This book constitutes a self-contained and unified approach to automated reasoning in multiple-valued logics (MVL) developed by the author. Moreover, it contains a virtually complete account of other approaches to automated reasoning in MVL. This is the first overview of this subfield of automatbd reasoning ever given. Finally, a variety of applications of automated reasoning in MVL including several short case studies are listed. Automated reasoning in non-classical logics is an essential subtask of many AI applications. Applications of MVL in particular include, for instance, hardware and software verification, reasoning with incomplete or inconsistent knowledge, and natural language processing. Therefore, efficient theorem proving methods in MVL are essential. In the historical part of the book it is demonstrated why existing approaches are inadequate. In the original part a simple, but powerful, concept called 'sets-as-sigps' is introduced in the context of semantic tableaux, and subsequently is applied to a variety of calculi including resolution and dissolution.
It is shown that 'sets-as-signs' naturally lead to a broad class of MVL with quasiclassical computational properties called 'regular 10gics'. Generalizing 'sets-as-signs' yields a manyvalued extension of the well-known relationship between classical logic and integer programming. As a consequence, automated reasoning in infinitely-valued logics can be done uniformly and efficiently for the first time.
3: The logical basis: Signed analytical tableaux
4: A new technique: Truth value sets as signs
5: Uniform notation regained: Regular logics
6: Beyond tableaux
8: A history of multiple-valued theorem proving