An algebraic representation of calendars.

This paper uses an algebraic approach to define temporal granularities and calendars. All the granularities in a calendar are expressed as algebraic expressions based on a single "bottom" granularity. The operations used in the algebra directly reflect the ways with which people construct new granularities from existing ones, and hence yield more natural and compact granularities definitions. Calendar is formalized on the basis of the algebraic operations, and properties of calendars are studied. As a step towards practical applications, the paper also presents algorithms for granule conversions between granularities in a calendar

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

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

A visual language for temporal specifications based on Spider diagrams

Spider Diagrams are a well-established visual language to specify sets, their relationships, and constraints on their cardinalities. However, they do not support evolution of specifications, where one wants to state that under certain circumstances a specification becomes invalid and a new one must be used, nor transformation of specifications, where one needs operators to manipulate specifications. In this paper, we attack the first problem by developing a new system of timed Spider Diagrams which allow modellers to indicate the temporal range of validity of a specification. The approach is illustrated with examples of policies for library management

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

Unterstützung von Periodizität in Informationssystemen - Herausforderungen und Lösungsansätze

Die systemseitige Unterstützung von Periodizität bzw. periodischen Spezifikationen weist Anforderungen auf, die weit über die temporalen Fähigkeiten heutiger Informationssysteme hinausgehen. Im Allgemeinen charakterisieren periodische Spezifikationen Vorgänge, die aus regelmäßig wiederkehrenden Aktivitäten bestehen. Neben der Ausdrucksstärke ist die größte Herausforderung periodische Spezifikationen miteinander vergleichen zu können. Diese Vergleichbarkeit ist ein wichtiger Aspekt in einer Vielzahl von Anwendungen, etwa um vorausschauend sich eventuell ergebende potentielle Ressourcen- oder Terminkonflikte erkennen zu können. Erschwert wird dieses durch unterschiedliche (zeitliche) Granularitäten sowie Ausnahmen in entsprechenden Spezifikationen. Für den praktischen Einsatz ist es darüber hinaus unumgänglich, periodische Zusammenhänge auch im Kontext einer großen (umfangreichen) Menge periodischer Daten effizient verwalten und auswerten zu können. Der vorliegende Beitrag gibt einen Einblick in die Herausforderungen sowie einen Überblick zu in der aktuellen Literatur vorliegenden Lösungsansätzen einer systemseitigen Unterstützung von periodischen Spezifikationen