Communications of the ACM
Propositional Satisfiability and Constraint Programming: A comparative survey
ACM Computing Surveys (CSUR)
A Schemata Calculus for Propositional Logic
TABLEAUX '09 Proceedings of the 18th 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
A Resolution Calculus for First-order Schemata
Fundamenta Informaticae
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We describe the system RegStab (for regular schemata tableau) that solves the satisfiability problem for a class of propositional schemata. Our formalism extends propositional logic by considering indexed propositions (such as $P_1,P_{{\tt i}},P_{{\tt j}+1},\ldots$) and iterated connectives (e.g. $\bigvee_{i={\tt i}}^{\tt n} \phi$). The indices and bounds are linear arithmetic expressions (possibly containing variables, interpreted as integers). Our system allows one to check the satisfiability of sequences of formulae such as $(\bigvee_{{\tt i}=1}^{\tt n} P_{\tt i}) \wedge (\bigwedge_{{\tt i}=1}^{\tt n} \neg P_{\tt i})$.