Computation Theory and Logic pp 20-36 | Cite as

# Existential fixed-point logic

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## Abstract

The purpose of this paper is to draw attention to existential fixed-point logic. Among other things, we show that: (1) If a structure *A* satisfies an existential fixed-point formula *φ*, then *A* has a finite subset *F* such that every structure *B* with *A|F* = *B|F* satisfies *φ*. (2) Using existential fixed-point logic instead of first-order logic removes the expressivity hypothesis in Cook's completeness theorem for Hoare logic. (3) In the presence of a successor relation, existential fixed-point logic captures polynomial time.

## Keywords

Atomic Formula Predicate Symbol Satisfiability Problem Existential Quantifier Weak Precondition
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## Copyright information

© Springer-Verlag Berlin Heidelberg 1987