Automated deduction in nonclassical logics
Automated deduction in nonclassical logics
Information and Computation
A framework for defining logics
Journal of the ACM (JACM)
Logic for applications
Handbook of logic in artificial intelligence and logic programming (vol. 1)
Basic proof theory
A New Method for Bounding the Complexity of Modal Logics
KGC '97 Proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory
A Context-Based Logic for Distributed Knowledge Representation and Reasoning
CONTEXT '99 Proceedings of the Second International and Interdisciplinary Conference on Modeling and Using Context
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Labelled Natural Deduction for Interval Logics
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Natural Deduction for First-Order Hybrid Logic
Journal of Logic, Language and Information
Disjunction and modular goal-directed proof search
ACM Transactions on Computational Logic (TOCL)
Automated reasoning in quantified modal and temporal logics
AI Communications
Mechanizing common knowledge logic using COQ
Annals of Mathematics and Artificial Intelligence
Safety and liveness in concurrent pointer programs
FMCO'05 Proceedings of the 4th international conference on Formal Methods for Components and Objects
Model checking quantified computation tree logic
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
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In previous work we gave an approach, based on labelled naturaldeduction, for formalizing proof systems for a large class ofpropositional modal logics that includes K, D, T,B, S4, S4.2, KD45, and S5. Here we extend this approach to quantified modal logics, providing formalizations for logics with varying, increasing, decreasing, or constant domains. The result is modular withrespect to both properties of the accessibility relation in the Kripke frame and the way domains of individuals change between worlds. Our approach has a modular metatheory too; soundness, completeness and normalization are proved uniformly for every logic in our class. Finally, our work leads to a simple implementation of a modal logic theorem prover in a standard logical framework.