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An Introduction to Paraconsistent Logics

Manuel Bremer

This book gives an overview of paraconsistent logics – that is logics which allow for inconsistency. Although allowing for inconsistency, paraconsistent logics are worth considering: Logical systems are worth considering in their own right since we can learn about very abstract structural properties of logics and the concepts employed within them such as negation, necessity and consistency. Some non-classical logics are especially of interest from a philosophical perspective since they alone offer the possibility of solving or even stating some philosophical problems. These introductory lectures argue from a philosophical perspective that some paraconsistent logics are of interest or even the best candidates for dealing with specific philosophical problems. Although logic is seen from the point of view of its philosophical use, various formal systems are described, compared and employed.
Contents: Semantic Closure – The Logic of Paradox – Relevant Logics – Adaptive Logics – LFI-Systems – Paraconsistent Set Theory – Inconsistent Mathematics and Meta-Logic – Inconsistent Ontology – Universal Logic.