Paraconsistent Logic (Substantive Revision)

1. Paraconsistency A logic is paraconsistent iff its logical consequence relation \((\vDash\), either semantic or proof theoretic) is not explosive. Paraconsistency is a property of a consequence relation. The argument ex contradictione quodlibet (ECQ) is paraconsistently invalid: in general, it is not the case that \(A\), \(\neg A \vDash B\). The role often played by the notion of consistency in logics, namely, the most basic requirement that any theory must meet, is relaxed to the notion of coherence: no theory can include every sentence whatsoever if it is to be considered tenable. Simple consistency of a theory (no contradictions) is a special case of absolute consistency, or non-triviality (not every sentence is a part of the theory).

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