Stephan Tobies. PSPACE reasoning for graded modal logics. J. of Logic and Computation, 11(1):85-106, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Baldoni et al. 1998] The latter result is closely related to the undecidability proof in [Wessel, 2001] Here, we are concerned with (a) multi modal logics that provide for a converse operator on modal parameters and graded modalities (to restrict the number of accessible worlds; see, e.g. [Tobies, 2001]) and (b) a certain sub class of context free grammars. In our undecidability proof in Section 3, the main difficulty was to develop a grammar that generates the language 0 using only productions of the form R RS or R SR. We can construct a similar grammar G with L(G) ab) ....

S. Tobies. PSPACE reasoning for graded modal logics. J. of Logic and Computation, 11(1):85--106, 2001.

....have been generalized to express that, for a non negative integer n, at least n individuals or all but n individuals satisfy a formula. For example, predicate logic has been extended with so called counting quantifiers 9 and 9 n [GOR97,PST00] In modal logics, graded modalities [Fin72,vD95,Tob01] generalize standard existential and universal modalities in that they express, e.g. that there exist at least n accessible worlds satisfying a certain formula. In description logics, number restrictions have always played a central role; e.g. they are present in almost all ....

....coincides with the complexity of first order two variable logic without counting [GKV97] the complexity of C with binary coding is, to the best of our knowledge, unknown so far. Similarly, all the above mentioned complexity results for description and modal logics, with the exception of [Tob00,Tob01] assume unary coding of numbers. In [Tob00,Tob01] Tobies studies graded modal logic, the extension of modal logic with graded modalities. He proves that the satisfiability problem for this logic is PSPACEcomplete not harder than the satisfiability problem for classical modal logic [Lad77] ....

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S. Tobies. PSPACE reasoning for graded modal logics. Journal of Logic and Computation, 11(1):85--106, 2001.

....decision procedure for the hybrid calculus or, at least, for fragments of this logic. We return to the practicality issue at the end of the paper. Unfortunately, this new queen logic is still not the queen since it is missing a prominent feature, namely number restrictions graded modalities [17, 12, 38]. This is due to the fact that, in the presence of converse roles and universal programs roles (or any other means to internalise axioms) nominals and number restrictions graded modalities lead to NExpTime hardness [37] From the tense logic perspective [4] the hybrid calculus can also be ....

S. Tobies. PSPACE reasoning for graded modal logics. J. of Logic and Computation, 2001. To appear.

.... forks as those connections having 1 input and at least 2 outputs: 5 Connection u ( 1 c part of Gamma In) u ( 1 c part of Gamma Out) Connection u ( 1 c part of Gamma In) u ( 2 c part of Gamma Out) Since number restrictions are mostly harmless from an algorithmic point of view [26], we have added them to SHI. Definition 5 A (possibly inverse) role is called simple if it is neither transitive nor has a transitive sub role. SHIQ is obtained from SHI by allowing, additionally, for concepts of the form ( nR:C) and (6nR:C) for n a non negative integer, R a simple role, and C ....

S. Tobies, `PSPACE reasoning for graded modal logics', J. of Logic and Computation, (2000). To appear.

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Stephan Tobies. PSPACE reasoning for graded modal logics. J. of Logic and Computation, 11(1):85-106, 2001.

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S. Tobies. PSPACE reasoning for graded modal logics. Journal of Logic and Computation, 2000. To appear.

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