Journal of Logic, Language and Information
, Volume 13, Issue 3, pp 241266
First online:
Logics for Classes of Boolean Monoids
 Gerard AllweinAffiliated withNaval Research Laboratory
 , Hilmi DemirAffiliated withNaval Research Laboratory
 , Lee PikeAffiliated withNaval Research Laboratory
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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 ScottMontague 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.
 Title
 Logics for Classes of Boolean Monoids
 Journal

Journal of Logic, Language and Information
Volume 13, Issue 3 , pp 241266
 Cover Date
 200412
 DOI
 10.1023/B:JLLI.0000028336.64373.f6
 Print ISSN
 09258531
 Online ISSN
 15729583
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 algebras of relations
 Boolean monoids
 CMOS circuits
 correspondence theory
 Kripke frames
 relative modalities
 Authors

 Gerard Allwein ^{(1)}
 Hilmi Demir ^{(1)}
 Lee Pike ^{(1)}
 Author Affiliations

 1. Naval Research Laboratory, Code 5543, 4555 Overlook Ave. SW, Washington, DC, 20375, U.S.A.