Canonical inference for implicational systems

Maria Paola Bonacina, Nachum Dershowitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


Completion is a general paradigm for applying inferences to generate a canonical presentation of a logical theory, or to semi-decide the validity of theorems, or to answer queries. We investigate what canonicity means for implicational systems that are axiomatizations of Moore families - or, equivalently, of propositional Horn theories. We build a correspondence between implicational systems and associative-commutative rewrite systems, give deduction mechanisms for both, and show how their respective inferences correspond. Thus, we exhibit completion procedures designed to generate canonical systems that are "optimal" for forward chaining, to compute minimal models, and to generate canonical systems that are rewrite-optimal. Rewrite-optimality is a new notion of "optimality" for implicational systems, one that takes contraction by simplification into account.

Original languageEnglish
Title of host publicationAutomated Reasoning - 4th International Joint Conference, IJCAR 2008, Proceedings
Number of pages16
StatePublished - 2008
Event4th International Joint Conference on Automated Reasoning, IJCAR 2008 - Sydney, NSW, Australia
Duration: 12 Aug 200815 Aug 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5195 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference4th International Joint Conference on Automated Reasoning, IJCAR 2008
CitySydney, NSW


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