Automated reasoning: 33 BASIC research problems
Automated reasoning: 33 BASIC research problems
First-order logic and automated theorem proving
First-order logic and automated theorem proving
Automated reasoning (2nd ed.): introduction and applications
Automated reasoning (2nd ed.): introduction and applications
Unification of infinite sets of terms schematized by primal grammars
Theoretical Computer Science
Note on the generalization of calculations
Theoretical Computer Science
SPIKE, an Automatic Theorem Prover
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Short Proofs of Tautologies Using the Schema of Equivalence
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
Proceedings of the 10th International Conference on Automated Deduction
On Finite Representations of Infinite Sequences of Terms
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
Abstract Notions and Inference Systems for Proofs by Mathematical Induction
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
Automatic 'descente infinie' induction reasoning
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Simplified handling of iterated term schemata
Annals of Mathematics and Artificial Intelligence
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
Complexity of the satisfiability problem for a class of propositional schemata
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
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
Reasoning on schemata of formulæ
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
A Resolution Calculus for First-order Schemata
Fundamenta Informaticae
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We define a notion of formula schema handling arithmetic parameters, indexed propositional variables (e.g. P i ) and iterated conjunctions/disjunctions (e.g. $\bigwedge_{i=1}^n P_i$, where n is a parameter ). Iterated conjunctions or disjunctions are part of their syntax. We define a sound and complete (w.r.t. satisfiability) tableaux-based proof procedure for this language. This schemata calculus (called stab ) allows one to capture proof patterns corresponding to a large class of problems specified in propositional logic. Although the satisfiability problem is undecidable for unrestricted schemata, we identify a class of them for which stab always terminates. An example shows evidence that the approach is applicable to non-trivial practical problems. We give some precise technical hints to pursue the present work.