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Given a finite consistent set of ground literals, we present an algorithm that generates a complete first-order logic interpretation, i.e., an interpretation for all ground literals over the signature and not just those in the input set, that is ...

Clause sets saturated by hierarchic ordered resolution do not offer a model representation that can be effectively queried, in general. They only offer the guarantee of the existence of a model. We present an effective symbolic model construction ...

KBO constraint solving is very well-known to be an NP-complete problem. Motivated by the needs of the family of SCL calculi, we consider the particular case where all terms occurring in a constraint are bound by a (single) ground term. We show ...

We show that SCL(FOL) can simulate the derivation of non-redundant clauses by superposition for first-order logic without equality. Superposition-based reasoning is performed with respect to a fixed reduction ordering. The completeness proof of ...

We present an Isabelle/HOL formalization of Simple Clause Learning for first-order logic without equality: SCL(FOL). The main results are formal proofs of soundness, non-redundancy of learned clauses, termination, and refutational completeness. ...

We propose a new calculus SCL(EQ) for first-order logic with equality that only learns non-redundant clauses. Following the idea of CDCL (Conflict Driven Clause Learning) and SCL (Clause Learning from Simple Models) a ground literal model ...

Shortly before Larry Wos passed away, he sent a manuscript for discussion to Sophie Tourret, the editor of the AAR newsletter. We present excerpts from this final manuscript, put it in its historic context and explain its relevance for today’s ...

We propose a new calculus SCL(EQ) for first-order logic with equality that only learns non-redundant clauses. Following the idea of CDCL (Conflict Driven Clause Learning) and SCL (Clause Learning from Simple Models) a ground literal model ...

A clause C is syntactically relevant in some clause set N, if it occurs in every refutation of N. A clause C is syntactically semi-relevant, if it occurs in some refutation of N. While syntactic relevance coincides with satisfiability (if C is ...$$

Abduction in description logics finds extensions of a knowledge base to make it entail an observation. As such, it can be used to explain why the observation does not follow, to repair incomplete knowledge bases, and to provide possible ...$\mathcal{}$

The importance of subsumption testing for redundancy elimination in first-order logic automatic reasoning is well-known. Although the problem is already NP-complete for first-order clauses, the meanwhile developed test pipelines efficiently decide ...

In a previous paper, we have shown that clause sets belonging to the Horn Bernays-Schönfinkel fragment over simple linear real arithmetic (HBS(SLR)) can be translated into HBS clause sets over a finite set of first-order constants. The translation ...

The Bernays-Schönfinkel first-order logic fragment over simple linear real arithmetic constraints BS(SLR) is known to be decidable. We prove that BS(SLR) clause sets with both universally and existentially quantified verification conditions (...

We prove the SOS strategy for first-order resolution to be refutationally complete on a clause set N and set-of-support S if and only if there exists a clause in S that occurs in a resolution refutation from $N\cup S$. This strictly generalizes and ...$$$$

Simple clause learning over theories SCL(T) is a decision procedure for the Bernays-Schoenfinkel fragment over bounded difference constraints BS(BD). The BS(BD) fragment consists of clauses built from first-order literals without function symbols ...

Future cyber-physical systems are expected to be dynamic, evolving while already being deployed. Frequent updates of software components are likely to become the norm even for safety-critical systems. In this setting, a full re-certification ...

We consider feasibility of linear integer problems in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer problems is decidable, many state-of-the-art implementations ...

A number of first-order calculi employ an explicit model representation formalism in support of non-redundant inferences and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of ...

SPASS-SATT is a CDCL(LA) solver for linear rational and linear mixed/integer arithmetic. This system description explains its specific features: fast cube tests for integer solvability, bounding transformations for unbounded problems, close ...

Several decision procedures for the Bernays-Schoenfinkel (BS) fragment of first-order logic rely on explicit model assumptions. In particular, the procedures differ in their respective model representation formalisms. We introduce a new decision ...