Logics for classes of Boolean monoids

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

Download options

PhilArchive



    Upload a copy of this work     Papers currently archived: 72,694

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2009-01-28

Downloads
49 (#235,136)

6 months
1 (#388,311)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
The Theory of Representations for Boolean Algebras.M. H. Stone - 1936 - Journal of Symbolic Logic 1 (3):118-119.
The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1977 - Journal of Symbolic Logic 42 (2):315-316.
Boolean Algebras with Operators.Alfred Tarski - 1953 - Journal of Symbolic Logic 18 (1):70-71.

View all 7 references / Add more references

Citations of this work

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

Add more citations