Abstract
In this paper we classify all rigid rooted IPC-frames of depth 3. Among other things we show that these have at most 3 maximal elements. The interest in rigid frames arose from the paper [5]. In this paper quasi-characterizing inference rules were discussed. These rules are built on the pattern of Jankov-formulas of finite rooted frames but a Jankov-formula of the form ϕ→p is transformed into a quasi-characterizing rule ϕ/p. Such a rule is called self-admissible if it is admissible in the logic generated by the frame corresponding to the rule itself. The important results of [5] are that self-admissible rules are admissible in IPC itself, and that such a quasi-characterizing inference rule is self-admissible iff the frame it derives from is not rigid. The classification of rigid frames thus becomes of interest.
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Oner, T., de Jongh, D. (2009). The Structure of Rigid Frames of Depth 3 Only. In: Bosch, P., Gabelaia, D., Lang, J. (eds) Logic, Language, and Computation. TbiLLC 2007. Lecture Notes in Computer Science(), vol 5422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00665-4_2
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DOI: https://doi.org/10.1007/978-3-642-00665-4_2
Publisher Name: Springer, Berlin, Heidelberg
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