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Studia Logica

, Volume 50, Issue 3–4, pp 571–605 | Cite as

Dynamic algebras: Examples, constructions, applications

  • Vaughan Pratt
Article

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.

Keywords

Mathematical Logic Binary Relation Additive Function Basic Result Computational Linguistic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Polish Academy of Sciences 1991

Authors and Affiliations

  • Vaughan Pratt
    • 1
  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA

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