Deciding the Inductive Validity of ∀ ∃ * Queries

Horbach, Matthias; Weidenbach, Christoph

doi:10.1007/978-3-642-04027-6_25

Cited by 13 publications

(16 citation statements)

References 15 publications

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“…We build on the notions of [3,27,16] and shortly recall here the most important concepts concerning terms and orderings and the specific extensions (concerning constrained clauses) needed in this article. To keep the presentation concise, we restrict ourselves to single-sorted signatures.…”

Section: General Definitionsmentioning

confidence: 99%

“…To reason about such constrained clauses, we use the standard inference rules for constrained ordered resolution and superposition (cf. [16]), enriched by an on-the-fly induction rule called melting.…”

Section: A Constrained Inference Calculusmentioning

confidence: 99%

“…We now extend the calculus to an inference system including a melting rule [16], which serves as a limited form of induction. To define melting, we need the notion of an ancestor.…”

Section: The Melting Calculus For Constrained Clausesmentioning

confidence: 99%

“…The latter can for instance be ensured by considering only Horn clauses where all clauses with a positive literal are unconstrained; cf. [16,12] for more details.…”

Section: Correctnessmentioning

confidence: 99%

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Obtaining Finite Local Theory Axiomatizations via Saturation

Horbach

Sofronie-Stokkermans

2013

Frontiers of Combining Systems

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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

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Section: General Definitionsmentioning

confidence: 99%

Section: A Constrained Inference Calculusmentioning

confidence: 99%

“…We now extend the calculus to an inference system including a melting rule [16], which serves as a limited form of induction. To define melting, we need the notion of an ancestor.…”

Section: The Melting Calculus For Constrained Clausesmentioning

confidence: 99%

“…The latter can for instance be ensured by considering only Horn clauses where all clauses with a positive literal are unconstrained; cf. [16,12] for more details.…”

Section: Correctnessmentioning

confidence: 99%

See 2 more Smart Citations

Obtaining Finite Local Theory Axiomatizations via Saturation

Horbach

Sofronie-Stokkermans

2013

Frontiers of Combining Systems

Self Cite

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show abstract

“…Although loop detection techniques and termination results already exist for the calculus in [17] (see also [16]), strong restrictions are imposed on the syntax of the formulae (e.g. they must be Horn), which are not in general fulfilled by the formulae we consider in the present paper, even in the propositional case.…”

Section: Introductionmentioning

confidence: 99%

A Resolution Calculus for First-order Schemata

Aravantinos

Echenim

Peltier

2013

Fundamenta Informaticae

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We devise a resolution calculus that tests the satisfiability of infinite families of clause sets, called clause set schemata. For schemata of propositional clause sets, we prove that this calculus is sound, refutationally complete, and terminating. The calculus is extended to first-order clauses, for which termination is lost, since the satisfiability problem is not semi-decidable for nonpropositional schemata. The expressive power of the considered logic is strictly greater than the one considered in our previous work.

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On Invariant Synthesis for Parametric Systems

Peuter

Sofronie-Stokkermans

2019

Lecture Notes in Computer Science

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We study possibilities for automated invariant generation in parametric systems. We use (a refinement of) an algorithm for symbol elimination in theory extensions to devise a method for iteratively strengthening certain classes of safety properties to obtain invariants of the system. We identify conditions under which the method is correct and complete, and situations in which the method is guaranteed to terminate. We illustrate the ideas on various examples.

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Deciding the Inductive Validity of ∀ ∃ * Queries

Cited by 13 publications

References 15 publications

Obtaining Finite Local Theory Axiomatizations via Saturation

Obtaining Finite Local Theory Axiomatizations via Saturation

A Resolution Calculus for First-order Schemata

On Invariant Synthesis for Parametric Systems

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