Deciding the inductive validity of ∀∃* queries

Authors:
Matthias Horbach;Christoph Weidenbach
Affiliations:
Max Planck Institute for Informatics, Saarbrücken, Germany;Max Planck Institute for Informatics, Saarbrücken, Germany
Venue:
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Year:
2009

Citing 11
Cited 5

Equational problems anddisunification

Journal of Symbolic Computation
Automating inductionless induction using test sets

Journal of Symbolic Computation
A method for simultaneous search for refutations and models by equational constraint solving

Journal of Symbolic Computation
Automated theorem proving by test set induction

Journal of Symbolic Computation
Induction = I-axiomatization + first-order consistency

Information and Computation - Special issue on RTA-98
Inductive Theorem Proving by Consistency for First-Order Clauses

CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Combining superposition, sorts and splitting

Handbook of automated reasoning
Automata-driven automated induction

LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
A Superposition Decision Procedure for the Guarded Fragment with Equality

LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Model building with ordered resolution: extracting models from saturated clause sets

Journal of Symbolic Computation - Special issue: First order theorem proving
Inductive decidability using implicit induction

LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning

Superposition for fixed domains

ACM Transactions on Computational Logic (TOCL)
Disunification for ultimately periodic interpretations

LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
System description: SPASS-FD

CADE'11 Proceedings of the 23rd international conference on Automated deduction
Completeness and decidability results for first-order clauses with indices

CADE'13 Proceedings of the 24th international conference on Automated Deduction
A Resolution Calculus for First-order Schemata

Fundamenta Informaticae

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a new saturation-based decidability result for inductive validity. Let Σ be a finite signature in which all function symbols are at most unary and let N be a satisfiable Horn clause set without equality in which all positive literals are linear. If N ∪ {A1, ... , An →} belongs to a class that can be finitely saturated by ordered resolution modulo variants, then it is decidable whether a sentence of the form ¬x.∃y→.A1 ∧ ... ∧ An is valid in the minimal model of N.