Diana Cukierman

TIME Conference 2004 Conference Paper

The SOL Time Theory: A Formalization of Structured Temporal Objects and Repetition

• Diana Cukierman
• James P. Delgrande

We propose to formally represent time with structured temporal objects. Structured temporal objects denote related time intervals (and recursively, related temporal objects) which are conceived as structured objects, rather than relations among such intervals. The major emphasis in this approach is on temporal repetition. To that effect, a new temporal object, the time loop, is defined. The intent of a time loop is to capture a structured notion of repetition. We propose a first order theory formalizing these objects. The building blocks of this formalism are time intervals and Allen's qualitative interval relations. We prove a number of key desirable results including the consistency of the theory, and extensively compare expressions in this theory with previous related work. We argue that this theory presents temporality and temporal repetition in a simple, commonsense manner. Furthermore, we argue that it presents an alternative, succinct and more general view than previous proposals to represent temporal repetition.

TIME Conference 2000 Conference Paper

A Formalization of Structured Temporal Objects and Repetition

• Diana Cukierman
• James P. Delgrande

We propose an approach to formally representing structured temporal objects. These new temporal objects are recursively made up of convex intervals and Allen's convex relations. The major emphasis in our approach is on temporal repetition. To that effect we define the time loop. Time loops allow us to abstract common elements in repetitive temporal patterns. A loop is parameterized by a cycle which is a structured temporal element possibly including subloops, a relation between instances of the cycle and a repetition factor or dimension. Atemporal assertions are true during these temporal objects, and thus this formalism allows one to concisely represent and reason with assertions which have an inherent temporal structure. Hence, this formalism allows one to concisely represent, for example, the scheduling of regular meetings in a university, where meeting may in turn be composed of structured repetitive processes such as those occurring in an assembly line.

ECAI Conference 2000 Conference Paper

A Formalization of Structured Temporal Objects and Repetition

• Diana Cukierman
• James P. Delgrande

TIME Conference 1998 Conference Paper

Towards a Formal Characterization of Temporal Repetition with Closed Time

• Diana Cukierman
• James P. Delgrande

Proposes a novel approach to formally characterize temporal repetition. This differs from what has appeared so far in the AI/temporal reasoning literature, where time and particularly temporal repetition are represented within a linear structure. We propose to model temporal objects representing repetition with a closed time structure. Based on convex intervals and J. F. Allen's (1983) convex relations, we define a new temporal object: the time loop. Such an object captures in one cycle the core of what is repeated and which relations hold between each repetition. Hence, this formalism allows one, for example, to concisely represent the scheduling of regular meetings in a university, to specify calendars and to represent repetitive processes, such as those occurring in an assembly line.

TIME Conference 1996 Conference Paper

Characterizing Temporal Repetition

• Diana Cukierman
• James P. Delgrande

This paper is a preliminary investigation of temporal repetition. We review work in Artificial Intelligence of both formal and practical systems that deal with repetitive temporal objects (i. e. repetitive points and/or intervals). We analyze the essence of repetition, and present an extensive classification of types of repetition.

AAAI Conference 1996 Short Paper

Characterizing Temporal Repetition

• Diana Cukierman

We are investigating the representation and reasoning about schedulable, repeated activities, specified using calendars. Examples of such activities include meeting every Tuesday and Thursday during a semester and at tending a seminar every first day of a month. This research provides for a valuable framework for scheduling systems, financial systems and, in general, date-based systems. Very recently work has been done related to reasoning about repetition in the Artificial Intelligence community and others. A partial reference list is provided here. However, to our knowledge no extensive taxonomy of repetition has been proposed in the literature. We believe that reasoning about repeated activities calls for a study and precise definition of the topological characteristics in a repetitive series. In this abstract we summarize a proposal to classify types of repetition according to parameters. The combination of all possible values of these parameters provides a complete taxonomy of repetitive classes with respect to the proposed parameters. Several notions of repetition are considered, some are extremely general, some are very specific.

AAAI Conference 1994 Short Paper

Time Units and Calendars

• Diana Cukierman

We are investigating a formal representation of time units and calendars, as restricted temporal entities for reasoning about activities. We examine characteristics of time units, and provide a categorization of the hierarchical relations among them. Hence we define an abstract hierarchical unit structure (a calendar structure) that expresses specific relations and properties among the units that compose it. Calendar structures subsume systems that can be based on discrete units together with a repetitive containment relation.