Combining deduction modulo and logics of fixed-point definitions

David Baelde, Gopalan Nadathur

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of recursive specifications. These specifications are not directly complemented by fixed-point reasoning techniques and, correspondingly, do not have to satisfy strong monotonicity restrictions. We show how to incorporate a rewriting capability into logics of fixed-point definitions towards additionally supporting recursive specifications. Specifically, we describe a natural deduction calculus that adds a form of ''closed-world'' equality - -a key ingredient to supporting fixed-point definitions - -to deduction modulo, a framework for extending a logic with a rewriting layer operating on formulas. We show that our calculus enjoys strong normalizability when the rewrite system satisfies general properties and we demonstrate its usefulness in specifying and reasoning about syntax-based descriptions. Our integration of closed-world equality into deduction modulo is based on an elimination principle for this form of equality that, for the first time, allows us to require finiteness of proofs without sacrificing stability under reduction.

Original languageEnglish (US)
Title of host publicationProceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012
Pages105-114
Number of pages10
DOIs
StatePublished - 2012
Event2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012 - Dubrovnik, Croatia
Duration: Jun 25 2012Jun 28 2012

Publication series

NameProceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012

Other

Other2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012
CountryCroatia
CityDubrovnik
Period6/25/126/28/12

Keywords

  • closed-world equality
  • deduction modulo
  • fixed-point and recursive definitions
  • strong normalizability

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