Equational problems anddisunification
Journal of Symbolic Computation
The resolution calculus
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Resolution Methods for the Decision Problem
Resolution Methods for the Decision Problem
Parametric Circuit Representation Using Inductive Boolean Functions
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
Superposition and Chaining for Totally Ordered Divisible Abelian Groups
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
CERES: An analysis of Fürstenberg's proof of the infinity of primes
Theoretical Computer Science
A Schemata Calculus for Propositional Logic
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Superposition for fixed domains
ACM Transactions on Computational Logic (TOCL)
Deciding the inductive validity of ∀∃* queries
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Superposition modulo linear arithmetic SUP(LA)
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Decidability and undecidability results for propositional schemata
Journal of Artificial Intelligence Research
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
A decidable class of nested iterated schemata
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
RegSTAB: a SAT solver for propositional schemata
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Integrating linear arithmetic into superposition calculus
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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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.