TY - GEN
T1 - Canonical inference for implicational systems
AU - Bonacina, Maria Paola
AU - Dershowitz, Nachum
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=53049084295&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-71070-7_33
DO - 10.1007/978-3-540-71070-7_33
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AN - SCOPUS:53049084295
SN - 3540710698
SN - 9783540710691
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 380
EP - 395
BT - Automated Reasoning - 4th International Joint Conference, IJCAR 2008, Proceedings
T2 - 4th International Joint Conference on Automated Reasoning, IJCAR 2008
Y2 - 12 August 2008 through 15 August 2008
ER -