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A complete logic forn-permutable congruence lattices

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Abstract

A family of logical systems, which may be regarded as extending equational logic, is studied. The equationsf=g of equational logic are generalized to congruence equivalence formulasf≡g (modx), wheref andg are terms interpreted as elements of an algebraV of some specified type. and termx is interpreted as a member of ann-permutable lattice of congruences forV. Formal concepts of proof and derivability from systems of hypotheses are developed. These proofs, like those of equational logic. require only finite algebraic processes, without manipulation of logical quantifiers or connectives. The logical systems are shown to be correct and complete: a well-formed statement is derivable from a system of hypotheses if and only if it is valid in all models of these hypotheses.

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Authors and Affiliations

  1. National Institutes of Health, Bethesda, Maryland, USA

    George Hutchinson

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  1. George Hutchinson
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Hutchinson, G. A complete logic forn-permutable congruence lattices. Algebra Universalis 13, 206–224 (1981). https://doi.org/10.1007/BF02483835

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  • DOI: https://doi.org/10.1007/BF02483835

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