Formal Theories of Time and Temporal Incidence

Vila, Lluís

doi:10.1016/s1574-6526(05)80003-3

Cited by 11 publications

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“…Following [1], we do some operations like union and intersection over temporal intervals. We deal only with temporal intervals open on the left and closed on the right (to avoid the dividing instant problem [19]). …”

Section: The Event Calculusmentioning

confidence: 99%

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Event Calculus for Reasoning about Erlang Systems

́ndez

2011

2011 10th Mexican International Conference on Artificial Intelligence

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Section: The Event Calculusmentioning

confidence: 99%

“…Because the event A can inhibit at all sends(M 1 , P 3 , P 2 ), this atom is not placed within the body of clause (19), in contrast to clauses (17) and (18). Similarly, an event could omit any modification to M 0 , so that M 0 = M 1 .…”

Section: B Client-server Configurationsmentioning

confidence: 99%

Event Calculus for Reasoning about Erlang Systems

́ndez

2011

2011 10th Mexican International Conference on Artificial Intelligence

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Section: Introductionmentioning

confidence: 99%

“…A theory evaluating these is known as a theory of temporal incidence [17]. These, propositional entities, we refer to as eventualities in this paper following Galton [7] and generalizing Vila's fluent/state dichotomy [17]. Various taxonomies of temporal propositions have emerged over the years, starting from McDermott's dichotomy of facts and events to Allen's states/events/processes trichotomy [3], to Shoham's more elaborate classification, based on temporal properties [16].…”

Section: Introductionmentioning

confidence: 99%

The problem of coincidence in a theory of temporal multiple recurrence

Akinkunmi

2016

Journal of Applied Logic

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Logical theories have been developed which have allowed temporal reasoning about eventualities (a la Galton) such as states, processes, actions, events, processes and complex eventualities such as sequences and recurrences of other eventualities. This paper presents the problem of coincidence within the framework of a first order logical theory formalizing temporal multiple recurrence of two sequences of fixed duration eventualities and presents a solution to it The coincidence problem is described as: if two complex eventualities (or eventuality sequences) consisting respectively of component eventualities x 0 , x 1 ,....,x r and y 0 , y 1 , ..,y s both recur over an interval k and all eventualities are of fixed durations, is there a subinterval of k over which the incidence x t and y u for 0 t  r and 0  u  s coincide. The solution presented here formalizes the intuition that a solution can be found by temporal projection over a cycle of the multiple recurrence of both sequences.

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“…(3) The establishment of a truth-relation between temporal propositions and spatio-temporal reality, also termed the problem of temporal incidence (Vila, 2005). (4) The elaboration of a unifying formal axiomatization of the ontology of time and of material entities of the spatio-temporal reality, the formalization problem.…”

Section: Introductionmentioning

confidence: 99%

Axiomatic theories of the ontology of time in GFO

Baumann

Loebe

Herre³

2014

Applied Ontology

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Time is a pervasive notion of high impact in information systems and computer science altogether. Respective understandings of the domain of time are fundamental for numerous areas, frequently in combination with closely related entities such as events, changes and processes. The conception and representation of time entities and reasoning about temporal data and knowledge are thus significant research areas. Each representation of temporal knowledge bears ontological commitments concerning time. Thus it is important to base temporal representations on a foundational ontology that covers general categories of time entities.In this article we introduce and discuss two consecutive ontologies of time that have been developed for the top-level ontology General Formal Ontology (GFO). The first covers intervals, named chronoids, and time boundaries of chronoids, as a kind of time points. One important specialty of time boundaries is their ability to coincide with other time boundaries. The second theory extends the first one by additionally addressing time regions, i.e., mereological sums of chronoids.Both ontologies are partially inspired by ideas of Franz Brentano, especially from his writings about the continuum. In particular, we view continuous time intervals as a genuine phenomenon which should not be identified with intervals (sets) of real numbers. On these grounds the resulting ontologies allow for proposing novel contributions to several problematic issues in temporal representation and reasoning, among others, the Dividing Instant Problem and the problem of persistence and change.Following our general approach to ontology development, both ontologies are axiomatized as formal theories in first-order logic and are analyzed metalogically. We prove the consistency of both ontologies, and completeness and decidability for one. Moreover, standard time theories with points and intervals are covered by both theories.

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Formal Theories of Time and Temporal Incidence

Cited by 11 publications

References 0 publications

Event Calculus for Reasoning about Erlang Systems

Event Calculus for Reasoning about Erlang Systems

The problem of coincidence in a theory of temporal multiple recurrence

Axiomatic theories of the ontology of time in GFO

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