S. Demri and D. Gabbay. On modal logics characterized by models with relative accessibility relations: Part II. Studia Logica, 66(3):349-384, 2000.  Home/Search   Document Not in Database   Summary   Related Articles

....with nominals have been introduced in [Kon98] in order to facilitate the design of Rasiowa Sikorski style proof systems (dual tableaux) for SIM. Such a technique has been also useful to show decidability of SIM [DK98] and for some fragments of Boolean modal logic BML [LS01, Sect. 5] see also [DG00] In this paper, we use a normal form for the Boolean modal expressions with nominals. We recall below some de nitions. For l 1 and n 1, let Y = fE 1 ; E l g be distinct parameter nominals and be X = fC 1 ; C n g distinct parameter variables. For every integer k 2 f0; ....

....relations, each c i is interpreted as a re exive and symmetric relation, and the logic contains propositional variables and nominals. The logic SIM can be viewed as the standard (and simpli ed) version of SIM; more details about the relationsip between SIM and SIM can be found in [Dem99a,DG00] More importantly, by slightly adapting the ExpTime completeness proof for SIM one can show the following result. Corollary 12. The satis ability problem for the logic SIM is ExpTime complete. However, it is open whether replacing symmetry by transitivity in SIM preserves decidability ....

S. Demri and D. Gabbay. On modal logics characterized by models with relative accessibility relations: Part II. Studia Logica, 66(3):349-384, 2000.

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