F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In Exploring Artificial Intelligence in the New Millenium, pages 175--216. Morgan Kaufmann, 2002. 5  Home/Search   Document Details and Download   Summary   Related Articles   Check

....method requires representation of all possible first order models, while the resolution method requires the maximal combination of all temporal clauses. In this paper, we focus on an important subclass of temporal models, having a wide range of applications, for example in spatio temporal logics [21, 10] and temporal description logics [1] namely those models that have expanding domains. In such models, the domains over which first order terms range can increase at each temporal step. The focus on this class of models allows us to produce a simplified clausal resolution calculus, termed a ....

F. Wolter and M. Zakharyaschev. Qualitative spatiotemporal representation and reasoning: a computational perspective. In Exploring Artificial Intelligence in the New Millenium, pages 175--216. Morgan Kaufmann, 2002.

....considered using the completeness of the monodic temporal resolution calculus. Interestingly, the classification of temporal problems considered in Section 4 exactly corresponds to the classification of monodic formulae obtained by translation from distinctive fragments of spatio temporal logic [9, 10, 17]. Consequently, we are going to apply monodic temporal resolution to checking the satisfiability of formulae in spatiotemporal logic. The complexity of our reductions given in theorems 3, 4, and 5, within Section 4, agrees with the complexity bounds on corresponding spatio temporal fragments ....

....(Consequently, we are going to apply monodic temporal resolution to checking the satisfiability of formulae in spatiotemporal logic. The complexity of our reductions given in theorems 3, 4, and 5, within Section 4, agrees with the complexity bounds on corresponding spatio temporal fragments from [10, 17]. In Section 5 we consider an extension of the monodic fragment which allows a local next time operator to be applied to formulae with more than one free variable. Such kind of extension is motivated by possible applications in transaction protocol verification and temporal databases where ....

F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In G. Lakemeyer and B. Nebel, editors, Exploring Artifitial Intelligence in the New Millenium, pages 175--216. Morgan Kaufmann, 2002. 14

....method requires representation of all possible first order models, while the resolution method requires the maximal combination of all temporal clauses. In this paper, we focus on an important subclass of temporal models, having a wide range of applications, for example in spatio temporal logics [19, 9] and temporal description logics [1] namely those models that have expanding domains. In such models, the domains over which first order terms range can increase at each temporal step. The focus on this class of models allows us to produce a simplified clausal resolution calculus, termed a ....

F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In G. Lakemeyer and B. Nebel, editors, Exploring Artifitial Intelligence in the New Millenium, pages 175--216. Morgan Kaufmann, 2002. 13

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F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In G. Lakemeyer and B. Nebel, editors, Exploring Artifitial Intelligence in the New Millenium, pages 175--216. Morgan Kaufmann, 2002. 17

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F. Wolter and M. Zakharyaschev. Qualitative Spatiotemporal Representation and Reasoning: A Computational perspective. In Artificial Intelligence in the New Millenium, G. Lakemeyer and B. Nebel, eds, pp. 175--215. Morgan Kaufmann, 2002.

....) a : C) fa=xg (aRb) R fa=x; b=yg ( A ) A and similarly for the other temporal operators. It is readily checked that a formula is satis able i its rst order translation is satis able. Our second example is a family of logics devised in [59, 62] for qualitative representation and reasoning about spatial regions moving in time. The logics are obtained by combining (propositional) temporal logics with the region connection calculus RCC 8. 7 Recall that RCC 8 contains eight binary relations between regions in topological spaces: DC ....

....(FSA stands for the nite state assumption . In all these cases, the satis ability problem for spatio temporal formulas can be (polynomially) reduced to satis ability of rst order temporal formulas with only one individual variable. This (rather non trivial) reduction can be found in [62, 29]. 4 Natural borders of decidability The following theorems indicate some limits beyond which one cannot hope to nd decidable fragments of rst order temporal logics. Given a rst order temporal language T L and , we denote by T L the variable fragment of T L (i.e. every formula in T ....

[Article contains additional citation context not shown here]

F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In G. Lakemeyer and B. Nebel, editors, Exploring Arti cial Intelligence in the New Millenium, Morgan Kaufmann, 2001.

....fragments. This opens a way to various applications of the monodic FOTL in knowledge representation, temporal databases, program specification and verification, and other fields. For example, many temporal description logics and spatio temporal logics can be regarded as fragments of monodic FOTL [11, 6, 22]. Unfortunately, the decision procedures provided in [10] are of model theoretic character and cannot be used as a basis for implementations. In [1] a resolution based approach was developed for certain subfragments of the monodic fragment. A tableau based analysis of the decision problem for ....

....FOTL and for the temporalisation of the modal logic S4 u . These logics are su#ciently simple to serve as examples but also have some rather serious applications: The tableau system for 1 , i.e. the one variable fragment of FOTL, can be used for various spatio temporal reasoning tasks, see [22] for an embedding of spatiotemporal logics in this fragment. In the case of constant domains, the tableau for 1 actually yields a tableau decision procedure for the Cartesian product of propositional linear temporal logic PTL and S5 (see e.g. 6] The tableau system for the ....

F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In Exploring Artifitial Intelligence in the New Millenium. Morgan Kaufmann, 2002. In print.

....= T T ; T = T (A ) T = A T and similarly for the other temporal operators. It is readily checked that a DPCT L formula is satis able i its rst order translation T is satis able. 3. 2 Spatio temporal logics Our second example is a family of logics devised in [59, 62] for qualitative representation and reasoning about spatial regions moving in time. The logics are obtained by combining (propositional) temporal logics with the region connection calculus RCC 8. 7 Recall that RCC 8 contains eight binary relations between regions in topological spaces: DC ....

....(FSA stands for the nite state assumption . In all these cases, the satis ability problem for spatio temporal formulas can be (polynomially) reduced to satis ability of rst order temporal formulas with only one individual variable. This (rather non trivial) reduction can be found in [62, 29]. 4 Natural borders of decidability The following theorems indicate some limits beyond which one cannot hope to nd decidable fragments of rst order temporal logics. Given a rst order temporal language T L and , we denote by T L the variable fragment of T L (i.e. every formula in T ....

[Article contains additional citation context not shown here]

F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In G. Lakemeyer and B. Nebel, editors, Exploring Articial Intelligence in the New Millenium, Morgan Kaufmann, 2001.

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F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In Exploring Artificial Intelligence in the New Millenium, pages 175--216. Morgan Kaufmann, 2002. 5

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F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In G. Lakemeyer and B. Nebel, editors, Exploring Artifitial Intelligence in the New Millenium, pages 175--216. Morgan Kaufmann, 2002. 10

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F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In G. Lakemeyer and B. Nebel, editors, Exploring Artificial Intelligence in the New Millenium. Morgan Kaufmann, 2002. 10

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F. Wolter, M. Zakharyaschev, Qualitative spatio-temporal representation and reasoning: a computational perspective, in: Exploring Artificial Intelligence in the New Millenium, Morgan Kaufmann, 2002, pp. 175--216.

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F. Wolter and M. Zakharyaschev. Qualitative spatiotemporal representation and reasoning: a computational perspective. In G. Lakemeyer and B. Nebel, editors, Exploring Artifitial Intelligence in the New Millenium, pages 175--216. Morgan Kaufmann, 2002.

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