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JAIR
2011

Decidability and Undecidability Results for Propositional Schemata

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Decidability and Undecidability Results for Propositional Schemata
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions (e.g., pi) and iterated connectives ∨ or ∧ ranging over intervals parameterized by arithmetic variables (e.g., ∧n i=1 pi, where n is a parameter). The satisfiability problem is shown to be undecidable for this new logic, but we introduce a very general class of schemata, called bound-linear, for which this problem becomes decidable. This result is obtained by reduction to a particular class of schemata called regular, for which we provide a sound and complete terminating proof procedure. This schemata calculus (called stab) allows one to capture proof patterns corresponding to a large class of problems specified in propositional logic. We also show that the satisfiability problem becomes again undecidable for slight extensions of this class, thus demonstrating that bound-linear schemata represent a good compromise between expressivity and decidability.
Vincent Aravantinos, Ricardo Caferra, Nicolas Pelt
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where JAIR
Authors Vincent Aravantinos, Ricardo Caferra, Nicolas Peltier
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