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

Time granularity impact on propagation of disruptions in a system-of-systems simulation of infrastructure and business networks

System-of-systems (SoS) approach is often used for simulating disruptions to business and infrastructure system networks allowing for integration of several models into one simulation. However, the integration is frequently challenging as each system is designed individually with different characteristics, such as time granularity. Understanding the impact of time granularity on propagation of disruptions between businesses and infrastructure systems and finding the appropriate granularity for the SoS simulation remain as major challenges. To tackle these, we explore how time granularity, recovery time, and disruption size affect the propagation of disruptions between constituent systems of an SoS simulation. To address this issue, we developed a High Level Architecture (HLA) simulation of 3 networks and performed a series of simulation experiments. Our results revealed that time granularity and especially recovery time have huge impact on propagation of disruptions. Consequently, we developed a model for selecting an appropriate time granularity for an SoS simulation based on expected recovery time. Our simulation experiments show that time granularity should be less than 1.13 of expected recovery time. We identified some areas for future research centered around extending the experimental factors space.Comment: 26 pages, 11 figures, 2 tables, Submitted to International Journal of Environmental Research and Public Health: Special Issue on Cascading Disaster Modelling and Preventio

An efficient algorithm for minimizing time granularity periodical representations

This paper addresses the technical problem of efficiently reducing the periodic representation of a time granularity to its minimal form. The minimization algorithm presented in the paper has an immediate practical application: it allows users to intuitively define granularities (and more generally, recurring events) with algebraic expressions that are then internally translated to mathematical characterizations in terms of minimal periodic sets. Minimality plays a crucial role, since the value of the recurring period has been shown to dominate the complexity when processing periodic sets.

Processing count queries over event streams at multiple time granularities

Management and analysis of streaming data has become crucial with its applications in web, sensor data, network tra c data, and stock market. Data streams consist of mostly numeric data but what is more interesting is the events derived from the numerical data that need to be monitored. The events obtained from streaming data form event streams. Event streams have similar properties to data streams, i.e., they are seen only once in a fixed order as a continuous stream. Events appearing in the event stream have time stamps associated with them in a certain time granularity, such as second, minute, or hour. One type of frequently asked queries over event streams is count queries, i.e., the frequency of an event occurrence over time. Count queries can be answered over event streams easily, however, users may ask queries over di erent time granularities as well. For example, a broker may ask how many times a stock increased in the same time frame, where the time frames specified could be hour, day, or both. This is crucial especially in the case of event streams where only a window of an event stream is available at a certain time instead of the whole stream. In this paper, we propose a technique for predicting the frequencies of event occurrences in event streams at multiple time granularities. The proposed approximation method e ciently estimates the count of events with a high accuracy in an event stream at any time granularity by examining the distance distributions of event occurrences. The proposed method has been implemented and tested on di erent real data sets and the results obtained are presented to show its e ectiveness

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

Time granularity in simulation models within a multi-agent system

The understanding of how processes in natural phenomena interact at different scales of time has been a great challenge for humans. How information is transferred across scales is fundamental if one tries to scale up from finer to coarse levels of granularity. Computer simulation has been a powerful tool to determine the appropriate amount of detail one has to impose when developing simulation models of such phenomena. However, it has proved difficult to represent change at many scales of time and subject to cyclical processes. This issue has received little attention in traditional AI work on temporal reasoning but it becomes important in more complex domains, such as ecological modelling. Traditionally, models of ecosystems have been developed using imperative languages. Very few of those temporal logic theories have been used for the specification of simulation models in ecology. The aggregation of processes working at different scales of time is difficult (sometimes impossible) to do reliably. The reason is because these processes influence each other, and their functionality does not always scale to other levels. Thus the problems to tackle are representing cyclical and interacting processes at many scales and providing a framework to make the integration of such processes more reliable. We propose a framework for temporal modelling which allows modellers to represent cyclical and interacting processes at many scales. This theory combines both aspects by means of modular temporal classes and an underlying special temporal unification algorithm. To allow integration of different models they are developed as agents with a degree of autonomy in a multi-agent system architecture. This Ecoagency framework is evaluated on ecological modelling problems and it is compared to a formal language for describing ecological systems

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