Towards a general temporal theory

The research work presented herein addresses time representation and temporal reasoning in the domain of artificial intelligence. A general temporal theory, as an extension of Alien and Hayes', Gallon's and Vilain's theories, is proposed which treats both time intervals and time points on an equal footing; that is, both intervals and points are taken as primitive time elements in the theory. This means that neither do intervals have to be constructed out of points, nor do points have to be created as some limiting construction of intervals. This approach is different from that of Ladkin, of Van Beek, of Dechter, Meiri and Pearl, and of Maiocchi, which is either to construct intervals out of points, or to treat points and intervals separately. The theory is presented in terms of a series of axioms which characterise a single temporal relation, "meets", over time elements. The axiomatisation allows non-linear time structures such as branching time and parallel time, and additional axioms specifying the linearity and density of time are specially presented. A formal characterisation for the open and closed nature of primitive intervals, which has been a problematic question of time representation in artificial intelligence, is provided in terms of the "meets" relation. It is shown to be consistent with the conventional definitions of open/closed intervals which are constructed out of points. It is also shown that this general theory is powerful enough to subsume some representative temporal theories, such as Alien and Hayes's interval based theory, Bruce's and McDermott's point based theories, and the interval and point based theory of Vilain, and of Gallon. A finite time network based on the theory is specially addressed, where a consistency checker in two different forms is provided for cases with, and without, duration reasoning, respectively. Utilising the time axiomatisation, the syntax and semantics of a temporal logic for reasoning about propositions whose truth values are associated with particular intervals/points are explicitly defined. It is shown that the logic is more expressive than that of some existing systems, such as Alien's interval-based logic, the revised theory proposed by Gallon, Shoham's point-based interval logic, and Haugh's MTA based logic; and the corresponding problems with these systems are satisfactorily solved. Finally, as an application of the temporal theory, a new architecture for a temporal database system which allows the expression of relative temporal knowledge of data transaction and data validity times is proposed. A general retrieval mechanism is presented for a database with a purely qualitative temporal component which allows queries with temporal constraints in terms of any logical combination of Alien's temporal relations. To reduce the computational complexity of the consistency checking algorithm when quantitative time duration knowledge is added, a class of databases, termed time-limited databases, is introduced. This class allows absolute-time-stamped and relative time information in a form which is suitable for many practical applications, where qualitative temporal information is only occasionally needed, and the efficient retrieval mechanisms for absolute-time-stamped databases may be adopted

Open-World Probabilistic Databaseṡ

Abstract Large-scale probabilistic knowledge bases are becoming increasingly important in academia and industry alike. They are constantly extended with new data, powered by modern information extraction tools that associate probabilities with database tuples. In this paper, we revisit the semantics underlying such systems. In particular, the closed-world assumption of probabilistic databases, that facts not in the database have probability zero, clearly conflicts with their everyday use. To address this discrepancy, we propose an open-world probabilistic database semantics, which relaxes the probabilities of open facts to intervals. While still assuming a finite domain, this semantics can provide meaningful answers when some probabilities are not precisely known. For this openworld setting, we propose an efficient evaluation algorithm for unions of conjunctive queries. Our open-world algorithm incurs no overhead compared to closed-world reasoning and runs in time linear in the size of the database for tractable queries. All other queries are #P-hard, implying a data complexity dichotomy between linear time and #P. For queries involving negation, however, open-world reasoning can become NP-, or even NP PP -hard. Finally, we discuss additional knowledge-representation layers that can further strengthen open-world reasoning about big uncertain data

Real-time and Probabilistic Temporal Logics: An Overview

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

Non-constructive interval simulation of dynamic systems

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Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

Expressive Stream Reasoning with Laser

An increasing number of use cases require a timely extraction of non-trivial knowledge from semantically annotated data streams, especially on the Web and for the Internet of Things (IoT). Often, this extraction requires expressive reasoning, which is challenging to compute on large streams. We propose Laser, a new reasoner that supports a pragmatic, non-trivial fragment of the logic LARS which extends Answer Set Programming (ASP) for streams. At its core, Laser implements a novel evaluation procedure which annotates formulae to avoid the re-computation of duplicates at multiple time points. This procedure, combined with a judicious implementation of the LARS operators, is responsible for significantly better runtimes than the ones of other state-of-the-art systems like C-SPARQL and CQELS, or an implementation of LARS which runs on the ASP solver Clingo. This enables the application of expressive logic-based reasoning to large streams and opens the door to a wider range of stream reasoning use cases.Comment: 19 pages, 5 figures. Extended version of accepted paper at ISWC 201