Rita V. Rodriguez

Temporal reasoning: A relativistic model

In 1983, Allen presented an ingenious method for the representation and maintenance of temporal information in the presence of imprecise, uncertain, and relative knowledge about time of occurrence. He introduced 13 relations between his primitive “temporal intervals,” providing for the expression of “any relationship which can hold between two intervals.” the model, however, did not address the problem of temporally incomparable events, such as events occurring in a distributed system without a common clock. Lamports interprocessor communication model furnishes an axiomatic system for describing such events and their possible relationships. This article demonstrates that Allens temporal model can be subsumed in a more general model based on Lamports axiomatics. It is further suggested that this extended model can provide the underpinnings of a temporal knowledge base containing time‐dependent information measured by unsynchronized clocks or in relativistic space‐time. In this model, the number of relations between intervals increases dramatically from Allens 13 or Lamports 2 or 3 to over 80. Within this context, a modification of Allens algorithm for the maintenance of a temporal reasoning system is presented, thus permitting the advantages of such a system to extend to reasoning about a wider range of phenomena.

A relativistic temporal algebra for efficient design of distributed systems

Adequate methods for checking the specification and design of distributed systems must allow for reasoning about asynchronous activities; efficient methods must perform the reasoning in polynomial time. This paper lays the groundwork for such an efficient deductive system by providing a very general temporal relation algebra that can be used by constraint propagation techniques to perform the required reasoning. Major choices exist when selecting an appropriate temporal model: discrete/dense, linear/nonlinear, and point/interval. James Allen and others have indicated the possible atomic relations between two intervals for the dense-linear-interval model, while Anger, Ladkin, and Rodriguez have shown those needed for a dense-branching-interval model. Rodriguez and Anger further developed a dense-relativistic-interval model based on Lamportsprecede andcan affect arrows, determining a large number of atomic relations. This paper shows that those same atomic relations are exactly the correct ones for intervals in dense relativistic space-time if intervals are taken as pairs of points (Es,Ef) in space-time such that it is possible to move fromEs toEf at less than the speed of light. The relations are defined and named consistently with the earlier work of Rodriguez and Anger, and the relationship between the two models is pursued. The relevance of the results to the verification of distributed specifications and algorithms is discussed.

Temporal complexity and software faults

Software developers use complexity metrics to predict development costs before embarking on a project and to estimate the likelihood of faults once the system is built. Traditional measures, however, were designed principally for sequential programs, providing little insight into the added complexity of concurrent systems or increased demands of real-time systems. For the purpose of predicting cost and effort of development, the CoCoMo model considers factors such as real-time and other performance requirements; for fault prediction, however, most complexity metrics are silent on concurrency. An outline for developing a measure of what we term temporal complexity, including significant and encouraging results of preliminary validation, is presented. 13 standard measures of software complexity are shown to define only two distinct domains of variance in module characteristics. Two new domains of variance are uncovered through 6 out of 10 proposed measures of temporal complexity. The new domains are shown to have predictive value in the modeling of software faults.<<ETX>>

Time, Tense and Relativity Revisited

Interest in the problem of expressing temporal relations between events in a coherent fashion has undergone a revival due to the creation of data bases and knowledge bases containing time-dependent information and also through the scrutiny of concurrent algorithms and real-time systems. Presented herein is a simple temporal model, designated an F-complex, which develops from a single future operator and a single order axiom yet encompasses several of the current proposals for models to systematize reasoning about one or more of the aforementioned areas. The rudimentary F-complex commits to no special ontology of time, giving the advantage of clarifying the properties which are common to most methods of temporal modeling. Concepts of past, future, and temporal precedence are formulated within the posited structure, allowing comparison to the published temporal models of Lamport [11], Allen [1], Milner [14], Rodriguez [17], and others [21]. Specifically, Allens thirteen linear-time and Rodriguezs eighty-two relativistic atomic relations are characterized, as well as the axiomatic scheme of Lamport. The models are treated more thoroughly than in [6]. Furthermore, the main theorem is strengthened.

Space, time, and computation: Trends and problems

At the International Joint Conference on Artificial Intelligence (IJCAI) in Chambéry, France, the authors organized and ran a Workshop on Spatial and Temporal Reasoning with the purpose of both presenting current research and development in these areas and fostering an interchange of ideas among attendees of differing interests. In particular, discussion was focussed on the interfaces between three separate concerns: spatial reasoning in AI, temporal reasoning in AI, and temporal methods for concurrent systems. The authors reflect on the outcome of the workshop as well as introduce the extended papers selected for this special issue. Research goals for the immediate future are presented.

Effective Scheduling of Tasks under Weak Temporal Interval Constraints

Numerous AI planning applications and real-time system scheduling problems do not fit the traditional scenarios of the scheduling literature; instead, they are better expressed in terms of the temporal interval relations between the tasks. Given a set of tasks and a set of constraints expressed in terms of the atomic temporal interval relations, the problem of finding the shortest consistent schedule often arises. In the most general situation, the interval constraints leave some degree of uncertainty: the problem is under-specified. It is first shown herein that, in the completely specified case, the greatest lower bound of all schedule lengths can be calculated as the “Size” of a chain of intervals playing a role similar to that of a critical path in the familiar critical path analysis. Subsequently, a heuristic search algorithm is presented to reduce the general under-determined case to a completely specified one.

An Analysis of the Temporal Relations of Intervals in Relativistic Space-Time

Concurrent systems are subject to a form of temporal uncertainty due to the non-deterministic order of execution. Distributed systems cause additional uncertainty by the lack of a common clock and the communication delays. Adequate methods for checking the specification and design of such systems must allow for sound reasoning about asynchronous activities, while automated methods should perform the reasoning in polynomial time. This paper presents the basis for such deductive systems through a very general temporal relation algebra which can be used with constraint propagation techniques. Based on intervals in relativistic space-time, it naturally incorporates the expression of uncertain and ambiguous temporal relations, as well as concurrent actions. The possible temporal relations are analyzed and named consistently with earlier work of the authors, followed by an explanation of the calculation of compositions of the atomic temporal relations. The resulting table of compositions is the cornerstone of a temporal constraint-based reasoner that presently supports a prototype concurrent system debugger by deducing from partial run-time information the existence of temporal behavior inconsistent with specifications.

Lattice structure of temporal interval relations

Due to increasing interest in representation of temporal knowledge, automation of temporal reasoning, and analysis of distributed systems, literally dozens of temporal models have been proposed and explored during the last decade. Interval-based temporal models are especially appealing when reasoning about events with temporal extent but pose special problems when deducing possible relationships among events. The paper delves deeply into the structure of the set of atomic relations in a class of temporal interval models assumed to satisfy density and homogeneity properties. An order structure is imposed on the atomic relations of a given model allowing the characterization of the compositions of atomic relations (or even lattice intervals) as lattice intervals. By allowing the utilization of lattice intervals rather than individual relations, this apparently abstract result explicitly leads to a concrete approach which speeds up constraint propagation algorithms.

Spatial and Temporal Reasoning

In the last few decades significant progress has been made in the area of spatial and temporal reasoning. There is a growing interest in this area, especially within the artificial intelligence community, which may be attributed to the large number of application domains in which one has to deal directly or indirectly with temporal or spatial information, or both. However, dealing with time and space is not restricted to artificial intelligence. The analysis of concurrent programs, for example, faces difficult temporal questions, while the design of complex hardware for modern computing machines is plagued by spatial problems. Geographic information systems, tracking systems, mobile networks, distributed systems, cooperating autonomous agents, distributed databases, planning, robot motion, and many other complex systems challenge the capabilities of existing knowledge representation methods and reasoning techniques. Even long-standing research areas such as natural language understanding and production line management are brimming with unanswered questions about the interpretation and control of time and space. There is a large body of methods and techniques to attack problems involving space and time, including nonmonotonic and modal logics, circumscription methods, chronological minimization methods, relation algebras, and applications of constraint-based reasoning. At the International Joint Conference on Artificial Intelligence (IJCAI) in Chambéry, France in 1993, a first Workshop on Spatial and Temporal Reasoning was held with the purpose of both presenting current research

Using Constraint Propagation to Reason about UnsynchronizedClocks

Numerous AI problems in planning, robot motion, distributed systems, cooperating agents, and intelligence gathering have domains with sub-collections of events or actions over time which are measured on incomparable or unsynchronized time scales from one to another. In such situations, a temporal model providing only a partial order on time moments is appropriate. Unlike a branching-time model, no sense of a common past and divergent futures occurs; unlike a “parallel worlds” model, check points or intercommunication between the sub-collections of events may exist, providing a true, rich partially ordered set of temporal information. In applications for which temporal intervals and their relations are appropriate, constraint propagation is a recognized reasoning tool. We discuss several temporal interval models and their relationship to one another but particularly focus on the general partial order model. In each model the emphasis is on the atomic relations, so we amplify on the meaning of atomic and show that what is atomic in one model may not be so in another. Utilizing results established earlier about the lattice properties of the models, the paper describes the closure of the atomic relations under composition and conjunction, relating the structures of relations in linear time, partially ordered time, and relativistic time. Lattice and algebraic isomorphisms explain what appeared to be only coincidental similarities between different models. The results are shown to provide especially efficient representations for constraint propagation algorithms.