1999 | OriginalPaper | Buchkapitel
Tractable Transformations from Modal Provability Logics into First-Order Logic
verfasst von : Stéephane Demri, Rajeev Goré
Erschienen in: Automated Deduction — CADE-16
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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We define a class of modal logics LF by uniformly extending a class of modal logics L. Each logic L is characterised by a class of first-order definable frames, but the corresponding logic LF is sometimes characterised by classes of modal frames that are not first-order definable. The class LF includes provability logics with deep arithmetical interpretations. Using Belnap’s proof-theoretical framework Display Logic we characterise the “pseudo-displayable” subclass of LF and show how to define polynomial-time transformations from each such LF into the corresponding L, and hence into first-order classical logic. Theorem provers for classical first-order logic can then be used to mechanise deduction in these “psuedo-displayable second order” modal logics.