development in light of requirements arising from their successful application in areas such as Computer Science and AI language. An overview of the current state as well as open problems and perspectives are clarified in such fields as non-standard inferences in description logics, logic of provability, logical dynamics, and computability theory. The book contains interesting contributions concerning the role of logic today, including some unexpected aspects of contemporary logic and the application of logic. |

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### Contents

Franz Baader and Ralf Küsters | 1 |

Lev Beklemishev and Albert Visser | 77 |

Johan van Benthem | 137 |

Dynamic Epistemic Logic | 157 |

Background in Standard Logics | 164 |

From Information Update to Belief Revision | 170 |

Temporal Epistemic logic | 178 |

Game Logics and Game Theory | 184 |

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### Common terms and phrases

agents algorithmic content Amsterdam applied logic Arabic areas arithmetical theory Artificial Intelligence axiomatic axioms Baader basic belief revision Benthem bisimulation bounded arithmetic calculus cognitive common knowledge complexity computer science concept description concept names corresponding Curry–Howard defined definition description logics description trees developed dynamic logic emergence epistemic logic equivalence example existence existential restrictions finite formal formulas fragments given Gödel graded provability algebra graphs homomorphism ILLC interaction interesting interpretability logic intuition intuitionist logic Jurj¯an¯ı lambda calculus language least common subsumer linguistics matching problem Math mathematical logic minimal rewriting modal logic model theory modulo natural numbers nonstandard inferences normal form notion order logic polynomial principle product update proof theory propositional logic provability logic question reasoning recursive reduction relations rules Section semantics sentences specific structure Symbolic Logic syntax TBox theorem tion Turing universe variables Visser