A sound and complete reified temporal logic

There are mainly two known approaches to the representation of temporal information in Computer Science: modal logic approaches (including tense logics and hybrid temporal logics) and predicate logic approaches (including temporal argument methods and reified temporal logics). On one hand, while tense logics, hybrid temporal logics and temporal argument methods enjoy formal theoretical foundations, their expressiveness has been criticised as not power enough for representing general temporal knowledge; on the other hand, although current reified temporal logics provide greater expressive power, most of them lack of complete and sound axiomatic theories. In this paper, we propose a new reified temporal logic with a clear syntax and semantics in terms of a sound and complete axiomatic formalism which retains all the expressive power of the approach of temporal reification.

Characterizing the most general temporal constraint

This paper introduces a characterization of the so-called most general temporal constraint (GTC), which guarantees the common-sense assertion that "the beginning of the effect cannot precede the beginning of the cause". The formalism is based on general time theory which takes both points and intervals as primitive. It is shown that there are in fact 8 possible causal relationships which satisfy GTC, including cases where, on the one hand, effects start simultaneously with, during, immediately after, or some time after their causes, and on the other hand, events end before, simultaneously with, or after their causes. These causal relationships are versatile enough to subsume those representatives in the literature.

Deriving explanations from partial temporal information

The representation and manipulation of natural human understanding of temporal phenomena is a fundamental field of study in Computer Science, which aims both to emulate human thinking, and to use the methods of human intelligence to underpin engineering solutions. In particular, in the domain of Artificial Intelligence, temporal knowledge may be uncertain and incomplete due to the unavailability of complete and absolute temporal information. This paper introduces an inferential framework for deriving logical explanations from partial temporal information. Based on a graphical representation which allows expression of both absolute and relative temporal knowledge in incomplete forms, the system can deliver a verdict to the question if a given set of statements is temporally consistent or not, and provide understandable logical explanation of analysis by simplified contradiction and rule based reasoning.

The completeness and soundness of temporal theories

Generally speaking, the term temporal logic refers to any system of rules and symbolism for representing and reasoning about propositions qualified in terms of time. In computer science, particularly in the domain of Artificial Intelligence, there are mainly two known approaches to the representation of temporal information: modal logic approaches including tense logic and hybrid temporal logic, and predicate logic approaches including temporal arguement method and reified temporal logic. On one hand, while tense logic, hybrid temporal logic and temporal argument method enjoy formal theoretical foundations, their expressiveness has been criticised as not power enough for representing general temporal knowledge; on the other hand, although reified temporal logic provides greater expressive power, most of the current systems following the temporal reification lack of complete and sound axiomatic theories. With there observations in mind, a new reified temporal logic with clear syntax and semantics in terms of a sound and complete axiomatic formalism is introduced in this paper, which retains all the expressive power of temporal reification.

Temporal pattern recognition in video clips detection

Temporal representation and reasoning plays an important role in Data Mining and Knowledge Discovery, particularly, in mining and recognizing patterns with rich temporal information. Based on a formal characterization of time-series and state-sequences, this paper presents the computational technique and algorithm for matching state-based temporal patterns. As a case study of real-life applications, zone-defense pattern recognition in basketball games is specially examined as an illustrating example. Experimental results demonstrate that it provides a formal and comprehensive temporal ontology for research and applications in video events detection.