Canonical Inference for Implicational Systems ⋆

by Maria Paola Bonacina

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Datum	Value	Source
TITLE	Canonical Inference for Implicational Systems ⋆	SVM HeaderParse 0.2
AUTHOR NAME	Maria Paola Bonacina	SVM HeaderParse 0.2
AUTHOR AFFIL	; Nachum Dershowitz; 1 Dipartimento di Informatica, Università degli Studi di Verona; 2 School of Computer Science, Tel Aviv University	SVM HeaderParse 0.2
AUTHOR ADDR	; Italy; Ramat Aviv 69978, Israel	SVM HeaderParse 0.2
ABSTRACT	Abstract. 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. 1	SVM HeaderParse 0.2
CITATIONS	14 found	ParsCit 1.0