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Temporal Representation and Reasoning in Artificial Intelligence: Issues and Approaches
, 2002
"... this paper, we survey a wide range of research in temporal representation and reasoning, without committing ourselves to the point of view of any speci c application ..."
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Cited by 15 (1 self)
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this paper, we survey a wide range of research in temporal representation and reasoning, without committing ourselves to the point of view of any speci c application
Representing and Reasoning about Temporal Granularities
, 2004
"... In this paper, we propose a new logical approach to represent and to reason about different time granularities. We identify a time granularity as an infinite sequence of time points properly labelled with proposition symbols marking the starting and ending points of the corresponding granules, and ..."
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Cited by 10 (0 self)
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In this paper, we propose a new logical approach to represent and to reason about different time granularities. We identify a time granularity as an infinite sequence of time points properly labelled with proposition symbols marking the starting and ending points of the corresponding granules, and we symbolically model sets of granularities by means of linear time logic formulas. Some realworld granularities are provided, from a clinical domain and from the Gregorian Calendar, to motivate and exemplify our approach. Different formulas are introduced, which represent relations between different granularities. The proposed framework permits one to algorithmically solve the consistency, the equivalence, and the classification problems in a uniform way, by reducing them to the validity problem for the considered linear time logic.
A Logical Approach to Represent and Reason about Calendars
, 2002
"... and reason about different time granularities. We identify a time granularity as a discrete infinite sequence of time points properly labelled with proposition symbols marking the starting and ending points of the corresponding granules, and we intensively model sets of granularities with linear tim ..."
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Cited by 7 (3 self)
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and reason about different time granularities. We identify a time granularity as a discrete infinite sequence of time points properly labelled with proposition symbols marking the starting and ending points of the corresponding granules, and we intensively model sets of granularities with linear time logic formulas. Some realworld granularities are provided, to motivate and exemplify our approach. The proposed framework permits to algorithmically solve the consistency, the equivalence, and the classification problems in a uniform way, by reducing them to the validity problem for the considered linear time logic.
The Taming (Timing) of the States
"... Logic and computer science communities have traditionally followed a different approach to the problem of representing and reasoning about time and states. Research in logic resulted in a family of (metric) tense logics that take time as a primitive notion and de ne (timed) states as sets of atomic ..."
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Cited by 7 (7 self)
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Logic and computer science communities have traditionally followed a different approach to the problem of representing and reasoning about time and states. Research in logic resulted in a family of (metric) tense logics that take time as a primitive notion and de ne (timed) states as sets of atomic propositions which are true at given instants, while research in computer science concentrated on the socalled (realtime) temporal logics of programs that take state as a primitive notion, and define time as an attribute of states. In this paper, we provide a unifying framework within which the two approaches can be reconciled. Our main tools are metric and layered temporal logics originally proposed to model time granularity in various contexts. In such a framework, states and time instants can be uniformly referred to as elements of a (decidable) theory of !layered metric temporal structures. Furthermore, we show that the theory of timed state sequences, underlying realtime logics, is na...
Extending Kamp's Theorem to Model Time Granularity
, 2001
"... In this paper, a generalization of Kamp's theorem relative to the functional completeness of the until operator is proved. Such a generalization consists in showing the functional completeness of more expressive temporal operators with respect to the extension of the rstorder theory of linear orde ..."
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Cited by 6 (6 self)
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In this paper, a generalization of Kamp's theorem relative to the functional completeness of the until operator is proved. Such a generalization consists in showing the functional completeness of more expressive temporal operators with respect to the extension of the rstorder theory of linear orders MFO[<] with an extra binary relational symbol. The result is motivated by the search of a modal language capable of expressing properties and operators suitable to model time granularity in !layered temporal structures.
Branching within Time: an Expressively Complete and Elementary decdable Temporal Logic for Time Granularity
 Journal of Language and Computation
, 2002
"... Suitable extensions of monadic secondorder theories of k successors have been proposed in the literature to specify in a concise way reactive systems whose behaviour can be naturally modeled with respect to a (possibly infinite) set of differentlygrained temporal domains. This is the case, for ins ..."
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Cited by 5 (5 self)
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Suitable extensions of monadic secondorder theories of k successors have been proposed in the literature to specify in a concise way reactive systems whose behaviour can be naturally modeled with respect to a (possibly infinite) set of differentlygrained temporal domains. This is the case, for instance, of the wideranging class of realtime reactive systems whose components have dynamic behaviours regulated by very different time constants, e.g., days, hours, and seconds. In this paper, we focus on the theory of krefinable downward unbounded layered structures i=0 ], that is, the theory of infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, whose satisfiability problem is nonelementarily decidable. We define a propositional temporal logic counterpart of MSO[< tot , (# i ) i=0 ] with set quantification restricted to infinite paths, called CTSL # k , which features an original mix of linear and branching temporal operators. We prove the expressive completeness of CTSL # k with respect to such a path fragment of MSO[< tot , (# i ) i=0 ] and show that its satisfiability problem is 2EXPTIMEcomplete.
The Way to Go: MultiLevel Temporal Logics
 Proceedings of IWTS'99: 1st International Workshop on Specification and Verification of Timed Systems, N. Yonezaki (Ed.) Kyoto Research Institute of Mathematical Science
, 1999
"... . In this paper we briefly survey the main contributions of our research on time granularity and outline some directions for current and future researches. The original motivation of our research was the design of a temporal logic embedding the notion of time granularity, suitable for the specif ..."
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. In this paper we briefly survey the main contributions of our research on time granularity and outline some directions for current and future researches. The original motivation of our research was the design of a temporal logic embedding the notion of time granularity, suitable for the specification of complex realtime systems, whose components evolve according to different time units. However, there are significant similarities between the problems we encountered in pursuing our goal, and those addressed by current research on combining logics, theories, and structures. Furthermore, exploiting interesting connections between multilevel temporal logics and automata theory that we recently established, a complementary point of view on time granularity arises: time granularity can be viewed not only as an important feature of a representation language, but as well as a formal tool to investigate expressiveness and decidability properties of temporal theories. Finally, a...
Model Checking for Combined Logics
 In Proceedings of the 3rd International Conference on Temporal Logic (ICTL
, 2000
"... We consider combined model checking procedures for the three ways of combining logics: temporalizations, independent combinations, and the join. We present results... ..."
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Cited by 4 (4 self)
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We consider combined model checking procedures for the three ways of combining logics: temporalizations, independent combinations, and the join. We present results...
Temporalized logics and automata for time granularity. Theory and Practice of Logic Programming
 Research on Language and Computation
, 2004
"... The ability of providing and relating temporal representations at different ‘grain levels’ of the same reality is an important research theme in computer science and a major requirement for many applications, including formal specification and verification, temporal databases, data mining, problem s ..."
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Cited by 4 (2 self)
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The ability of providing and relating temporal representations at different ‘grain levels’ of the same reality is an important research theme in computer science and a major requirement for many applications, including formal specification and verification, temporal databases, data mining, problem solving, and natural language understanding. In particular, the addition of a granularity dimension to a temporal logic makes it possible to specify in a concise way reactive systems whose behaviour can be naturally modeled with respect to a (possibly infinite) set of differentlygrained temporal domains. Suitable extensions of the monadic secondorder theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic secondorder theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automatatheoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them. 1