An analysis of the temporal relations of intervals in relativistic space-time

Rodríguez, Rita V.; Anger, Frank D.

doi:10.1007/3-540-56735-6_51

Cited by 5 publications

(5 citation statements)

References 8 publications

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“…Further evidence for the utility of orthocurrence appears in Pratt (2000) and Rodriguez and Anger (2001), where Allen interval algebras for various models of time, previously obtained tediously by ad hoc manual methods (Anger and Rodriguez 1991;Rodriguez and Anger 1993a;Rodriguez and Anger 1993b), are all obtained uniformly and automatically using orthocurrence. Further evidence for the utility of orthocurrence appears in Pratt (2000) and Rodriguez and Anger (2001), where Allen interval algebras for various models of time, previously obtained tediously by ad hoc manual methods (Anger and Rodriguez 1991;Rodriguez and Anger 1993a;Rodriguez and Anger 1993b), are all obtained uniformly and automatically using orthocurrence.…”

Section: Rationalementioning

confidence: 96%

“…Our standard example of orthocurrence has long been that of trains passing through stations, which this paper spices up with examples involving pigeons choosing holes subject to various constraints. Further evidence for the utility of orthocurrence appears in Pratt (2000) and Rodriguez and Anger (2001), where Allen interval algebras for various models of time, previously obtained tediously by ad hoc manual methods (Anger and Rodriguez 1991;Rodriguez and Anger 1993a;Rodriguez and Anger 1993b), are all obtained uniformly and automatically using orthocurrence.…”

Section: Rationalementioning

confidence: 96%

“…Referring to the original interval algebra as characterising linear time, they treat partially ordered time and relativistic time using 4 and 6 binary relations, respectively, to give 29 and 82 interval relationships, respectively (Anger and Rodriguez 1991;Rodriguez and Anger 1993a;Rodriguez and Anger 1993b). Partially ordered time corresponds to tracks that diverge only temporarily, with the same notion || of incomparability as above, while relativistic time is the same with two additional relations describing one endpoint at the point of divergence or convergence with the other on the diverged section, which corresponds to the boundary of the relativistic light cone.…”

Section: Comparison With Rodriguez-anger Branching Timementioning

confidence: 99%

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Transition and cancellation in concurrency and branching time

Pratt

2003

Math. Struct. Comp. Sci.

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We review the conceptual development of (true) concurrency and branching time starting from Petri nets and proceeding via Mazurkiewicz traces, pomsets, bisimulation, and event structures up to higher dimensional automata (HDAs), whose acyclic case may be identified with triadic event structures and triadic Chu spaces. Acyclic HDAs may be understood as extending the two truth values of Boolean logic with a third value expressing transition. We prove the necessity of such a third value under mild assumptions about the nature of observable events, and show that the expansion of any complete Boolean basis L to L with a third literal a expressing a = forms an expressively complete basis for the representation of acyclic HDAs. The main contribution is a new value × of cancellation, which is a sibling of , serving to distinguish a(b + c) from ab + ac while simplifying the extensional definitions of termination XA and sequence A B. We show that every HDAX (acyclic HDA with ×) is representable in the expansion of L to L × with a fourth literal a expressing a = ×.

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Section: Rationalementioning

confidence: 96%

Section: Rationalementioning

confidence: 96%

Section: Comparison With Rodriguez-anger Branching Timementioning

confidence: 99%

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Transition and cancellation in concurrency and branching time

Pratt

2003

Math. Struct. Comp. Sci.

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“…F. Anger and R. Rodriguez (Anger and Rodriguez 1991;Rodriguez and Anger 1993b;Rodriguez and Anger 1993a) have generalized Allen's 13 primitive relationships or states to richer situations motivated by relativistic considerations. In Allen's interval algebra a pair of endpoints one from each interval can only stand in three relationships to each other: before, at or after.…”

Section: Generalizations Of Allen's Interval Algebramentioning

confidence: 99%

Higher dimensional automata revisited

Pratt

2000

Math. Struct. Comp. Sci.

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The dual of a true concurrency schedule appears to be a false concurrency automaton, a paradox we resolved in a previous paper by extending the latter to higher dimensions. This extension may be formalized via such discrete geometries as n-categories, simplicial complexes, cubical complexes, and Chu spaces. We advocate the last as having a clear notion of event, a well-defined process algebra uniformly extending that for event structures, and ease of extension beyond the basic before-during-after analysis.

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“…The development of particular exam- [3]. In the case of relativistic space-time, Rodriguez [25,27] encountered 82 atomic interval relations. The case of spatial relations leads to further complications due to the diverse interpretations of "order" in space: frequently a collection of relations such as inside-outside, above-below, and intersectingdisjoint induces a collection of independent partial orders [22,23,14].…”

Section: The Lattice Of Temporal Relationsmentioning

confidence: 99%

Lattice structure of temporal interval relations

Anger

Rodríguez

1996

Appl Intell

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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.

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An analysis of the temporal relations of intervals in relativistic space-time

Cited by 5 publications

References 8 publications

Transition and cancellation in concurrency and branching time

Transition and cancellation in concurrency and branching time

Higher dimensional automata revisited

Lattice structure of temporal interval relations

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