publication . Article . Other literature type . 1989

Truth table logic, with a survey of embeddability results.

Tennant, Neil;
Open Access
  • Published: 01 Jun 1989 Journal: Notre Dame Journal of Formal Logic, volume 30, pages 459-484 (issn: 0029-4527, Copyright policy)
  • Publisher: Duke University Press
What logic is barely justified on the basis of the «meanings» given to the connectives by the left-right readings of their truth tables? We set out a system T, consisting of normal proofs constructed by means of elegantly symmetrical introduction and elimination rules. In the system T there are two requirements, called (□) and (>), on applications of discharge rules. T is sound and complete for Kalmaric arguments. We then consider a «Duhemian» extension T*, obtained simply by dropping the requirement (>). T* is a proper subsystem of intuitionistic relevant logic. Our main result is that T* is a double negation consistency companion to classical logic
free text keywords: Logic, Paraconsistent logic, Many-valued logic, Predicate functor logic, Intuitionistic logic, Truth value, Double negation, Discrete mathematics, Intermediate logic, Logical connective, Mathematics, Algorithm, Algebra, 03B20, 03F05
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