Perhaps the most counterintuitive property of classical logic (as well as of its most famous rival, intuitionistic logic) is the fact that it allows the inference of any proposition from a single pair of contradicting statements. A lot of work and efforts have been devoted over the years to develop alternatives to classical logic that do not have this drawback. Those alternatives are nowadays called `paraconsistent systems', and the corresponding research area --- paraconsistent reasoning.
The purpose of this book is to provide a comprehensive methodological presentation of the rich mathematical theory that exists by now concerning the most
fundamental part of paraconsistent reasoning: propositional (monotonic) logics. Among those logics it mainly concentrates on those which are effective
(in the sense that they are decidable, have a concrete semantics, and can be equipped with implementable analytic proof systems).
The first part of the book defines in precise terms all the basic notions
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