Discriminator logics (Research announcement)

Matthew Spinks, Robert Bignall, Robert Veroff

Abstract


A discriminator logic is the 1-assertional logic of a discriminator variety V having two constant terms 0 and 1 such that 0 \approx1 iff every member of V is trivial. Examples of such logics abound in the literature. The main result of this research announcement asserts that a certain non-Fregean deductive system SBPC, which closely resembles the classical propositional calculus, is canonical for the class of discriminator logics in the sense that any discriminator logic S can be presented (up to definitional equivalence) as an axiomatic extension of SBPC by a set of extensional logical connectives taken from the language of S. The results outlined in this research announcement are extended to several generalisations of the class of discriminator logics in the main work. 


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