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Qualitative Temporal Reasoning in GIS  Ordered Time Scales
, 1994
"... There is a strong request for GIS to include temporal information. Most efforts currently are addressing the incorporation of time qua calendar time. Events are dated according to the ordinary time and calendar, which are effectively measurements on an interval scale. Temporal information available ..."
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Cited by 11 (5 self)
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There is a strong request for GIS to include temporal information. Most efforts currently are addressing the incorporation of time qua calendar time. Events are dated according to the ordinary time and calendar, which are effectively measurements on an interval scale. Temporal information available only as relative order between events cannot be incorporated in this framework. Clearly knowledge about temporal order without measurement on the time scale is less precise but nevertheless useful. Human beings use qualitative temporal reasoning all the time. Qualitative ordinal information about events is typically encountered in archeology, urban development etc. where precise dates for events are not known but the relative order of events can be deduced from observations. Even in legal proceedings about parcel data, ordinal relations are often all what matters. These are among the disciplines which have asked for the inclusion of facilities to deal with temporal data in GIS. This paper gi...
On the Relationship between Filter Spaces and Equilogical Spaces
, 1998
"... It was already known that the category of T 0 topological spaces is not itself cartesian closed, but can be embedded into the cartesian closed categories FIL of filter spaces and EQU of equilogical spaces where the latter embeds into the cartesian closed category ASSM of assemblies over algebraic la ..."
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Cited by 6 (3 self)
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It was already known that the category of T 0 topological spaces is not itself cartesian closed, but can be embedded into the cartesian closed categories FIL of filter spaces and EQU of equilogical spaces where the latter embeds into the cartesian closed category ASSM of assemblies over algebraic lattices. Here, we first clarify the notion of filter spacethere are at least three versions FIL a ' FIL b ' FIL c in the literature. We establish adjunctions between FIL a and ASSM and between FIL c and ASSM, and show that FIL b and FIL c are equivalent to reflective full subcategories of ASSM. The corresponding categories FIL b 0 and FIL c 0 of T 0 spaces are equivalent to full subcategories of EQU. Keywords: Categorical models and logics, domain theory and applications Author's address: Reinhold Heckmann, FB 14  Informatik, Universitat des Saarlandes, Postfach 151150, D66041 Saarbrucken, Germany Phone: +49 681 302 2454 Fax: +49 681 302 3065 email: heckmann@cs.un...
Power Domains Supporting Recursion and Failure
 In CAAP'92
, 1998
"... Following the program of Moggi, the semantics of a simple nondeterministic functional language with recursion and failure is described by a monad. We show that this monad cannot be any of the known power domain constructions, because they do not handle nontermination properly. Instead, a novel con ..."
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Cited by 3 (1 self)
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Following the program of Moggi, the semantics of a simple nondeterministic functional language with recursion and failure is described by a monad. We show that this monad cannot be any of the known power domain constructions, because they do not handle nontermination properly. Instead, a novel construction is proposed and investigated. It embodies both nondeterminism (choice and failure) and possible nontermination caused by recursion. 1 Introduction Following the proposals of Moggi [Mog89, Mog91b], functional languages with various notions of computations can be denotationally described by means of monads. Monads are constructions mapping domains of values into domains of computations for these values. Computations involving destructive assignments, for instance, are handled by the state transformer monad [Wad90], whereas computations by nondeterministic choice are handled by power domain constructions [Plo76, Smy78, Gun90]. All known power domain constructions and many others ar...
Colimit Library for Graph Transformations and Algebraic Development Techniques
, 1998
"... ions are defined both for objects and layers. There are several compatibility requirements for the definition of these functions. The set of objects contains a specific ?element which allows the source and target functions to be total on the set of objects. Up to now there exists no implementation ..."
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Cited by 2 (0 self)
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ions are defined both for objects and layers. There are several compatibility requirements for the definition of these functions. The set of objects contains a specific ?element which allows the source and target functions to be total on the set of objects. Up to now there exists no implementation of general colimits in the AGGsystem. This problem is currently fixed by the integration of the colimit library. Again we can use the colimit computation for Alpha algebras. For this purpose we have to find an Alpha representation of AGGgraphs. Here we will outline the idea. r0 r1 r2 object layer label v0 r4 r0 Item Data The picture above presents a possible Alpha type algebra for AGGgraphs. r 0 ; r 1 and r 2 correspond to the abstraction, source and target functions, r 4 represents the assignment of layers to objects and v 0 is the labelling function. Note that although not shown in the picture, since all references are total, r 1 ; r 2 and r 3 are defined also for layer. This shows ...
A Fully Complete PER Model for ML Polymorphic Types
 Proceedings of CSL 2000, Springer LNCS Volume 1862
, 2000
"... . We present a linear realizability technique for building Partial Equivalence Relations (PER) categories over Linear Combinatory Algebras. These PER categories turn out to be linear categories and to form an adjoint model with their coKleisli categories. We show that a special linear combinato ..."
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Cited by 2 (1 self)
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. We present a linear realizability technique for building Partial Equivalence Relations (PER) categories over Linear Combinatory Algebras. These PER categories turn out to be linear categories and to form an adjoint model with their coKleisli categories. We show that a special linear combinatory algebra of partial involutions, arising from Geometry of Interaction constructions, gives rise to a fully and faithfully complete model for ML polymorphic types of system F. Keywords: MLpolymorphic types, linear logic, PER models, Geometry of Interaction, full completeness. Introduction Recently, Game Semantics has been used to define fullycomplete models for various fragments of Linear Logic ([AJ94a,AM99]), and to give fullyabstract models for many programming languages, including PCF [AJM96,HO96,Nic94], richer functional languages [McC96], and languages with nonfunctional features such as reference types and nonlocal control constructs [AM97,Lai97]. All these results are cru...
Dynamics in Information Systems: Specification, Construction, and Correctness  An Algebraic Approach
, 1996
"... . A formal framework based on algebraic graph theory is presented that integrates specification and construction of dynamics in information systems. Specifications are based on temporal logic whose semantics is given by algebras and partial homomorphisms. Constructions are given by graph transformat ..."
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. A formal framework based on algebraic graph theory is presented that integrates specification and construction of dynamics in information systems. Specifications are based on temporal logic whose semantics is given by algebras and partial homomorphisms. Constructions are given by graph transformation rules whose operational nature provides a first step towards actual implementations. Both are related by a correctness notion. The formal framework is especially suited as a semantical basis for graphical notations as used in conceptual modeling, thus combining intuitiveness of such notations with precision of formal methods. 1 Introduction Conceptual modeling, i.e., specification of information systems and database applications is traditionally done by employing semantic data models [26, 27, 15, 23]. Although structure and behavior of information systems must be taken into account, conceptual modeling classically focuses on the structural aspects only, for instance by using the welltr...