SGGS theorem proving: an exposition

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, model based, semantically guided, proof confluent, and goal sensitive, 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

Set of support, demodulation, paramodulation: a historical perspective

This article is a tribute to the scientific legacy of automated reasoning pioneer and JAR founder Lawrence T. (Larry) Wos. Larry's main technical contributions were the set-of-support strategy for resolution theorem proving, and the demodulation and paramodulation inference rules for building equality into resolution. Starting from the original definitions of these concepts in Larry's papers, this survey traces their evolution, unearthing the often forgotten trails that connect Larry's original definitions to those that became standard in the field

Semantically-guided goal-sensitive reasoning: decision procedures and the Koala prover

The main topic of this article are SGGS decision procedures for fragments of first-order logic without equality. SGGS (Semantically-Guided Goal-Sensitive reasoning) is an attractive basis for decision procedures, because it generalizes to first-order logic the Conflict-Driven Clause Learning (CDCL) procedure for propositional satisfiability. As SGGS is both refutationally complete and model-complete in the limit, SGGS decision procedures are model-constructing. We investigate the termination of SGGS with both positive and negative results: for example, SGGS decides Datalog and the stratified fragment (including Effectively PRopositional logic) that are relevant to many applications. Then we discover several new decidable fragments, by showing that SGGS decides them. These fragments have the small model property, as the cardinality of their SGGS-generated models can be upper bounded, and for most of them termination tools can be applied to test a set of clauses for membership. We also present the first implementation of SGGS - the Koala theorem prover - and we report on experiments with Koala

Partial instantiation methods for inference in first-order logic

Satisfiability algorithms for propositional logic have improved enormously in recently years. This improvement increases the attractiveness of satisfiability methods for first-order logic that reduce the problem to a series of ground-level satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolution-based methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (1) extending it to logic with functions, (2) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (3) simplifying it to obtain further speedup. We provide a similar development for a dual partial instantiation approach defined by Hooker and suggest a primal-dual strategy. We prove correctness of the primal and dual algorithms for full first-order logic with functions, as well as termination on unsatisfiable formulas. We also report some preliminary computational results

DRUM-II : efficient model based diagnosis of technical systems

[no abstract

Combining Enumeration and Deductive Techniques in order to Increase the Class of Constructible Infinite Models

AbstractA new method for building infinite models for first-order formulae is presented. The method combines enumeration techniques with existing deductive (in a broad sense) ones. Its soundness and completeness w.r.t. the class of models that can be represented by equational constraints are proven. This shows that the use of enumeration techniques strictly increases the power of existing methods for building Herbrand models that are not complete in this sense. Some strategies are proposed to reduce the search space. We give examples and show how to use this approach for building interactively a model of a formula introduced by Goldfarb in his proof of the undecidability of the Gödel class with identity. This formula is satisfiable but has no finite model