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单词 logics of formal inconsistency
释义
logics of formal inconsistency

Logic
  • A family of paraconsistent deductive systems that include some syntactic method of representing the consistency of a formula φ, e.g., the unary consistency connective . While logics of formal inconsistency (or LFIs) reject the principle of explosion, they share a property of gentle explosion, that is, while one may not infer an arbitrary formula ψ from a contradiction φ¬φ, one may infer ψ from a contradiction φ¬φ in conjunction with the assertion that φ is consistent.

    More formally, a logic of formal inconsistency is a deductive system L with a negation connective ¬ such that

    • L is not explosive with respect to ¬, i.e., there are formulae φ and ψ such that φ,¬φLψ

    • there is a set of formulae (p) with atomic variable p such that for all formulae φ and ψ, (φ),φ,¬φLψ

    where (φ) is the set of formulae in which p is uniformly replaced by φ.

    The family of C-systems—in which (φ)={φ}—is the most well-known collection of logics of formal inconsistency.


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