Local Reductions for the Modal Cube

Nalon, C. and Hustadt, U. and Papacchini, F. and Dixon, C. (2022) Local Reductions for the Modal Cube. In: International Joint Conference on Automated Reasoning :. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 13385 . UNSPECIFIED, pp. 486-505. ISBN 9783031107689

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The modal logic K is commonly used to represent and reason about necessity and possibility and its extensions with combinations of additional axioms are used to represent knowledge, belief, desires and intentions. Here we present local reductions of all propositional modal logics in the so-called modal cube, that is, extensions of K with arbitrary combinations of the axioms B, D, T, 4 and 5 to a normal form comprising a formula and the set of modal levels it occurs at. Using these reductions we can carry out reasoning for all these logics with the theorem prover. We define benchmarks for these logics and experiment with the reduction approach as compared to an existing resolution calculus with specialised inference rules for the various logics.

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Export Date: 5 September 2022 Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/N007565/1, EP/R026084/1, EP/R026092/1 Funding text 1: C. Dixon was partially supported by the EPSRC funded RAI Hubs FAIR-SPACE (EP/R026092/1) and RAIN (EP/R026084/1), and the EPSRC funded programme Grant S4 (EP/N007565/1).
?? formal logic% reductionsinference rulesmodal logicnormal formtheorem proverscalculations ??
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01 Nov 2022 12:30
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28 Nov 2023 10:39