E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997. Home/Search Document Details and Download
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Description Logics as Ontology Languages for the Semantic Web - Baader, Horrocks, Sattler (2003) (20 citations) (Correct)
....decidability of extended with a slightly more general type of concrete domains is shown. Concerning nominals, things become a bit more complicated. Firstly, it can be shown that extended with nominals is a fragment of C2, the twovariable fragment of first order logic with counting quantifiers [39, 65, 77]. Thus, satisfiability and subsumption are decidable in NExpTime. This is optimal since the problem is also NExpTime hard [77] Roughly speaking, the combination of GCIs (or transitive roles and role hierarchies) inverse roles, and number restrictions with nominals is responsible for this leap in ....
E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Proc. of the 12th Ann. IEEE Symp. on Logic in Computer Science (LICS-97), 1997. Available via http://speedy.informatik.rwth-aachen.de/WWW/papers.html.
DAML+OIL: a Reason-able Web Ontology Language - Horrocks (2002) (Correct)
....value that is equal to every one of the specified data values and is an instance of every one of the specified data types. 5 Research Challenges for DAML OIL Class consistency subsumption reasoning in DAML OIL is know to be decidable (as it is contained in the C2 fragment of first order logic [14]) but many challenges remain for implementors of practical reasoning systems, i.e. systems that perform well with the kinds of reasoning problem generated by realistic applications. 5.1 Individuals The OIL language was designed so that it could be mapped to the DL, thereby providing a ....
E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Proc. of the 12th IEEE Symp. on Logic in Computer Science (LICS'97), pages 306--317. IEEE Computer Society Press, 1997.
Reasoning with Expressive Description Logics: Theory and Practice - Horrocks (2002) (3 citations) (Correct)
.... been used in first order theorem provers, e.g. the proof condensation technique employed in the HARP theorem prover [45] 6 Research Challenges for DAML OIL Class consistency subsumption reasoning in DAML OIL is know to be decidable (as it is contained in the C2 fragment of first order logic [21]) but many challenges remain for implementors of practical reasoning systems, i.e. systems that perform well with the kinds of reasoning problem generated by realistic applications. 6.1 Individuals The OIL language was designed so that it could be mapped to the DL, thereby providing a ....
E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Proc. of the 12th IEEE Symp. on Logic in Computer Science (LICS'97), pages 306--317. IEEE Computer Society Press, 1997.
Controlled Model Exploration - Infante-Lopez, Areces, de Rijke (Correct)
....forms. Finite variable fragments of first order logic are yet another family of fragments whose computational properties have been studied extensively, with decidability results going back to the early 1960s [20] while the late 1990s saw detailed complexity analyses of the two variable fragment [10, 11, 16]. Despite the fact that the computational properties of prenex normal form and finite variable fragments have been (almost) completely investigated, these fragments leave something to be desired: their meta logical properties are often poor, and, in particular, they usually do not enjoy a decent ....
E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Proceedings of LICS 1997.
On Expressive Description Logics with Composition of Roles in.. - Grandi (2002) (1 citation) (Correct)
....a sound and complete Tableau algorithm for deciding satisfiability (#) concepts. They also observed that is decidable since #, #) concepts can easily be translated into a formula in [6] that is the two variable FOL fragment with counting quantifiers, which has proved to be decidable [17]. In fact, satisfiability of formulae can be decided in NExpTime [23] if unary coding of numbers is used (which is a common assumption in the field of Description Logics; if binary coding is adopted we have a 2 NExpTime upper bound) We can further observe that a similar translation is still ....
E. Gradel, M. Otto, and E. Rosen. Two-variable Logic with Counting is Decidable. In Proc. Annual IEEE Symp. on Logic in Computer Science (LICS'97), pages 306-- 317, 1997.
Decomposing Modal Logic - Infante-Lopez, Areces, de Rijke (2002) (Correct)
....forms. Finite variable fragments of first order logic are yet another family of fragments whose computational properties have been studied extensively, with decidability results going back to the early 1960s [18] while the late 1990s saw detailed complexity analyses of the two variable fragment [9, 10, 15]. Despite the fact that the computational properties of prenex normal form and finite variable fragments have been (almost) completely investigated, these fragments leave something to be desired: their meta logical properties are often poor, and, in particular, they usually do not enjoy a decent ....
E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Proceedings of LICS 1997.
The Complexity of the Graded µ-Calculus - Kupferman, Sattler, Vardi (Correct)
....satisfy a formula. In many logics, these quantifiers 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 ....
E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Proc. of LICS-97, 1997.
Finite Variable Logics In Descriptive Complexity Theory - Grohe (1998) (4 citations) (Correct)
.... A distinguishing feature of L 2 compared to all L k for k 2 is the decidability of its satisfiability problem (due to Mortimer [60] Starting with a paper of Gradel, Kolaitis, and Vardi [24] the complexity of the satisfiability problem for 2 variable logics has been studied systematically [27, 28, 65]. See [26] for a survey on 2 variable logics. However, our emphasis is on logics with three or more variables. Central issues are the complexity of equivalence testing and the complexity of computing canonical models for finite variable theories. As we will see, these questions are closely ....
E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Proceedings of the 12th IEEE Symposium on Logic in Computer Science, pages 306--317, 1997.
On Spatial Conjunction as Second-Order Logic - Kuncak, Rinard (2004) (Correct)
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E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
On Modular Pluggable Analyses Using Set Interfaces - Lam, Kuncak, Rinard (2003) (Correct)
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Erich Gradel, Martin Otto, and Eric Rosen. Two-variable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
On Generalized Records and Spatial Conjunction in Role Logic - Kuncak, Rinard (2004) (Correct)
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Erich Gradel, Martin Otto, and Eric Rosen. Two-variable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
On Decision Procedures for Set-Valued Fields - Kuncak, Rinard (2004) (Correct)
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Gradel, E., M. Otto and E. Rosen, Two-variable logic with counting is decidable, in: Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
On Role Logic - Kuncak, Rinard (2003) (Correct)
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Erich Gradel, Martin Otto, and Eric Rosen. Twovariable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
A Survey of Decidable First-Order Fragments and.. - Hustadt, Schmidt.. (2004) (Correct)
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E. Gradel, M. Otto, and E. Rosen. Two-Variable Logic with Counting is Decidable. In Proc. LICS'97, 1997.
On Modular Pluggable Analyses Using Set Interfaces - Lam, Kuncak, Rinard (2003) (Correct)
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Erich Gradel, Martin Otto, and Eric Rosen. Two-variable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
On Role Logic - Kuncak, Rinard (2003) (Correct)
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Erich Gradel, Martin Otto, and Eric Rosen. Twovariable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
On Generalized Records and Spatial Conjunction in Role Logic - Kuncak, Rinard (2004) (Correct)
No context found.
Erich Gradel, Martin Otto, and Eric Rosen. Two-variable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
Canonical Graph Shapes - Rensink (2004) (Correct)
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E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Logic in Computer Science, pp. 306--317. Computer Society Press, 1997.
A Logic of Local Graph Shapes - Rensink (2003) (Correct)
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E. Gradel, M. Otto, and E. Rosen. Two-variable logic with counting is decidable. In Twelfth Annual IEEE Symposium on Logic in Computer Science, pages 306--317. IEEE, Computer Society Press, 1997. 29
On Role Logic - Kuncak, Rinard (2003) (Correct)
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Erich Gradel, Martin Otto, and Eric Rosen. Twovariable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
Finite Model Reasoning in ALCQI is ExpTime-complete - Lutz, Sattler, Tendera (Correct)
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E. Gradel, M. Otto, and E. Rosen. Two-Variable Logic with Counting is Decidable. In Proceedings of Twelfth IEEE Symposium on Logic in Computer Science (LICS'97), 1997.
On Expressive Number Restrictions in Description Logics - Grandi (2001) (1 citation) (Correct)
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E. Gradel, M. Otto, and E. Rosen. Two-variable Logic with Counting is Decidable. In Proc. 12th Annual IEEE Symposium on Logic in Computer Science, 1997.
A Tableau Algorithm for - Fabio Grandi Ieiit (Correct)
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E. Gradel, M. Otto, and E. Rosen. Two-variable Logic with Counting is Decidable. In Proc. Annual IEEE Symp. on Logic in Computer Science (LICS'97), pages 306-- 317, 1997.
On Generalized Records and Spatial Conjunction in Role Logic - Kuncak, Rinard (2004) (Correct)
No context found.
Erich Gradel, Martin Otto, and Eric Rosen. Two-variable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
On Modular Pluggable Analyses Using Set Interfaces - Lam, Kuncak, Rinard (2003) (Correct)
No context found.
Erich Gradel, Martin Otto, and Eric Rosen. Two-variable logic with counting is decidable. In Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS `97, Warschau, 1997.
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