Logics for classes of Boolean monoids

Journal of Logic, Language and Information 13 (3):241-266 (2004)
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Abstract

This paper presents the algebraic and Kripke modelsoundness and completeness ofa logic over Boolean monoids. An additional axiom added to thelogic will cause the resulting monoid models to be representable as monoidsof relations. A star operator, interpreted as reflexive, transitiveclosure, is conservatively added to the logic. The star operator isa relative modal operator, i.e., one that is defined in terms ofanother modal operator. A further example, relative possibility,of this type of operator is given. A separate axiom,antilogism, added to the logic causes the Kripke models to support acollection of abstract topological uniformities which become concretewhen the Kripke models are dual to monoids of relations. The machineryfor the star operator is shownto be a recasting of Scott-Montague neighborhood models. An interpretationof the Kripke frames and properties thereof is presented in terms ofcertain CMOS transister networks and some circuit transformation equivalences.The worlds of the Kripke frame are wires and the Kripke relation is a specializedCMOS pass transistor network

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Citations of this work

Distributed Relation Logic.Gerard Allwein, William L. Harrison & Thomas Reynolds - 2017 - Logic and Logical Philosophy 26 (1):19-61.

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References found in this work

Modal Logic: An Introduction.Brian F. Chellas - 1980 - New York: Cambridge University Press.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1973 - In Hugues Leblanc (ed.), Truth, Syntax, and Modality: Proceedings Of The Temple University Conference On Alternative Semantlcs. Amsterdam and London: North-Holland Publishing Company. pp. 199-243.
Algebraic Methods in Philosophical Logic.J. Michael Dunn - 2001 - Oxford, England: Oxford University Press.
The theory of Representations for Boolean Algebras.M. H. Stone - 1936 - Journal of Symbolic Logic 1 (3):118-119.

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