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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 20 (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.
LTL over integer periodicity constraints
 PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE ON FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES (FOSSACS), VOLUME 2987 OF LNCS
, 2004
"... Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic PLTL mod, an extension of LinearTime Temporal Logic LTL with pasttime operators whose a ..."
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Cited by 12 (4 self)
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Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic PLTL mod, an extension of LinearTime Temporal Logic LTL with pasttime operators whose atomic formulae are defined from a firstorder constraint language dealing with periodicity. Although the underlying constraint language is a fragment of Presburger arithmetic shown to admit a pspacecomplete satisfiability problem, we establish that PLTL mod modelchecking and satisfiability problems remain in pspace as plain LTL (full Presburger LTL is known to be highly undecidable). This is particularly interesting for dealing with periodicity constraints since the language of PLTL mod has a language more concise than existing languages and the temporalization of our firstorder language of periodicity constraints has the same worst case complexity as the underlying constraint language. Finally, we show examples of introduction the quantification in the logical language that provide to PLTL mod, expspacecomplete problems. As another application, we establish that the equivalence problem for extended singlestring automata, known to express the equality of time granularities, is pspacecomplete by designing a reduction from QBF and by using our results for PLTL mod.
Time granularities and ultimately periodic automata
 Dipartimento di Matematica e Informatica, Universita di
, 2003
"... Abstract. The relevance of the problem of managing periodic phenomena is widely recognized in the area of knowledge representation and reasoning. One of the most eective attempts at dealing with this problem has been the addition of a notion of time granularity to knowledge representation systems ..."
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Abstract. The relevance of the problem of managing periodic phenomena is widely recognized in the area of knowledge representation and reasoning. One of the most eective attempts at dealing with this problem has been the addition of a notion of time granularity to knowledge representation systems. Dierent formalizations of such a notion have been proposed in the literature, following algebraic, logical, stringbased, and automatonbased approaches. In this paper, we focus our attention on the automatonbased one, which allows one to represent a large class of granularities in a compact and suitable to algorithmic manipulation form. We further develop such an approach to make it possible to deal with (possibly innite) sets of granularities instead of single ones. We dene a new class of automata, called Ultimately Periodic Automata, we give a characterization of their expressiveness, and we show how they can be used to encode and to solve a number of fundamental problems, such as the membership problem, the equivalence problem, and the problem of granularity comparison. Moreover, we give an example of their application to a concrete problem taken from clinical medicine. 1
Representing and reasoning about temporal granularities
 Journal of Logic and Computation
, 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 w ..."
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Cited by 6 (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 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.
On the Equivalence of Automatonbased Representations of Time Granularities
"... A time granularity can be viewed as the partitioning of a temporal domain in groups of elements, where each group is perceived as an indivisible unit. In this paper we explore an automatonbased approach to the management of time granularity that compactly represents time granularities as singlestr ..."
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A time granularity can be viewed as the partitioning of a temporal domain in groups of elements, where each group is perceived as an indivisible unit. In this paper we explore an automatonbased approach to the management of time granularity that compactly represents time granularities as singlestring automata with counters, that is, Büchi automata, extended with counters, that accept a single infinite word. We focus our attention on the equivalence problem for the class of restricted labeled singlestring automata (RLA for short). The equivalence problem for RLA is the problem of establishing whether two given RLA represent the same time granularity. The main contribution of the paper is the reduction of the (non)equivalence problem for RLA to the satisfiability problem for linear diophantine equations with bounds on variables. Since the latter problem has been shown to be NPcomplete, we have that the RLA equivalence problem is in coNP. 1.
Compact and Tractable Automatonbased Representations of Time Granularities
"... Most approaches to time granularity proposed in the literature are based on algebraic and logical formalisms [11]. Here we follow an alternative automatonbased approach, originally outlined in [7], which makes it possible to deal with infinite time granularities in an effective and efficient way. ..."
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Most approaches to time granularity proposed in the literature are based on algebraic and logical formalisms [11]. Here we follow an alternative automatonbased approach, originally outlined in [7], which makes it possible to deal with infinite time granularities in an effective and efficient way. Such an approach provides a neat solution to fundamental algorithmic problems, such as the granularity equivalence and granule conversion problems, which have been often neglected in the literature. In this paper, we focus our attention on two basic optimization problems for the automatonbased representation of time granularities, namely, the problem of computing the smallest representation of a time granularity and that of computing the most tractable representation of it, that is, the one on which crucial algorithms, such as granule conversion algorithms, run fastest. 1
Evaluating Exceptions on Time Slices
"... Abstract. Public transport schedules contain temporal data with many regular patterns that can be represented compactly. Exceptions come as modifications of the initial schedule and break the regular patterns increasing the size of the representation. A typical strategy to preserve the compactness o ..."
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Abstract. Public transport schedules contain temporal data with many regular patterns that can be represented compactly. Exceptions come as modifications of the initial schedule and break the regular patterns increasing the size of the representation. A typical strategy to preserve the compactness of schedules is to keep exceptions separately. This, however, complicates the automated processing of schedules and imposes a more complex model on applications. In this paper we evaluate exceptions by incorporating them into the patterns that define schedules. We employ sets of time slices, termed multislices, as a representation formalism for schedules and exceptions. The difference of multislices corresponds to the evaluation of exceptions and produces an updated schedule in terms of a multislice. We propose a relational model for multislices, provide an algorithm for efficient evaluating the difference of multislices, and show analytically and experimentally that the evaluation of exceptions is a feasible strategy for realistic schedules. 1
A Theory of Ultimately Periodic
"... Languages and Automata with an Application to Time Granularity Abstract In this paper, we develop a theory of regular ωlanguages that consist of ultimately periodic words only and we provide it with an automatonbased characterization. The resulting class of automata, called Ultimately Periodic Aut ..."
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Languages and Automata with an Application to Time Granularity Abstract In this paper, we develop a theory of regular ωlanguages that consist of ultimately periodic words only and we provide it with an automatonbased characterization. The resulting class of automata, called Ultimately Periodic Automata (UPA), is a subclass of the class of Büchi automata and inherits some properties of automata over finite words (NFA). Taking advantage of the similarities among UPA, Büchi automata, and NFA, we devise efficient solutions to a number of basic problems for UPA, such as the inclusion, the equivalence, and the size optimization problems. The original motivation for developing a theory of ultimately periodic languages and automata was to represent and to reason about sets of time granularities in knowledgebased and database systems. In the last part of the paper, we show that UPA actually allow one to represent (possibly infinite) sets of granularities, instead of single ones, in a compact and suitable to algorithmic manipulation way. In particular, we describe an application of UPA to a concrete time granularity scenario taken from clinical medicine. A short preliminary version of this paper appeared in [4].