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The logic of recursive equations

Published online by Cambridge University Press:  12 March 2014

A. J. C. Hurkens ,
Monica McArthur ,
Yiannis N. Moschovakis ,
Lawrence S. Moss  and
Glen T. Whitney
A. J. C. Hurkens
Affiliation:
Klaasstokseweg 7, 5443 NS HAPS, The Netherlands, E-mail: [email protected]
Monica McArthur
Affiliation:
Department of Mathematics, Indiana University, Bloomington IN 47405, USA, E-mail: [email protected]
Yiannis N. Moschovakis
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90024, USA, E-mail: [email protected]
Lawrence S. Moss
Affiliation:
Departments of Mathematics and Computer Science, Indiana University, Bloomington IN 47405, USA, E-mail: [email protected]
Glen T. Whitney
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA, E-mail: [email protected]
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Abstract

We study logical systems for reasoning about equations involving recursive definitions. In particular, we are interested in “propositional” fragments of the functional language of recursion FLR [18, 17], i.e., without the value passing or abstraction allowed in FLR. The “pure,” propositional fragment FLR0 turns out to coincide with the iteration theories of [1]. Our main focus here concerns the sharp contrast between the simple class of valid identities and the very complex consequence relation over several natural classes of models.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 2 , June 1998 , pp. 451 - 478
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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