What is a Qualitative Calculus? A General Framework

What is a qualitative calculus? Many qualitative spatial and temporal calculi arise from a set of JEPD (jointly exhaustive and pairwise disjoint) relations: a stock example is Allen's calculus, which is based on thirteen basic relations between interval

Allen's Interval Algebra Makes the Difference

Allen's Interval Algebra constitutes a framework for reasoning about temporal information in a qualitative manner. In particular, it uses intervals, i.e., pairs of endpoints, on the timeline to represent entities corresponding to actions, events, or tasks, and binary relations such as precedes and overlaps to encode the possible configurations between those entities. Allen's calculus has found its way in many academic and industrial applications that involve, most commonly, planning and scheduling, temporal databases, and healthcare. In this paper, we present a novel encoding of Interval Algebra using answer-set programming (ASP) extended by difference constraints, i.e., the fragment abbreviated as ASP(DL), and demonstrate its performance via a preliminary experimental evaluation. Although our ASP encoding is presented in the case of Allen's calculus for the sake of clarity, we suggest that analogous encodings can be devised for other point-based calculi, too.Comment: Part of DECLARE 19 proceeding

A general approach to temporal reasoning about action and change

Reasoning about actions and change based on common sense knowledge is one of the most important and difficult tasks in the artificial intelligence research area. A series of such tasks are identified which motivate the consideration and application of reasoning formalisms. There follows a discussion of the broad issues involved in modelling time and constructing a logical language. In general, worlds change over time. To model the dynamic world, the ability to predict what the state of the world will be after the execution of a particular sequence of actions, which take time and to explain how some given state change came about, i.e. the causality are basic requirements of any autonomous rational agent. The research work presented herein addresses some of the fundamental concepts and the relative issues in formal reasoning about actions and change. In this thesis, we employ a new time structure, which helps to deal with the so-called intermingling problem and the dividing instant problem. Also, the issue of how to treat the relationship between a time duration and its relative time entity is examined. In addition, some key terms for representing and reasoning about actions and change, such as states, situations, actions and events are formulated. Furthermore, a new formalism for reasoning about change over time is presented. It allows more flexible temporal causal relationships than do other formalisms for reasoning about causal change, such as the situation calculus and the event calculus. It includes effects that start during, immediately after, or some time after their causes, and which end before, simultaneously with, or after their causes. The presented formalism allows the expression of common-sense causal laws at high level. Also, it is shown how these laws can be used to deduce state change over time at low level. Finally, we show that the approach provided here is expressive

A Complete Classification of Tractability in RCC-5

We investigate the computational properties of the spatial algebra RCC-5 which is a restricted version of the RCC framework for spatial reasoning. The satisfiability problem for RCC-5 is known to be NP-complete but not much is known about its approximately four billion subclasses. We provide a complete classification of satisfiability for all these subclasses into polynomial and NP-complete respectively. In the process, we identify all maximal tractable subalgebras which are four in total.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl

On the representation of temporal knowledge

The growing interest in an adequate modelling of time in Artificial Intelligence has given rise to the research discipline of Temporal Reasoning (TR). Due to different views, different approaches towards TR such as PL1, modal logics or Allen\u27s intervall logic have been investigated. It was realized at an early stage that each of this approaches has some strong points whereas it suffers from certain drawbacks. Thus recently, a number of research activities have emerged aiming at a combination of the classical paradigms for representing time. In the first part of this paper, we present an overview of the most important approaches to the integration of temporal knowledge into logic programming. In the second part, we present the CRONOLOG temporal logic programming language which has been developed to cover the quintessence of the approaches presented before. The third part of the paper describes TRAM, which it is an extension of CRONOLOG to a temporal knowledge representation system. Using TRAM it is possible to represent knowledge depending on time and to reason about this knowledge. TRAM has been conceptually based on a combination of modal logics with Allen\u27s interval logic. We present the Extended Modal Logics (EML) which establishes the theoretical framework for TRAM. We define an operational semantics and a horizontal compilation scheme for TRAM

A Critical Review of Temporal Database Management Systems

There have been significant research activities in Temporal Databases during the last decade. However, the developments of a semantics of time, a temporal model for efficient database systems and temporal query languages still need much study. Based on the researches of the TDB group [Snodgrass 1987], the review of research about TDBMS in this dissertation mainly emphasises three aspects as follows. 1) The formulation of a semantics of time at the conceptual level. A topology of time and types of time attributes are introduced. A new taxonomy for time attributes is presented: assertion time, event time, and recording time. 2) The development of a model for TDBMS analogous to relational databases. Based on Snodgrass' classification, four kinds of databases: snapshot, rollback, historical and temporal are discussed in depth. But the discussion distinguishes some important differences from the representation of the TDB model: - historical relation for most enterprises is an interval relation, but not a sequence of snapshot slices indexed by valid time. The term "tuple" no longer simply refers to an entity as in traditional relational databases. It refers to different level representations of an object: entity, entity state, observation of entity, and observation of entity state in different types of databases. 3) The design of temporal query languages. We do not present a new temporal query language in this dissertation, but we discuss a Quel-like temporal query language, TQuel, in some depth. TQuel is compared with two other temporal query languages TOSQL and Legol 2.0. We centre the main discussion on TQuel's semantics for tuple calculus. The classification for the relationships between overlapping intervals suggests an approach using temporal logic to classify the derived tuples in tuple calculus. Under such an approach, a new presentation for tuple modification calculus is proposed, not only for interval relations, but also for event relations

A cognitive model for the representation of time in a man-machine dialogue.

This paper develops the foundations of a model for time representation in the framework of a man-machine dialogue system. While we analyse other approaches, especially Allen's interval calculus, we show how the relations that we commonly manipulate in everyday reasoning can in fact be reduced to two fondamental ones : succession and inclusion. By the way, we insist on the fact that a temporal model intended to reproduce some features of the human cognitive abilities shall include in a common representation linguistic information and conceptual objects. We then present the main characteristics of our temporal model, introducing the concept of coherence zone, and how this one can be used to represent tense information in natural language. Finally, we briefly show the mechanisms that ensure temporal consistency when combining new temporal information to an existing structure, and present the main elements that allow learning and predicting mechanisms within this model