Paraconsistency in classical logic

Gabriele Pulcini, Achille C. Varzi

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Classical propositional logic can be characterized, indirectly, by means of a complementary formal system whose theorems are exactly those formulas that are not classical tautologies, i.e., contradictions and truth-functional contingencies. Since a formula is contingent if and only if its negation is also contingent, the system in question is paraconsistent. Hence classical propositional logic itself admits of a paraconsistent characterization, albeit “in the negative”. More generally, any decidable logic with a syntactically incomplete proof theory allows for a paraconsistent characterization of its set of theorems. This, we note, has important bearing on the very nature of paraconsistency as standardly characterized.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalSynthese
DOIs
Publication statusAccepted/In press - 16 Jun 2017

Keywords

  • Classical logic
  • Complementary system
  • Consequence relation
  • Decidability
  • Paraconsistency
  • Unprovability

Fingerprint Dive into the research topics of 'Paraconsistency in classical logic'. Together they form a unique fingerprint.

Cite this