Abstract
In this chapter we show how bounds from substructural analysis can be combined with bounds for relational reasoning to provide decision procedures with space complexity upper-bounds. In particular, we show that contraction elimination for S(K) and bounded contraction for S(T), S(K4) and S(S4), combined with the soundness and completeness of our systems with respect to the corresponding Kripke semantics, tell us that the provability (validity) problems for the modal logics K, T, K4 and S4 are decidable in PSPACE.
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© 2000 Springer Science+Business Media Dordrecht
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Viganò, L. (2000). Complexity of Proof Search in K, T, K4 and S4. In: Labelled Non-Classical Logics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3208-5_12
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DOI: https://doi.org/10.1007/978-1-4757-3208-5_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4962-2
Online ISBN: 978-1-4757-3208-5
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