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Fixed Point Logics

Published online by Cambridge University Press:  15 January 2014

Anuj Dawar  and
Yuri Gurevich
Anuj Dawar
Affiliation:
Cambridge University Computer Laboratory, Cambridge CB2 3QG, UKE-mail: anuj.dawar@cl.cam.ac.uk
Yuri Gurevich
Affiliation:
Microsoft Research, One Microsoft Way, Redmond, WA 98052, USAE-mail: gurevich@microsoft.com
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Abstract

We consider fixed point logics, i.e., extensions of first order predicate logic with operators defining fixed points. A number of such operators, generalizing inductive definitions, have been studied in the context of finite model theory, including nondeterministic and alternating operators. We review results established in finite model theory, and also consider the expressive power of the resulting logics on infinite structures. In particular, we establish the relationship between inflationary and nondeterministic fixed point logics and second order logic, and we consider questions related to the determinacy of games associated with alternating fixed points.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 8 , Issue 1 , March 2002 , pp. 65 - 88
Copyright
Copyright © Association for Symbolic Logic 2002

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