Reactive Kripke Semantics [electronic resource] / by Dov M. Gabbay.

Chap.1 - A Theory of Hypermodal Logics -- Chap.2 - Introducing Reactive Kripke Semantics and Arc Accessibility -- Chap.3 - Introducing Reactive Modal Tableaux -- Chap.4 - Reactive Intuitionistic Tableaux -- Chap.5 - Completeness Theorems for Reactive Modal Logics -- Chap.6 - Modal Logics of Reactive Frames -- Chap.7 - Global View on Reactivity: Switch Graphs and their Logics -- Chap.8 - Reactive Automata -- Chap.9 - Reactivity and Grammars: An Exploration -- Chap.10 - Reactive Flow Products -- Chap.11 - Reactive Standard Deontic Logic -- Chap.12 - Reactive Preferential Structures and Nonmonotonic Consequence -- References -- Index.

This text offers an extension to the traditional Kripke semantics for non-classical logics by adding the notion of reactivity. Reactive Kripke models change their accessibility relation as we progress in the evaluation process of formulas in the model. This feature makes the reactive Kripke semantics strictly stronger and more applicable than the traditional one. Here we investigate the properties and axiomatisations of this new and most effective semantics, and we offera wide landscape of applications of the idea of reactivity. Applied topics includereactive automata, reactive grammars, reactive products, reactive deontic logic and reactive preferential structures. Reactive Kripke semantics is the next step in the evolution of possible world semantics for non-classical logics, and this book, written by one of the leading authorities in the field, is essential reading for graduate students and researchers in applied logic, and it offers many research opportunities for PhD students.