Temporal Data Modeling and Reasoning for Information Systems

Temporal knowledge representation and reasoning is a major research field in Artificial Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to model and process time and calendar data is essential for many applications like appointment scheduling, planning, Web services, temporal and active database systems, adaptive Web applications, and mobile computing applications. This article aims at three complementary goals. First, to provide with a general background in temporal data modeling and reasoning approaches. Second, to serve as an orientation guide for further specific reading. Third, to point to new application fields and research perspectives on temporal knowledge representation and reasoning in the Web and Semantic Web

Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order 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 automata-theoretic 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.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200

Clock specifications for temporal tasks in planning and learning

Recently, Linear Temporal Logics on finite traces, such as LTL (or LDL ), have been advocated as high-level formalisms to express dynamic properties, such as goals in planning domains or rewards in Reinforcement Learning (RL). This paper addresses the challenge of separating high-level temporal specifications from the low-level details of the underlying environment (domain or MDP), by allowing for expressing the specifications at a different time granularity than the environment. We study the notion of a clock which progresses the high-level LTL specification, whose ticks are triggered by dynamic (low-level) properties defined on the underlying environment. The obtained separation enables terse high-level specifications while allowing for very expressive forms of clock expressed as general LTL properties over low-level features, such as counting or occurrence/alternation of special events. We devise an automata-based construction to compile away the clock into a deterministic automaton that is polynomial in the size of the automata characterizing the high-level and clock specifications. We show the correctness of the approach and discuss its application in several contexts, including FOND planning, RL with LTL Restraining Bolts, and Reward Machines

Supporting Temporal Reasoning by Mapping Calendar Expressions to Minimal Periodic Sets

In the recent years several research efforts have focused on the concept of time granularity and its applications. A first stream of research investigated the mathematical models behind the notion of granularity and the algorithms to manage temporal data based on those models. A second stream of research investigated symbolic formalisms providing a set of algebraic operators to define granularities in a compact and compositional way. However, only very limited manipulation algorithms have been proposed to operate directly on the algebraic representation making it unsuitable to use the symbolic formalisms in applications that need manipulation of granularities. This paper aims at filling the gap between the results from these two streams of research, by providing an efficient conversion from the algebraic representation to the equivalent low-level representation based on the mathematical models. In addition, the conversion returns a minimal representation in terms of period length. Our results have a major practical impact: users can more easily define arbitrary granularities in terms of algebraic operators, and then access granularity reasoning and other services operating efficiently on the equivalent, minimal low-level representation. As an example, we illustrate the application to temporal constraint reasoning with multiple granularities. From a technical point of view, we propose an hybrid algorithm that interleaves the conversion of calendar subexpressions into periodical sets with the minimization of the period length. The algorithm returns set-based granularity representations having minimal period length, which is the most relevant parameter for the performance of the considered reasoning services. Extensive experimental work supports the techniques used in the algorithm, and shows the efficiency and effectiveness of the algorithm

Representing Calendar Expressions with Finite-State Transducers that Bracket Periods of Time on a Hierachical Timeline

Proceedings of the 16th Nordic Conference of Computational Linguistics NODALIDA-2007. Editors: Joakim Nivre, Heiki-Jaan Kaalep, Kadri Muischnek and Mare Koit. University of Tartu, Tartu, 2007. ISBN 978-9985-4-0513-0 (online) ISBN 978-9985-4-0514-7 (CD-ROM) pp. 355-362

On Relaxing Metric Information in Linear Temporal Logic

Metric LTL formulas rely on the next operator to encode time distances, whereas qualitative LTL formulas use only the until operator. This paper shows how to transform any metric LTL formula M into a qualitative formula Q, such that Q is satisfiable if and only if M is satisfiable over words with variability bounded with respect to the largest distances used in M (i.e., occurrences of next), but the size of Q is independent of such distances. Besides the theoretical interest, this result can help simplify the verification of systems with time-granularity heterogeneity, where large distances are required to express the coarse-grain dynamics in terms of fine-grain time units.Comment: Minor change

On Relaxing Metric Information in Linear Temporal Logic

This paper studies the equi-satisfiability of metric linear temporal logic (LTL) and its qualitative subset. Metric LTL formulas rely on the next operator to encode distances, whereas qualitative LTL formulas use only the until modality. The paper shows how to transform any metric LTL formula M into a qualitative one Q, such that Q and M are equi-satisfiable over words with variability bounded with respect to the largest distances used in M (i.e., occurrences of next), but the size of Q is independent of such distances. Besides the theoretical interest, these results may help simplify the verification of systems with time-granularity heterogeneity, where large distances are required to express the coarse-grain dynamic

Automata for branching and layered temporal structures: An investigation into regularities of infinite transition systems

This manuscript is a revised version of the PhD Thesis I wrote under the supervision of Prof. Angelo Montanari at Udine University. The leitmotif underlying the results herein provided is that, given any infinite complex system (e.g., a computer program) to be verified against a finite set of properties, there often exists a simpler system that satisfies the same properties and, in addition, presents strong regularities (e.g., periodicity) in its structure. Those regularities can then be exploited to decide, in an effective way, which property is satisfied by the system and which is not. Perhaps the most natural and effective way to deal with inherent regularities of infinite systems is through the notion of finite-state automaton. Intuitively, a finite-state automaton is an abstract machine with only a bounded amount of memory at its disposal, which processes an input (e.g., a sequence of symbols) and eventually outputs true or false, depending on the way the machine was designed and on the input itself. The present book focuses precisely on automaton-based approaches that ease the representation of and the reasoning on properties of infinite complex systems. The most simple notion of finite-state automaton, is that of single-string automaton. Such a device outputs true on a single (finite or infinite) sequence of symbols and false on any other sequence. We will show how single-string automata processing infinite sequences of symbols can be successfully applied in various frameworks for temporal representation and reasoning. In particular, we will use them to model single ultimately periodic time granularities, namely, temporal structures that are left-bounded and that, ultimately, periodically group instants of the underlying temporal domain (a simple example of such a structure is given by the partitioning of the temporal domain of days into weeks). The notion of single-string automaton can be further refined by introducing counters in order to compactly represent repeated occurrences of the same subsequence in the given input. By introducing restricted policies of counter update and by exploiting suitable abstractions of the configuration space for the resulting class of automata, we will devise efficient algorithms for reasoning on quasi-periodic time granularities (e.g., the partitioning of the temporal domain of days into years). Similar abstractions can be used when reasoning on infinite branching (temporal) structures. In such a case, one has to consider a generalized notion of automaton, which is able to process labeled branching structures (hereafter called trees), rather than linear sequences of symbols. We will show that sets of trees featuring the same properties can be identified with the equivalence classes induced by a suitable automaton. More precisely, given a property to be verified, one can first define a corresponding automaton that accepts all and only the trees satisfying that property, then introduce a suitable equivalence relation that refines the standard language equivalence and groups all trees being indistinguishable by the automaton, and, finally, exploit such an equivalence to reduce several instances of the verification problem to equivalent simpler instances, which can be eventually decided