An undecidable problem in correspondence theory
Journal of Symbolic Logic
Modal logic
Computing Circumscription Revisited: A Reduction Algorithm
Journal of Automated Reasoning
Second-Order Quantifier Elimination in Modal Contexts
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Journal of Logic and Computation
Completeness and Correspondence in Hybrid Logic via an Extension of SQEMA
Electronic Notes in Theoretical Computer Science (ENTCS)
Second Order Quantifier Elimination: Foundations, Computational Aspects and Applications
Second Order Quantifier Elimination: Foundations, Computational Aspects and Applications
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In earlier papers we have introduced an algorithm, SQEMA, for computing first-order equivalents and proving canonicity of modal formulae. However, SQEMA is not complete with respect to the so called complex Sahlqvist formulae. In this paper we, first, introduce the class of complex inductive formulae, which extends both the class of complex Sahlqvist formulae and the class of polyadic inductive formulae, and second, extend SQEMA to SQEMA$^{sub}$ by allowing suitable substitutions in the process of transformation. We prove the correctness of SQEMA$^{sub}$ with respect to local equivalence of the input and output formulae and d-persistence of formulae on which the algorithm succeeds, and show that SQEMA$^{sub}$ is complete with respect to the class of complex inductive formulae.