Decidability Results for Saturation-Based Model Building

Horbach, Matthias; Weidenbach, Christoph

doi:10.1007/978-3-642-02959-2_30

Cited by 7 publications

(9 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This inference system is sound and complete as a slight variation of [15,14], provided that constraint satisfiability is decidable. As an example, this is the case when the constraints are increasing (cf.…”

Section: The Melting Calculus For Constrained Clausesmentioning

confidence: 99%

Obtaining Finite Local Theory Axiomatizations via Saturation

Horbach

Sofronie-Stokkermans

2013

Frontiers of Combining Systems

Self Cite

View full text Add to dashboard Cite

In this paper we present a method for obtaining local sets of clauses from possibly non-local ones. For this, we follow the work of Basin and Ganzinger and use saturation under a version of ordered resolution. In order to address the fact that saturation can generate infinite sets of clauses, we use constrained clauses and show that a link can be established between saturation and locality also for constrained clauses: This often allows us to give a finite representation of possibly infinite saturated sets of clauses

show abstract

Section: The Melting Calculus For Constrained Clausesmentioning

confidence: 99%

Obtaining Finite Local Theory Axiomatizations via Saturation

Horbach

Sofronie-Stokkermans

2013

Frontiers of Combining Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…Hence techniques for reasoning about fixed domain properties can be also used for minimal model reasoning. This turns the previously mentioned constrained superposition calculus into a decision procedure for several classes of minimal model problems [7,8,6].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…It is furthermore possible to allow arbitrary disequations in constraints. This makes it possible to write completions in such a way that the non-constraint part of every clause is predicative [7].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Aiming at the long-standing goal to harvest the power of first-order reasoning for this setting [4], Horbach and Weidenbach [9,7] developed a superpositionbased algorithm that allows for fixed domain reasoning with a saturation-based first-order prover. Later, this was extended using predicate completion [2,4,6] to systems for minimal model reasoning that decide, e.g., validity of queries with one quantifier alternation for the above-mentioned contexts [8,7,6].…”

Section: Introductionmentioning

confidence: 99%

“…The tool Spass-FD is an implementation on top of the automated theorem prover Spass [14] of (i) the calculi for saturation-based reasoning with respect to fixed domains and minimal models as described in [7] (including the decision procedure for contexts), and (ii) the underlying disunification procedure from [6]. Spass provides a powerful superposition-based saturation machinery, which makes this prover well-suited as a basis for the implementation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

System Description: SPASS-FD

Horbach

2011

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Using a constrained superposition calculus and a disunification procedure, it is possible to employ superposition-based first-order reasoners for reasoning not only about all models of a first-order theory, but also about all models over a specific finite domain and often as well about the perfect models of the theory (or the unique minimal model in case of a Horn theory), both of which are second-order problems. In this paper, I describe the tool Spass-FD, an extension of the firstorder prover Spass that equips Spass with disunification and with fixed domain and minimal model theorem proving capabilities.

show abstract

First-Order Automatic Literal Model Generation

Bromberger,

Krasnopol,

Möhle

et al. 2024

Lecture Notes in Computer Science

View full text Add to dashboard Cite

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 also a model for the input set. The interpretation is represented by first-order linear literals. It can be effectively used to evaluate clauses. A particular application are SCL stuck states. The SCL (Simple Clause Learning) calculus always computes with respect to a finite number of ground literals. It then finds either a contradiction or a stuck state being a model with respect to the considered ground literals. Our algorithm builds a complete literal interpretation out of such a stuck state model that can then be used to evaluate the clause set. If all clauses are satisfied an overall model has been found. If it does not satisfy some clause, this information can be effectively explored to extend the scope of ground literals considered by SCL.

show abstract

Decidability Results for Saturation-Based Model Building

Cited by 7 publications

References 15 publications

Obtaining Finite Local Theory Axiomatizations via Saturation

Obtaining Finite Local Theory Axiomatizations via Saturation

System Description: SPASS-FD

First-Order Automatic Literal Model Generation

Contact Info

Product

Resources

About