Introduction to Mathematical Logic and Type Theory: To Truth through Proof
Introduction to Mathematical Logic and Type Theory: To Truth through Proof
Tableaux for Quantified Hybrid Logic
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Natural Deduction for First-Order Hybrid Logic
Journal of Logic, Language and Information
AI Communications - CASC
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
THF0 --- The Core of the TPTP Language for Higher-Order Logic
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Terminating Tableau Systems for Hybrid Logic with Difference and Converse
Journal of Logic, Language and Information
The TPTP Problem Library and Associated Infrastructure
Journal of Automated Reasoning
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Combining logics in simple type theory
CLIMA'10 Proceedings of the 11th international conference on Computational logic in multi-agent systems
Analytic tableaux for higher-order logic with choice
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Nitpick: a counterexample generator for higher-order logic based on a relational model finder
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
Combining and automating classical and non-classical logics in classical higher-order logics
Annals of Mathematics and Artificial Intelligence
Embedding and automating conditional logics in classical higher-order logic
Annals of Mathematics and Artificial Intelligence
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Prominent logics, including quantified multimodal logics, can be elegantly embedded in simple type theory (classical higher-order logic). Furthermore, off-the-shelf reasoning systems for simple type type theory exist that can be uniformly employed for reasoning within and about embedded logics. In this paper we focus on reasoning about modal logics and exploit our framework for the automated verification of inclusion and equivalence relations between them. Related work has applied first-order automated theorem provers for the task. Our solution achieves significant improvements, most notably, with respect to elegance and simplicity of the problem encodings as well as with respect to automation performance.