Dynamic algebras: Examples, constructions, applications

Studia Logica 50 (3-4):571 - 605 (1991)
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Abstract

Dynamic algebras combine the classes of Boolean (B 0) and regular (R ; *) algebras into a single finitely axiomatized variety (B R ) resembling an R-module with scalar multiplication . The basic result is that * is reflexive transitive closure, contrary to the intuition that this concept should require quantifiers for its definition. Using this result we give several examples of dynamic algebras arising naturally in connection with additive functions, binary relations, state trajectories, languages, and flowcharts. The main result is that free dynamic algebras are residually finite (i.e. factor as a subdirect product of finite dynamic algebras), important because finite separable dynamic algebras are isomorphic to Kripke structures. Applications include a new completeness proof for the Segerberg axiomatization of prepositional dynamic logic, and yet another notion of regular algebra.

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Citations of this work

A proof system for contact relation algebras.Ivo Düntsch & Ewa Orłowska - 2000 - Journal of Philosophical Logic 29 (3):241-262.
Some modal aspects of XPath.Balder ten Cate, Gaëlle Fontaine & Tadeusz Litak - 2010 - Journal of Applied Non-Classical Logics 20 (3):139-171.
PDL has interpolation.Tomasz Kowalski - 2002 - Journal of Symbolic Logic 67 (3):933-946.

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References found in this work

On the calculus of relations.Alfred Tarski - 1941 - Journal of Symbolic Logic 6 (3):73-89.
Algebraic Logic.Paul Richard Halmos - 2014 - New York, NY, USA: Chelsea.
Application of modal logic to programming.Vaughan R. Pratt - 1980 - Studia Logica 39 (2-3):257 - 274.
On sentences which are true of direct unions of algebras.Alfred Horn - 1951 - Journal of Symbolic Logic 16 (1):14-21.
Universal Algebra.George Grätzer - 1982 - Studia Logica 41 (4):430-431.

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