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The Heterogeneous Tool Set
 of Lecture Notes in Computer Science
, 2007
"... Abstract. Heterogeneous specification becomes more and more important because complex systems are often specified using multiple viewpoints, involving multiple formalisms. Moreover, a formal software development process may lead to a change of formalism during the development. However, current resea ..."
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Abstract. Heterogeneous specification becomes more and more important because complex systems are often specified using multiple viewpoints, involving multiple formalisms. Moreover, a formal software development process may lead to a change of formalism during the development. However, current research in integrated formal methods only deals with adhoc integrations of different formalisms. The heterogeneous tool set (Hets) is a parsing, static analysis and proof management tool combining various such tools for individual specification languages, thus providing a tool for heterogeneous multilogic specification. Hets is based on a graph of logics and languages (formalized as socalled institutions), their tools, and their translations. This provides a clean semantics of heterogeneous specification, as well as a corresponding proof calculus. For proof management, the calculus of development graphs (known from other largescale proof management systems) has been adapted to heterogeneous specification. Development graphs provide an overview of the (heterogeneous) specification module hierarchy and the current proof state, and thus may be used for monitoring the overall correctness of a heterogeneous development. 1
The Logic of Time Representation
, 1987
"... This investigation concerns representations of time by means of intervals, stemming from work of Allen [All83] and van Benthem [vBen83]. Allen described an Interval Calculus of thirteen binary relations on convex intervals over a linear order (the real numbers). He gave a practical algorithm for che ..."
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This investigation concerns representations of time by means of intervals, stemming from work of Allen [All83] and van Benthem [vBen83]. Allen described an Interval Calculus of thirteen binary relations on convex intervals over a linear order (the real numbers). He gave a practical algorithm for checking the consistency of a subclass of Boolean constraints. First, we describe a completeness theorem for Allen's calculus, in its corresponding formulation as a firstorder theory LM . LM is countably categorical, and axiomatises the complete theory of intervals over a dense unbounded linear order. Its only countable model up to isomorphism is the nontrivial intervals over the rational numbers. Algorithms are given for quantiferelimination, consistency checking, and satisfaction of arbitrary firstorder formulas in the Interval Calculus. A natural countable model of the calculus is presented, the TUS , in which clock and calendartime may be represented in a straightforward way. Allen an...
Database Models for Infinite and Indefinite Temporal Information
 Information Systems
, 1994
"... Representation and querying of temporal information can benefit from the integration of techniques from constraint databases, database models for indefinite information and reasoning about temporal constraints. With this perspective in mind, we present a hierarchy of temporal data models: temporal r ..."
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Cited by 28 (8 self)
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Representation and querying of temporal information can benefit from the integration of techniques from constraint databases, database models for indefinite information and reasoning about temporal constraints. With this perspective in mind, we present a hierarchy of temporal data models: temporal relations, generalized temporal relations and temporal tables. We study the semantics of these models and develop algebraic and calculus query languages for them. The proposed models can be useful to several novel applications include planning, scheduling, project management, medical information systems, geographical information systems and natural language processing systems. 1 Introduction Research in temporal databases has mostly concentrated on temporal models with definite temporal information (e.g., "the salary of Jones was $20,000 from January 1989 to April 1989") [62, 58]. There are few exceptions to this general rule. [11] was the first paper to investigate infinite periodic data (e...
Using Temporal Hierarchies to Efficiently Maintain Large Temporal Databases
 JOURNAL OF THE ACM
, 1989
"... Many realworld applications involve the management of large amounts of timedependent information. Temporal database systems maintain this information in order to support various sorts of inference (e.g., answering questions involving propositions that are true over some intervals and false over o ..."
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Cited by 27 (1 self)
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Many realworld applications involve the management of large amounts of timedependent information. Temporal database systems maintain this information in order to support various sorts of inference (e.g., answering questions involving propositions that are true over some intervals and false over others). For any given proposition, there are typically many different occasions on which that proposition becomes true and persists for some length of time. In this paper, these occasions are referred to as time tokens. Many routine database operations must search through the database for time tokens satisfying certain temporal constraints. To expedite these operations, this paper describes a set of techniques for organizing temporal information by exploiting the local and global structure inherent in a wide class of temporal reasoning problems. The global structure of time is exemplified in conventions for partitioning time according to the calendar and the clock. This global structure is used to partition the set of time tokens to facilitate retrieval. The local structure of time;is exemplified in the causal relationships between events and the dependencies between planned activities. This local structure is used as part of a strategy for reducing the computation required during constraint propagation. The organizational techniques described in this paper are quite general, and have been used to support a variety of powerful inference mechanisms. Integrating these techniques into an existing temporal database system has increased, by an order of magnitude or more in most applications, the number of time tokens that can be efficiently handled.
Representing and Integrating Multiple Calendars
, 1996
"... Whenever humans refer to time, they do so with respect to a specific underlying calendar. So do most software applications. However, most theoretical models of time refer to time with respect to the integers (or reals). Thus, there is a mismatch between the theory and the application of temporal rea ..."
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Whenever humans refer to time, they do so with respect to a specific underlying calendar. So do most software applications. However, most theoretical models of time refer to time with respect to the integers (or reals). Thus, there is a mismatch between the theory and the application of temporal reasoning. To lessen this gap, we propose a formal, theoretical definition of a calendar and show how one may specify dates, time points, time intervals, as well as sets of time points, in terms of constraints with respect to a given calendar. Furthermore, when multiple applications using different calendars wish to work together, there is a need to integrate those calendars together into a single, unified calendar. We show how this can be done. This work was supported by the Army Research Office under Grants DAAH049510174 and DAAH049610297, by ARPA/Rome Labs contract F3060293C0241 (ARPA Order Nr. A716), by an NSF Young Investigator award IRI9357756, NSF Grant No. IRI9423967 and b...
Representing and Reasoning about Temporal Granularities
, 2004
"... In this paper, we propose a new logical approach to represent and to reason about different time granularities. We identify a time granularity as an infinite sequence of time points properly labelled with proposition symbols marking the starting and ending points of the corresponding granules, and ..."
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In this paper, we propose a new logical approach to represent and to reason about different time granularities. We identify a time granularity as an infinite sequence of time points properly labelled with proposition symbols marking the starting and ending points of the corresponding granules, and we symbolically model sets of granularities by means of linear time logic formulas. Some realworld granularities are provided, from a clinical domain and from the Gregorian Calendar, to motivate and exemplify our approach. Different formulas are introduced, which represent relations between different granularities. The proposed framework permits one to algorithmically solve the consistency, the equivalence, and the classification problems in a uniform way, by reducing them to the validity problem for the considered linear time logic.
Satisfiability of Quantitative Temporal Constraints With Multiple Granularities
 IN PROC. CP
, 1997
"... Most work on temporal constraints has ignored the subtleties involved in dealing with multiple time granularities. This paper considers a constraint satisfaction problem (CSP) where binary quantitative constraints in terms of different time granularities can be specified on a set of variables, an ..."
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Cited by 6 (3 self)
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Most work on temporal constraints has ignored the subtleties involved in dealing with multiple time granularities. This paper considers a constraint satisfaction problem (CSP) where binary quantitative constraints in terms of different time granularities can be specified on a set of variables, and unary constraints are allowed to limit the domain of variables. Such a CSP cannot be trivially reduced to one of the known CSP problems. The main result of the paper is a complete algorithm for checking consistency and finding a solution. The complexity of the algorithm is studied in the paper under di#erent assumptions about the granularities involved in the CSP, and a second algorithm is proposed to improve the efficiency of the backtracking process needed to obtain all the solutions of the CSP.
Temporalized logics and automata for time granularity. Theory and Practice of Logic Programming
 Research on Language and Computation
, 2004
"... The ability of providing and relating temporal representations at different ‘grain levels’ of the same reality is an important research theme in computer science and a major requirement for many applications, including formal specification and verification, temporal databases, data mining, problem s ..."
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Cited by 4 (2 self)
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The ability of providing and relating temporal representations at different ‘grain levels’ of the same reality is an important research theme in computer science and a major requirement for many applications, including formal specification and verification, temporal databases, data mining, problem solving, and natural language understanding. In particular, the addition of a granularity dimension to a temporal logic makes it possible to specify in a concise way reactive systems whose behaviour can be naturally modeled with respect to a (possibly infinite) set of differentlygrained temporal domains. Suitable extensions of the monadic secondorder theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic secondorder theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automatatheoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them. 1
Simple Reasoning with TimeDependent Propositions
 International Journal of Interest Group in Pure and Applied Logic (IGPL), 10:379–399
, 2002
"... Simple practical reasoning with propositions whose truth values depend on time is a matter of logical engineering. One needs an expressive language in which simple inferences are productive. Here's one approach, along with some algorithms for implementing it. We also consider reified and nonreified ..."
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Simple practical reasoning with propositions whose truth values depend on time is a matter of logical engineering. One needs an expressive language in which simple inferences are productive. Here's one approach, along with some algorithms for implementing it. We also consider reified and nonreified logics, and show that, contrary to a claim of Bacchus et. al., a reified logic is more appropriate than its nonreified equivalent, even for Boolean logic, when time references are interpreted as unionofconvex intervals. 1 Introduction Many simple propositions may be true at one time and false at another. Any database containing data from the real world must consider such a possibility, and there are various ways of timestamping entries in relation tables (i.e., atomic formulae) to reflect temporal dependencies. However, not everything can easily be configured as relations amongst atomic formulae. Sometimes it is best to maintain small databases and use rapid inferences. What sort of rap...
Reasoning About Time and Change: a Knowledge Base Management Perspective
, 1990
"... this paper, I will survey a number of temporal formalisms and systems from Knowledge Representation and Databases. Work in these two areas is particularly relevant if one is interested in designing and implementing a Temporal Knowledge Base Management System (TKBMS). KBMSs have been recently propose ..."
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this paper, I will survey a number of temporal formalisms and systems from Knowledge Representation and Databases. Work in these two areas is particularly relevant if one is interested in designing and implementing a Temporal Knowledge Base Management System (TKBMS). KBMSs have been recently proposed for the construction, maintenance and querying of large shared knowledge bases [BM86], [Ull88], [Ull89], [ST89]. Since so many practical problems involve temporal reasoning, it is an interesting reasearch problem to design and implement a TKBMS which can be used for storing and retrieving large amounts of knowledge about these problems. For example, a jobshop scheduling system like ISIS [FS84], [FM86] could take advantage of a TKBMS for storing knowledge about orders, products, resources and schedules. This knowledge could be shared between schedulers and plant staff. A TKBMS would also be useful as a component of a medical information system used for recording and analyzing symptoms, diseases and their effects on patients over time [WBW86]. To keep the rest of the discussion in perspective, I will now present a number of requirements which must be met by a TKBMS