Areces, C., P. Blackburn and M. Marx, The computational complexity of hybrid temporal logics, Logic Journal of the IGPL 8 (2000), pp. 653--679.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....transitive trees, E# = # PF#) However, the above result does not hold on the class of any frames: on general frames, HL(#, F, P) is as expressive as the bounded fragment of first order logic, a strict subfragment of first order logic [3] 3. 2 Complexity of the satisfiability problem In [2], the authors notice that on linear frames, we can get rid of nominals and as soon as we have at disposal (strict) past and future temporal operators. Indeed, we can simulate nominals by singleton propositions, that is propositions true at exactly one state: i is a singleton proposition iff ....

C. Areces, P. Blackburn, and M. Marx. The computational complexity of hybrid temporal logics. Logic Journal of the IGPL, 8(5):653--679, 2000.

....is a set ### together with a subset p # # of ### for each p # and a subset r # # of ### # for each r # . 674 Internalization: The Case of Hybrid Logics It may seem a little strange to focus on such a richly expressive language as H . Much of the research on hybrid languages (for example, [5, 6, 2, 1]) has concentrated on fragments of H with much less expressive power and correspondingly lower computational complexity. We ensure that the rules developed for H can be applied to fragments by insisting that they have a subformula property. On the strictest interpretation, a rule is said to have ....

C. Areces, P. Blackburn, and M. Marx. The computational complexity of hybrid temporal logics. Logic Journal of the IGPL, 8, 653--679, 2000.

.... is useful in many applications; nominals (as such individuals can be called) are a prominent feature of hybrid logics [Blackburn and Seligman, 1998] and various extensions of modal and description logics with nominals have already been investigated (see, e.g. Schaerf, 1994; De Giacomo, 1995; Areces et al. 2000] As we have seen, nominals occur naturally in ontologies as names for specific persons, companies, countries etcetera. From a semantic point of view, it is important to distinguish between a nominal and an atomic concept simple class, since the nominal stands for exactly one individual in ....

C. Areces, P. Blackburn, and M. Marx. The computational complexity of hybrid temporal logics. Logic Journal of the IGPL, 2000. To appear.

.... is useful in many applications; nominals (as such individuals can be called) are a prominent feature of hybrid logics [Blackburn and Seligman, 1998] and various extensions of modal and description logics with nominals have already been investigated (see, e.g. Schaerf, 1994; De Giacomo, 1995; Areces et al. 2000] As we have seen, nominals occur naturally in ontologies as names for specific persons, companies, countries etcetera. From a semantic point of view, it is important to distinguish between a nominal and an atomic concept simple class, since the nominal stands for exactly one individual in ....

C. Areces, P. Blackburn, and M. Marx. The computational complexity of hybrid temporal logics. Logic Journal of the IGPL, 2000. To appear.

.... of the queen hybrid logics with ExpTime complete reasoning problems: our result extends ExpTime completeness results for, e.g. Priorean tense logic over transitive frames (which can be viewed as a notational variant of multimodal K4 with converse modalities) or converse PDL with nominals in [1]. 2 Preliminaries In this section, we introduce syntax and semantics of the hybrid calculus as well as two way automata. It is the extension of the propositional calculus with converse programs [40] a universal role, and nominals [30, 1] i.e. atomic formulae to refer to single points. De ....

....with converse modalities) or converse PDL with nominals in [1] 2 Preliminaries In this section, we introduce syntax and semantics of the hybrid calculus as well as two way automata. It is the extension of the propositional calculus with converse programs [40] a universal role, and nominals [30, 1], i.e. atomic formulae to refer to single points. De nition 1. Let AP be a set of atomic propositions, Var a set of propositional variables, Nom a set of nominals, and Prog a set of atomic programs with the universal program o 2 Prog. A program is either an atomic program or the converse a of an ....

C. Areces, P. Blackburn, and M. Marx. The computational complexity of hybrid temporal logics. Logic Journal of the IGPL, 8(5), 2000.

....basic modal language is Pspace complete, and we remain in Pspace if we add nominals and satisfaction operators. And the satisfaction problem for Propositional Dynamic Logic is ExpTime complete, and we remain in ExpTime is we add nominals, satisfaction operators, and even the global modality. See [4] for further discussion. 3. General completeness results. One of the oldest themes in hybrid logic is that hybridization leads to simpler and more general completeness results. In a nutshell, this is because the presence of nominals and satisfaction operators makes it possible to combine the ....

....of satisfaction operators, for A(i ) and E(i ) mean exactly the same thing as i . To some extent it s a matter of taste which approach is adopted, though it s worth knowing that adding nominals and satisfaction operators to the basic modal language does not take us out of Pspace (see [4]) whereas adding the global modality (even if we don t add nominals) leads to an ExpTime complete satisfaction problem (see [39] Binders A great deal could be said about binding. The basic idea is this: nominals, although they are formulas, are rather like the constants of rst order ....

[Article contains additional citation context not shown here]

C. Areces, P. Blackburn, and M. Marx. The computational complexity of hybrid temporal logics. Logic Journal of the IGPL, 8(5):653-679, 2000.

....or times, mechanisms such as nominals, satisfaction operators, binders, and quantifiers. Such mechanisms increase the expressive power of the underlying temporal (or modal) logic in a natural way, and in many interesting cases their introduction does not raise the computational complexity (see [2]) Moreover, hybrid logic has a number of relatives. For example, it is closely related to description logic (see [1] In addition, a formalism called half order modal logic, using freeze quantifiers to bind variables to the content of the current instant of evaluation, was independently ....

C. Areces, P. Blackburn, and M. Marx, The Computational Complexity of Hybrid Temporal Logics, Logic Journal of IGPL, 8(5), 2000, 653--679.

....that we can have access to both converse programs and A on arbitrary frames and still stay in exptime. And in fact, we can: Theorem 5.3 The satis ability problem for nominal Propositional Dynamic Logic with converse programs and the universal modality is solvable in exptime. Proof. Proved in [ABM00] using a spypoint argument. qed Corollary 5.4 The local K satis ability problem for H t ( plus the universal modality is exptime complete. Because of the availability of the Kleene star in PDL, we can also establish the exptime completeness of H t ( over transitive frames. More ....

....star in PDL, we can also establish the exptime completeness of H t ( over transitive frames. More interestingly, the complexity of H t ( drops back to pspace or below when considering more structured classes of frames, such as linear orders or transitive trees. For a full discussion, see [ABM00] 5.3 Sharpening Undecidability When H(#; is rst encountered, a common reaction is that it must be decidable: it seems plausible that some sort of # elimination argument could reduce its satis ability problem to that of H( But Theorem 3.11 tells us that every formula in the bounded ....

C. Areces, P. Blackburn, and M. Marx. The computational complexity of hybrid temporal logics. To appear in the Logic Journal of the IGPL, 2000.

No context found.

Areces, C., P. Blackburn and M. Marx, The computational complexity of hybrid temporal logics, Logic Journal of the IGPL 8 (2000), pp. 653--679.

No context found.

C. Areces, P. Blackburn, and M. Marx. The computational complexity of hybrid temporal logics. Logic Journal of the IGPL, 8(5):653--679, 2000.

No context found.

C. Areces, P. Blackburn, and M. Marx. The computational complexity of hybrid temporal logics. Logic Journal of the IGPL, 8:653--679, 2000.

No context found.

Areces, C., P. Blackburn and M. Marx, The computational complexity of hybrid temporal logics, Logic Journal of the IGPL 8 (2000), pp. 653-679.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC