Automated deduction by theory resolution
Journal of Automated Reasoning
Proc. of the 8th international conference on Automated deduction
Resolution and quantified epistemic logics
Proc. of the 8th international conference on Automated deduction
Generating connection calculi from tableau and sequent based proof systems
Artificial intelligence and its applications
Theorem Proving via General Matings
Journal of the ACM (JACM)
Journal of the ACM (JACM)
A Deductive Approach to Program Synthesis
ACM Transactions on Programming Languages and Systems (TOPLAS)
Expansion Tree Proofs and Their Conversion to Natural Deduction Proofs
Proceedings of the 7th International Conference on Automated Deduction
Proceedings of the 7th International Conference on Automated Deduction
Transforming Matings into Natural Deduction Proofs
Proceedings of the 5th Conference on Automated Deduction
Knowledge and common knowledge in a distributed environment
PODC '84 Proceedings of the third annual ACM symposium on Principles of distributed computing
A deduction model of belief and its logics
A deduction model of belief and its logics
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Deep-reasoning-centred dialogue
ENLG '07 Proceedings of the Eleventh European Workshop on Natural Language Generation
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We present matrix proof systems for both constant- and varying-domain versions of the first-order modal logics K, K4, D, D4, T, 84 and 86 based on modal versions of Herbrand's Theorem specifically formulated to support efficient automated proof search. The systems treat the mil modal language (no normal-forming) and admit straightforward structure sharing implementations. A key fsature of our approach is the use of a specialised unification algorithm to reflect the conditions on the accessibility relation for a given logic. The matrix system for one logic differs from the matrix eystem for another only in the nature of this unification algorithm. In addition, proof search may be interpreted as constructing generalised proof trees in an appropriate tableau- or sequent-based proof system. This facilitates the use of the matrix systems within interactive environments.