U. Hustadt (1993a): ``Automated Support for the Development of Non-classical Logics.'' In H.-J. Bürckert and W. Nutt, editors, Modeling Epistemic Propositions: Workshop during the 17th German Conference on Artificial Intelligence (KI'93) [Berlin, Germany, 13-14 September 1993].
Abstract, BibTeX, PDF.

The most natural means for specifying a non-classical logic is by means of a Hilbert calculus. Usually, the semantics of a non-classical logic is given in terms of possible worlds. Given an axiomatization of a non-classical logics, the correspondence problem in these logics is to find for every given Hilbert axiom an equivalent property of the accessibility relation (van Benthem (1984)). For mechanizing deduction in non-classical logics it is very important to find these correspondences (Ohlbach (1991)). So far the method for finding the correspondences was mostly by intuition and the verification required complex proofs (van Benthem (1984)). SCAN is an algorithm which offers a method for computing the correspondences fully automatically. Moreover, since SCAN preserves equivalences, the computed correspondence axioms are guaranteed to be complete in the sense that a formula is derivable in the Hilbert calculus if and only if it is valid in the frames which are models of the computed correspondence axiom. In this paper we present the SCAN algorithm and an application of it to the problem of collapsing modalities in multi-modal logics: Given a Hilbert calculus for modalities [m_1] and [m_2] we have to ensure that [m_1] P iff [m_2] P doesn't hold for all formulae P, because this is in general an unwanted consequence of the given axiomatization. [an error occurred while processing this directive]