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Modeling the Semantics of Geographic Categories through Conceptual Integration
 In GIScience. Lecture Notes in Computer Science
, 2002
"... Abstract. We apply the notion of conceptual integration from cognitive science to model the semantics of geographic categories. The paper shows the basic ideas, using the classical integration example of houseboats and boathouses. It extends the notion with imageschematic and affordancebased struc ..."
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Cited by 14 (2 self)
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Abstract. We apply the notion of conceptual integration from cognitive science to model the semantics of geographic categories. The paper shows the basic ideas, using the classical integration example of houseboats and boathouses. It extends the notion with imageschematic and affordancebased structure. A formalization in the functional language Haskell tests this approach and demonstrates how it generalizes to a powerful paradigm for building ontologies. 1.
Granularity transformations in wayfinding
 In Spatial Cognition
, 2003
"... Abstract. Wayfinding in road networks is a hierarchical process. It involves a sequence of tasks, starting with route planning, continuing with the extraction of wayfinding instructions, and leading to the actual driving. From one task level to the next, the relevant road network becomes more detail ..."
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Cited by 6 (0 self)
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Abstract. Wayfinding in road networks is a hierarchical process. It involves a sequence of tasks, starting with route planning, continuing with the extraction of wayfinding instructions, and leading to the actual driving. From one task level to the next, the relevant road network becomes more detailed. How does the wayfinding process change? Building on a previous, informal hierarchical highway navigation model and on graph granulation theory, we are working toward a theory of granularity transformations for wayfinding processes. The paper shows the first results: a formal ontology of wayfinding at the planning level and an informal model of granularity mappings.
CASL specifications of qualitative calculi
 Spatial Information Theory: Cognitive and Computational Foundations, Proceedings of COSIT’05, LNCS 3693
, 2005
"... Abstract. In AI a large number of calculi for efficient reasoning about spatial and temporal entities have been developed. The most prominent temporal calculi are the point algebra of linear time and Allen’s interval calculus. Examples of spatial calculi include mereotopological calculi, Frank’s car ..."
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Cited by 5 (1 self)
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Abstract. In AI a large number of calculi for efficient reasoning about spatial and temporal entities have been developed. The most prominent temporal calculi are the point algebra of linear time and Allen’s interval calculus. Examples of spatial calculi include mereotopological calculi, Frank’s cardinal direction calculus, Freksa’s double cross calculus, Egenhofer and Franzosa’s intersection calculi, and Randell, Cui, and Cohn’s region connection calculi. These calculi are designed for modeling specific aspects of space or time, respectively, to the effect that the class of intended models may vary widely with the calculus at hand. But from a formal point of view these calculi are often closely related to each other. For example, the spatial region connection calculus RCC5 may be considered a coarsening of Allen’s (temporal) interval calculus. And vice versa, intervals can be used to represent spatial objects that feature an internal direction. The central question of this paper is how these calculi as well as their mutual dependencies can be axiomatized by algebraic specifications. This question will be investigated within the framework of the Common Algebraic Specification Language (CASL), a specification language developed by the Common Framework Initiative for algebraic specification and development (COFI). We explain scope and expressiveness of CASL by discussing the specifications of some of the calculi mentioned before. 1
TerraHS: Integration of Functional Programming and Spatial Databases for GIS Application Development
, 2006
"... Recently, researchers in GIScience argued about the benefits on using functional programming for geospatial application development and prototyping of novel ideas. This paper presents an application that interfaces a functional language with a spatial database. It enables developing GIS application ..."
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Cited by 3 (1 self)
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Recently, researchers in GIScience argued about the benefits on using functional programming for geospatial application development and prototyping of novel ideas. This paper presents an application that interfaces a functional language with a spatial database. It enables developing GIS applications development in a functional language, while handling data are in a spatial database. We used this application develop a Map Algebra, that shows the benefits on using this paradigm in GIScience. Our work shows there are many gains in using a functional language, especially Haskell, to write concise and expressive GIS applications. The TerraHS application allows a good compromise between the expressive power of a functional language, and the data handling facilities of an imperative language.
Map Calculus in GIS: a proposal and demonstration
"... This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin’s (1990) Map Algebra, the term “Map Calculus” is used for this new representation. In Map Calculus, G ..."
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This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin’s (1990) Map Algebra, the term “Map Calculus” is used for this new representation. In Map Calculus, GIS layers are stored as functions, and new layers can be created by combinations of other functions. This paper explains the principles of Map Calculus and demonstrates the creation of functionbased layers and their supporting management mechanism. The proposal is based on Church’s (1941) Lambda Calculus and elements of functional computer languages (such as Lisp or Scheme).
Proceedings of the 6
"... specifications allow reusing the code which allows the designers to concentrate on the specific problems of the program without having to deal with standard tasks for too long. Using different classes allows the separation of the problem into smaller parts which can be modeled independent from each ..."
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specifications allow reusing the code which allows the designers to concentrate on the specific problems of the program without having to deal with standard tasks for too long. Using different classes allows the separation of the problem into smaller parts which can be modeled independent from each other. A combination of these algebras as described in [16] then leads to the specification of the whole problem. Algebraic specifications are also language independent, although they require a formal language which is capable of expressing algebraic style specifications. The purpose of a formal specification is to formally describe the behavior of objects. Algebraic specifications were introduced to describe data abstractions in software design [11].
Farid Karimipour, 1
"... Abstract: Early Geospatial Information Systems (GIS) dealt with static objects. There is much demand, however, to include temporal objects in these systems. Many have studied this problem and suggested technical solutions for different spatial operations. A common shortcoming is that the extension t ..."
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Abstract: Early Geospatial Information Systems (GIS) dealt with static objects. There is much demand, however, to include temporal objects in these systems. Many have studied this problem and suggested technical solutions for different spatial operations. A common shortcoming is that the extension techniques are highly dependent on the specific case studies and cannot be generalized. In this paper, we propose studying spatial operations via their dimensionindependent properties. This research intends to construct a mathematical framework that contains primitives for different operations. The framework will be independent of the space in which the operations are applied using algebraic structuresand more specifically category theorythat ignore those properties of operations which depend on the objects they are applied to. Implementations for some case studies are presented.