Reactive Kripke Semantics (Cognitive Technologies)

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 offer a wide landscape of applications of the idea of reactivity. Applied topics include reactive 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. Front Matter....Pages I-XII A Theory of Hypermodal Logics:Mode Shifting in Modal Logic....Pages 1-28 Introducing Reactive Kripke Semantics and Arc Accessibility....Pages 29-76 Introducing Reactive Modal Tableaux....Pages 77-99 Reactive Intuitionistic Tableaux....Pages 101-117 Completeness Theorems for Reactive Modal Logics....Pages 119-167 Modal Logics of Reactive Frames....Pages 169-202 Global View on Reactivity: Switch Graphs and their Logics....Pages 203-236 Reactive Automata....Pages 237-256 Reactivity and Grammars: An Exploration....Pages 257-308 Reactive Flow Products....Pages 309-343 Reactive Standard Deontic Logic....Pages 345-387 Reactive Preferential Structures and Non-monotonic Consequence....Pages 389-430 Back Matter....Pages 431-442