Paraconsistent Logic: Essays On The Inconsistent by Graham.
Paraconsistent logic refers to alternative (non-classical) systems of logic which reject the Principle of explosion, which states that once a contradiction has been asserted, any proposition can be inferred from it. Some (but not all) paraconsistent logics are also dialetheic, meaning they hold to a view known as dialetheism, the view that some contradictions are simultaneously true and false.
A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent (or “inconsistency-tolerant”) systems of logic. Inconsistency-tolerant logics have been discussed since at least 1910 (and arguably much earlier, for example.
A deductive theory is paraconsistent if its underlying logic is paraconsistent. A theory is inconsistent if there is a formula (a grammatically well-formed expression of its language) such that the formula and its negation are both theorems of the theory; otherwise, the theory is called consistent. A theory is trivial if all formulas of its language are theorems. In a trivial theory.
Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative.
Get this from a library! Paraconsistent Logic: Consistency, Contradiction and Negation. (Walter A Carnielli; Marcelo E Coniglio) -- This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics.
On preserving: essays on preservationism and paraconsistent logic Brown, Bryson, Schotch, Peter K., Jennings, Raymond Earl (eds.) Assembling the previously scattered works of the Preservationist School, this collection contains all of the most significant works on the basic theory of the preservationist approach to paraconsistent logic.
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