Comparing Instance Generation Methods for Automated Reasoning

We present a new calculus for first-order theorem proving with equality, ME+Sup, which generalizes both the Superposition calculus and the Model Evolution calculus (with equality) by integrating their inference rules and redundancy criteria in a non-trivial way. The main motivation is to combine the advantageous features of these two rather complementary calculi in a single framework. In particular, Model Evolution, as a lifted version of the propositional DPLL procedure, contributes a non-ground splitting rule that effectively permits to split a clause into \emph{non} variable disjoint subclauses. In the paper we present the calculus in detail. Our main result is its completeness under semantically justified redundancy criteria and simplification rules. We also show how under certain assumptions the model representation computed by a (finite and fair) derivation can be queried in an effective way

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“…Model Evolution belongs to the family of instance based methods [1,10,12]. Some of them include Resolution type inference rules.…”

Section: Related Workmentioning

confidence: 99%

A Combined Superposition and Model Evolution Calculus

Baumgartner

Waldmann

2010

J Autom Reasoning

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“…Perspectives on instance-based theorem proving were given in [23,25]. They distinguish between methods where the interleaving of instance generation and ground reasoning is fine-grained, as in the model-evolution calculus [4,5,7,8,6], and methods where it is coarse-grained, as in Inst-Gen [20,21,27,26], to facilitate the integration of SAT or SMT-solvers, taken "off the shelf."…”

Section: Discussionmentioning

confidence: 99%

SGGS Theorem Proving: an Exposition

Bonacina¹,

Plaisted²

EPiC Series in Computing

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We present in expository style the main ideas in SGGS, which stands for Semantically-Guided Goal-Sensitive theorem proving. SGGS uses sequences of constrained clauses to represent models, instance generation to go from a candidate model to the next, and resolution as well as other inferences to repair the model. SGGS is refutationally complete for first-order logic, DPLL-style model based, semantically guided, goal sensitive, and proof confluent, which appears to be a rare combination of features. In this paper we describe the core of SGGS in a narrative style, emphasizing ideas and trying to keep technicalities to a minimum, in order to advertise it to builders and users of theorem provers.

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