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Modal logics preserving admissible for S4 inference rules. (English) Zbl 1044.03515
Pacholski, Leszek (ed.) et al., Computer science logic. 8th workshop, CSL ’94, Kazimierz, Poland, September 25-30, 1994. Selected papers. Berlin: Springer-Verlag (ISBN 3-540-60017-5). Lect. Notes Comput. Sci. 933, 512-526 (1995).
Summary: The aim of this paper is to provide a complete semantic description for modal logics with finite model property which preserve all inference rules admissible in S4, with the intention of meeting some of the needs of computer science. It is shown that a modal logic \(\lambda\) with fmp above S4 preserves all inference rules admissible for S4 iff \(\lambda\) has the so-called co-cover property. In turns out that there are continuously many logics of this kind. Using the above-mentioned semantic criterion, we give a precise description of all tabular logics preserving rules admissible for S4.
For the entire collection see [Zbl 0847.00048].

03B45 Modal logic (including the logic of norms)