Finite-model theory—a personal perspective
ICDT Selected papers of the 4th international conference on Database theory
A machine program for theorem-proving
Communications of the ACM
Extending Decision Procedures with Induction Schemes
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Handbook of automated reasoning
Handbook of automated reasoning
A Schemata Calculus for Propositional Logic
TABLEAUX '09 Proceedings of the 18th 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
Decidability and undecidability results for propositional schemata
Journal of Artificial Intelligence Research
On Deciding Satisfiability by Theorem Proving with Speculative Inferences
Journal of Automated Reasoning
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
A Resolution Calculus for First-order Schemata
Fundamenta Informaticae
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Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called iterated schemata, allow to express such patterns. Schemata extend propositional logic with indexed propositions, e.g.Pi, Pi+1, P1 or Pn, and with generalized connectives, e.g. $\bigwedge_{\rm i = 1}^n$, or $\bigvee_{\rm i = 1}^n$, where n is an (unbound) integer variable called a parameter. The expressive power of iterated schemata is strictly greater than propositional logic: it is even out of the scope of first-order logic. We define a proof procedure, called dpll⋆, that can prove that a schema is satisfiable for at least one value of its parameter, in the spirit of the dpll procedure [9]. But proving that a schema is unsatisfiable for every value of the parameter, is undecidable [1] so dpll⋆ does not terminate in general. Still, dpll⋆ terminates for schemata of a syntactic subclass called regularly nested.