Extending resource-aware logics

Kamide, NorihiroNorihiro Kamide received his Ph.D. in Information Science from Japan Advanced Institute of Science and Technology in 2000. His research interests include mathematical logic, philosophical logic, and logics in computer science and in artificial intelligence.

This book introduces some extensions of resource- aware logics, and shows some fundamental (e.g., cut- elimination and completeness) theorems for these extensions. By resource-aware logics, we mean substructural logics without the structural rule of contraction in Gentzen-type sequent calculi. Typical examples of these resource-aware logics are linear logics, which are known to be useful for describing concurrent systems, and non-commutative logics, which are known to be useful for formalizing grammatical reasoning. These logics are known to be appropriate for representing resource-sensitive reasoning. In this book, we study (1) some temporal extensions (i.e., extensions by adding some temporal operators) of linear and non-commutative logics, (2) some generalizations of these temporal linear and non-commutative logics, (3) some paraconsistent and involutive extensions (i.e., extensions by adding a paraconsistent negation connective or an involution operator) of linear and non-commutative logics.