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Logic of Programs 1981: Logics of Programs pp 167-176 | Cite as

On induction vs. *-continuity

  • Dexter Kozen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 131)

Abstract

In this paper we study the relative expressibility of the infinitary *-continuity condition
$$< \alpha ^* > X \equiv V_n < \alpha ^n > X$$
(*-cont)
and the equational but weaker induction axiom
$$X \wedge [\alpha ^* ](X \supset [\alpha ]X) \equiv [\alpha ^* ]X$$
(ind)
in Propositional Dynamic Logic. We show: (1) under ind only, there is a first-order sentence distinguishing separable dynamic algebras from standard Kripke models; whereas (2) under the stronger axiom *-cont, the class of separable dynamic algebras and the class of standard Kripke models are indistinguishable by any sentence of infinitary first-order logic.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Dexter Kozen
    • 1
  1. 1.IBM Thomas J. Watson Research CenterYorktown Heights

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