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Mathematical logic and foundations


Theory of Effective Propositional Paraconsistent Logics

Arnon Avron, Ofer Arieli and Anna Zamansky

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 that are related to paraconsistency, after reviewing
all the necessary preliminaries. The other parts describe in detail
all of the main approaches to the subject. This includes
finite-valued semantics (both truth functional and non-deterministic);
logics of formal inconsistency; relevant logics; constructive
paraconsistent logics which are based on positive intuitionistic
logic; and paraconsistent logics which are based on modal logics.
The book covers thousands of paraconsistent logics, each of
which is studied both from a semantical and from a proof
theoretical points of view. In addition,
most of those logics are characterized in terms of minimality or maximality
properties that they may have.

23 May 2018


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