We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORD-Horn subclass is a polynomial-time problem and show that the path-consistency method is sufficient for deciding satisfiability. Further, using an extensive machine-generated case analysis, we show that the ORD-Horn subclass is a maximal tractable subclass of the full algebra (assuming<F NaN> P6=NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations. This work has been supported by the German Ministry for Research and Technology (BMFT) under grant ITW 8901 8 as part of the WIP project and under grant ITW 9201 as part of the TACOS project. 1 1 Introduction Temporal information is often conveyed qualitatively by specifying the relative positions of time intervals such as ". . . point to the figure while explaining the performance of the system . . . "...

In this paper we address the problem of scalability in temporal reasoning. In particular, new algorithms for efficiently managing large sets of relations in the Point Algebra are provided. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a rnetagraph data structure. The approach is an extension of the time representation proposed by Schubert, Taugher and Miller in the context of story comprehension. The algorithms presented in this work concern the construction of a timegraph from a given set of relations and are implemented in a temporal reasoning system called TG-II. Experimental results show that our approach is very efficient, especially when the given relations admit representation as a collection of chains connected by relatively few cross-chain links. 1

Although the computational perspective on cognitive tasks has always played a major role in Artificial Intelligence, the interest in the precise determination of the computational costs that are required for solving typical AI problems has grown only recently. In this paper, we will describe what insights a computational complexity analysis can provide and what methods are available to deal with the complexity problem. This work was partially supported by the European Commission as part of DRUMS-II, the ESPRIT Basic Research Project P6156. 1 Introduction It is well-known that typical AI problems, such as natural language understanding, scene interpretation, planning, configuration, or diagnosis are computationally difficult. Hence, it seems to be worthless to analyze the computational complexity of these problems. In fact, some people believe that all AI problems are NP-hard or even undecidable. Conceiving AI as a scientific field that has as its goal the analysis and synthesis of...

Reasoning about temporal information is an important task in many areas of Artificial Intelligence. In this paper we address the problem of scalability in temporal reasoning by providing a collection of new algorithms for efficiently managing large sets of qualitative temporal relations. We focus on the class of relations forming the Point Algebra (PA-relations) and on a major extension to include binary disjunctions of PA-relations (PA-disjunctions). Such disjunctions add a great deal of expressive power, including the ability to stipulate disjointness of temporal intervals, which is important in planning applications. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a metagraph data structure. The approach is an extension of the time representation proposed by Schubert, Taugher and Miller in the context of story comprehension. The algorithms herein enable construction of a timegraph from a given set of PA-r...

We define the SAS + planning formalism, which generalizes the previously presented SAS formalism. The SAS + formalism is compared with some better-known propositionalplanning formalisms with respect to expressiveness. Contrary to intuition, all formalisms turn out to be equally expressive in a very strong sense. We further present the SAS + -PUS planning problem which generalizes the previously presented, tractable SASPUS problem. We prove that also the SAS + - PUS problem is tractable by devising a provably correct polynomial time algorithm for this problem. 1 Introduction Much effort has gone into finding more and more general formalisms, mainly logic-based, for plans and actions and also into finding reasoning methods for these. Although such formalisms may be important for modelling problems and comparing different approaches we most probably have to identify subproblems and devise tailored algorithms for these in order to overcome the computational difficulties involved. ...

. Temporal Constraint Satisfaction is an information technology useful for representing and answering queries about the times of events and the temporal relations between them. Information is represented as a Constraint Satisfaction Problem (CSP) where variables denote event times and constraints represent the possible temporal relations between them. The main tasks are two: (i) deciding consistency, and (ii) answering queries about scenarios that satisfy all constraints. This paper overviews results on several classes of Temporal CSPs: qualitative interval, qualitative point, metric point, and some of their combinations. Research has progressed along three lines: (i) identifying tractable subclasses, (ii) developing exact search algorithms, and (iii) developing polynomial-time approximation algorithms. Most available techniques are based on two principles: (i) enforcing local consistency (e.g. path-consistency), and (ii) enhancing naive backtracking search. Keywords: Temporal Constra...

Constraint-based formalisms are a useful and common way to deal with temporal reasoning tasks. Assertions represent temporal constraints between temporal objects, time-points or intervals. Metric temporal constraints between time points permit us to express a minimum and maximum temporal distance between two time points and to define a valid temporal interval for each one. However, existing approaches have limited expressiveness for representing non-disjunctive qualitative constraints of point algebra and the empirical results do not seem very adequate for managing a great number of time points or when the time for management is limited. In this paper, an efficient and expressive time point and duration-based temporal representation model with metric constraints is presented. The main features of the model refer to the formal properties of the internal time model and the specific representation of temporal constraints, which integrates constraints on timepoints and on durations and is ...

Abstract. Temporal reasoning started to be considered as a subject of study in artificial intelligence in the late ’70s. Since that several ways to represent and use temporal knowledge have been suggested. As a result of that there are several formalisms capable of coping with temporal notions in some way or other. They range from isolated proposals to complexsystems where the temporal aspect is used together with other important features for the task of modelling an intelligent agent. The purposes of this article are to summarize logic-based temporal reasoning research and give a glance on the different research tracks envisaging future lines of research. It is intended to be useful to those who need to be involved in systems having these characteristics and also an occasion to present newcomers some problems in the area that still wait for a solution.

We describe two domain-independent temporal reasoning systems called TimeGraph I and II which can be used in AI-applications as tools for efficiently managing large sets of relations in the Point Algebra, in the Interval Algebra, and metric information such as absolute times and durations. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a metagraph data structure. TimeGraph I was originally developed by Taugher, Schubert and Miller in the context of story comprehension. TimeGraph II provides useful extensions, including efficient algorithms for handing inequations, and relations expressing point-interval exclusion and interval disjointness. These extensions make the system much more expressive in the representation of qualitative information and suitable for a large class of applications. Keywords: Temporal reasoning systems, Point algebra, Interval Algebra, Scalable systems 1 1 Introduction We ...

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