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