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96
Modelling Concurrency with Partial Orders
, 1986
"... Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic, inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a n ..."
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Cited by 236 (18 self)
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Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic, inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a natural class of models of concurrent processes. The heart of the approach is a notion of partial string derived from the view of a string as a linearly ordered multiset by relaxing the linearity constraint, thereby permitting partially ordered multisets or pomsets. Just as sets of strings form languages, so do sets of pomsets form processes. We introduce a number of operations useful for specifying concurrent processes and demonstrate their utility on some basic examples. Although none of the operations is particularly oriented to nets it is nevertheless possible to use them to express processes constructed as a net of subprocesses, and more generally as a system consisting of components. Th...
Temporal Reasoning Based on SemiIntervals
, 1992
"... A generalization of Allen's intervalbased approach to temporal reasoning is presented. The notion of `conceptual neighborhood' of qualitative relations between events is central to the presented approach. Relations between semiintervals rather than intervals are used as the basic units of knowledg ..."
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Cited by 234 (14 self)
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A generalization of Allen's intervalbased approach to temporal reasoning is presented. The notion of `conceptual neighborhood' of qualitative relations between events is central to the presented approach. Relations between semiintervals rather than intervals are used as the basic units of knowledge. Semiintervals correspond to temporal beginnings or endings of events. We demonstrate the advantages of reasoning on the basis of semiintervals: 1) semiintervals are rather natural entities both from a cognitive and from a computational point of view; 2) coarse knowledge can be processed directly; computational effort is saved; 3) incomplete knowledge about events can be fully exploited; 4) incomplete inferences made on the basis of complete knowledge can be used directly for further inference steps; 5) there is no tradeoff in computational strength for the added flexibility and efficiency; 6) for a natural subset of Allen's algebra, global consistency can be guaranteed in polynomial time; 7) knowledge about relations between events can be represented much more compactly.
A Propositional Modal Logic of Time Intervals
 Journal of the ACM
, 1996
"... : In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end we develop a modal temporal logic based on time intervals, a logic which can be viewed as a gener ..."
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Cited by 119 (2 self)
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: In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end we develop a modal temporal logic based on time intervals, a logic which can be viewed as a generalization of pointbased modal temporal logic. We discuss related logics, give an intuitive presentation of the new logic, and define its formal syntax and semantics. We make no assumption about the underlying nature of time, allowing it to be discrete (such as the natural numbers) or continuous (such as the rationals or the reals), linear or branching, complete (such as the reals) or not (such as the rationals). We show, however, that there are formulas in the logic that allow us to distinguish all these situations. We also give a translation of our logic into firstorder logic, which allows us to apply some results on firstorder logic to our modal one. Finally, we consider the difficulty o...
Time and time again: The many ways to represent time
 International Journal of Intelligent Systems
, 1991
"... issues remain essentially the same. One of the most crucial problems in any computer system that involves representing the world is the representation of time. This includes applications such as databases, simulation, expert systems and applications of Artificial Intelligence in general. In this bri ..."
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Cited by 104 (0 self)
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issues remain essentially the same. One of the most crucial problems in any computer system that involves representing the world is the representation of time. This includes applications such as databases, simulation, expert systems and applications of Artificial Intelligence in general. In this brief paper, I will give a survey of the basic techniques available for representing time, and then talk about temporal reasoning in a general setting as needed in AI applications. Quite different representations of time are usable depending on the assumptions that can be made about the temporal information to be represented. The most crucial issue is the degree of certainty one can assume. Can one assume that a time stamp can be assigned to each event, or barring that, that the events are fully ordered? Or can we only assume that a partial ordering of events is known? Can events be simultaneous? Can they overlap in time and yet not be simultaneous? If they are not instantaneous, do we know the durations of events? Different answers to each of these questions allow very different representations of time. I. Representations Based on Dating Schemes A good representation of time for instantaneous events, if it is possible, is using an absolute dating system. This involves time stamping each event with an absolute realtime, say taken off the system clock
A representation for collections of temporal intervals
 In Proceedings of AAAI
, 1986
"... Temporal representation and reasoning are necessary components of systems that consider events that occur in the real world. This work explores ways of considering collections of intervals of time. This line of research is motivated by related work being done by our research group on appointment sch ..."
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Cited by 64 (0 self)
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Temporal representation and reasoning are necessary components of systems that consider events that occur in the real world. This work explores ways of considering collections of intervals of time. This line of research is motivated by related work being done by our research group on appointment scheduling and time management. Natural language expressions that refer to collections of intervals are used naturally and routinely in these contexts, and an effective means of representing them is essential. Previous studies, which considered intervals primarily in isolation, have difficulties in representing some classes of expressions. This occurs not only with expressions that explicitly refer to collections of intervals, such as “the first of every month, ” but also with expressions that do so only
Temporal Logic in Information Systems
 Logics for Databases and Information Systems
, 1997
"... Temporal logic is obtained by adding temporal connectives to a logic language. Explicit references to time are hidden inside the temporal connectives. Different variants of temporal logic use different sets of such connectives. In this chapter, we survey the fundamental varieties of temporal logic a ..."
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Cited by 54 (12 self)
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Temporal logic is obtained by adding temporal connectives to a logic language. Explicit references to time are hidden inside the temporal connectives. Different variants of temporal logic use different sets of such connectives. In this chapter, we survey the fundamental varieties of temporal logic and describe their applications in information systems. Several features of temporal logic make it especially attractive as a query and integrity constraint language for temporal databases. First, because the references to time are hidden, queries and integrity constraints are formulated in an abstract, representationindependent way. Second, temporal logic is amenable to efficient implementation. Temporal logic queries can be translated to an algebraic language. Temporal logic constraints can be efficiently enforced using auxiliary stored information. More general languages, with explicit references to time, do not share these properties. Recent research has proposed various implementation t...
Fibring: Completeness Preservation
 Journal of Symbolic Logic
, 2000
"... A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by bring logics with congruence provided that congruence is retained in the resulting logic. The class of logics ..."
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Cited by 45 (23 self)
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A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by bring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under bring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by bring logics with equivalence and general semantics. An example is provided showing that completeness is not always preserved by bring logics endowed with standard (non general) semantics. A categorial characterization of bring is provided using coproducts and cocartesian liftings. 1 Introduction Much attention has been recently given to the problems of combining logics and obtaining transference results. Besides leading to very interesting applications whenever it is necessary to work with dierent logics at the same time, ...
Qualitative Spatial Representation and Reasoning
 An Overview”, Fundamenta Informaticae
, 2001
"... The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related ..."
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Cited by 45 (6 self)
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The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related fields of research, such as geographic information science
A Survey on Temporal Reasoning in Artificial Intelligence
, 1994
"... The notion of time is ubiquitous in any activity that requires intelligence. In particular, several important notions like change, causality, action are described in terms of time. Therefore, the representation of time and reasoning about time is of crucial importance for many Artificial Intelligenc ..."
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Cited by 42 (4 self)
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The notion of time is ubiquitous in any activity that requires intelligence. In particular, several important notions like change, causality, action are described in terms of time. Therefore, the representation of time and reasoning about time is of crucial importance for many Artificial Intelligence systems. Specifically during the last 10 years, it has been attracting the attention of many AI researchers. In this survey, the results of this work are analysed. Firstly, Temporal Reasoning is defined. Then, the most important representational issues which determine a Temporal Reasoning approach are introduced: the logical form on which the approach is based, the ontology (the units taken as primitives, the temporal relations, the algorithms that have been developed,. . . ) and the concepts related with reasoning about action (the representation of change, causality, action,. . . ). For each issue the different choices in the literature are discussed. 1 Introduction The notion of time i...