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FO(FD): Extending classical logic with rule-based fixpoint definitions

Published online by Cambridge University Press:  09 July 2010

PING HOU ,
BROES DE CAT  and
MARC DENECKER
PING HOU
Affiliation:
Department of Computer Science, K.U. Leuven, Belgium (e-mail: ping.hou@cs.kuleuven.be, broes.decat@cs.kuleuven.be, marc.denecker@cs.kuleuven.be)
BROES DE CAT
Affiliation:
Department of Computer Science, K.U. Leuven, Belgium (e-mail: ping.hou@cs.kuleuven.be, broes.decat@cs.kuleuven.be, marc.denecker@cs.kuleuven.be)
MARC DENECKER
Affiliation:
Department of Computer Science, K.U. Leuven, Belgium (e-mail: ping.hou@cs.kuleuven.be, broes.decat@cs.kuleuven.be, marc.denecker@cs.kuleuven.be)
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Abstract

We introduce fixpoint definitions, a rule-based reformulation of fixpoint constructs. The logic FO(FD), an extension of classical logic with fixpoint definitions, is defined. We illustrate the relation between FO(FD) and FO(ID), which is developed as an integration of two knowledge representation paradigms. The satisfiability problem for FO(FD) is investigated by first reducing FO(FD) to difference logic and then using solvers for difference logic. These reductions are evaluated in the computation of models for FO(FD) theories representing fairness conditions and we provide potential applications of FO(FD).

Keywords

fixpoint constructsfixpoint definitionsclassical logic extensions

Information

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 10 , Special Issue 4-6: 26th International Conference on Logic Programming , July 2010 , pp. 581 - 596
Copyright
Copyright © Cambridge University Press 2010

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