Abstract
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.
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Aravantinos, V., Caferra, R., Peltier, N. (2009). A Schemata Calculus for Propositional Logic. In: Giese, M., Waaler, A. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2009. Lecture Notes in Computer Science(), vol 5607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02716-1_4
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DOI: https://doi.org/10.1007/978-3-642-02716-1_4
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