386 research outputs found
Combining Spatial and Temporal Logics: Expressiveness vs. Complexity
In this paper, we construct and investigate a hierarchy of spatio-temporal
formalisms that result from various combinations of propositional spatial and
temporal logics such as the propositional temporal logic PTL, the spatial
logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a
clear picture of the trade-off between expressiveness and computational
realisability within the hierarchy. We demonstrate how different combining
principles as well as spatial and temporal primitives can produce NP-, PSPACE-,
EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out
of components that are at most NP- or PSPACE-complete
Topological Foundations of Cognitive Science
A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers:
** Topological Foundations of Cognitive Science, Barry Smith
** The Bounds of Axiomatisation, Graham White
** Rethinking Boundaries, Wojciech Zelaniec
** Sheaf Mereology and Space Cognition, Jean Petitot
** A Mereotopological Definition of 'Point', Carola Eschenbach
** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel
** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda
** Defining a 'Doughnut' Made Difficult, N .M. Gotts
** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts
** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi
** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki
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An Ontology for Grounding Vague Geographic Terms
Many geographic terms, such as “river” and “lake”, are vague, with no clear boundaries of application. In particular, the spatial extent of such features is often vaguely carved out of a continuously varying observable domain. We present a means of defining vague terms using standpoint semantics, a refinement of the
philosophical idea of supervaluation semantics. Such definitions can be grounded in actual data by geometric analysis and segmentation of the data set. The issues
raised by this process with regard to the nature of boundaries and domains of logical quantification are discussed. We describe a prototype implementation of a system capable of segmenting attributed polygon data into geographically significant regions and evaluating queries involving vague geographic feature terms
Algebraic Properties of Qualitative Spatio-Temporal Calculi
Qualitative spatial and temporal reasoning is based on so-called qualitative
calculi. Algebraic properties of these calculi have several implications on
reasoning algorithms. But what exactly is a qualitative calculus? And to which
extent do the qualitative calculi proposed meet these demands? The literature
provides various answers to the first question but only few facts about the
second. In this paper we identify the minimal requirements to binary
spatio-temporal calculi and we discuss the relevance of the according axioms
for representation and reasoning. We also analyze existing qualitative calculi
and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia
Spatial database implementation of fuzzy region connection calculus for analysing the relationship of diseases
Analyzing huge amounts of spatial data plays an important role in many
emerging analysis and decision-making domains such as healthcare, urban
planning, agriculture and so on. For extracting meaningful knowledge from
geographical data, the relationships between spatial data objects need to be
analyzed. An important class of such relationships are topological relations
like the connectedness or overlap between regions. While real-world
geographical regions such as lakes or forests do not have exact boundaries and
are fuzzy, most of the existing analysis methods neglect this inherent feature
of topological relations. In this paper, we propose a method for handling the
topological relations in spatial databases based on fuzzy region connection
calculus (RCC). The proposed method is implemented in PostGIS spatial database
and evaluated in analyzing the relationship of diseases as an important
application domain. We also used our fuzzy RCC implementation for fuzzification
of the skyline operator in spatial databases. The results of the evaluation
show that our method provides a more realistic view of spatial relationships
and gives more flexibility to the data analyst to extract meaningful and
accurate results in comparison with the existing methods.Comment: ICEE201
A Whiteheadian-type description of Euclidean spaces, spheres, tori and Tychonoff cubes
In the beginning of the 20th century, A. N. Whitehead and T. de Laguna
proposed a new theory of space, known as {\em region-based theory of space}.
They did not present their ideas in a detailed mathematical form.
In 1997, P. Roeper has shown that the locally compact Hausdorff spaces
correspond bijectively (up to homeomorphism and isomorphism) to some
algebraical objects which represent correctly Whitehead's ideas of {\em region}
and {\em contact relation}, generalizing in this way a previous analogous
result of de Vries concerning compact Hausdorff spaces (note that even a
duality for the category of compact Hausdorff spaces and continuous maps was
constructed by de Vries). Recently, a duality for the category of locally
compact Hausdorff spaces and continuous maps, based on Roeper's results, was
obtained by G. Dimov (it extends de Vries' duality mentioned above). In this
paper, using the dualities obtained by de Vries and Dimov, we construct
directly (i.e. without the help of the corresponding topological spaces) the
dual objects of Euclidean spaces, spheres, tori and Tychonoff cubes; these
algebraical objects completely characterize the mentioned topological spaces.
Thus, a mathematical realization of the original philosophical ideas of
Whitehead and de Laguna about Euclidean spaces is obtained.Comment: 29 page
Generating Relation Algebras for Qualitative Spatial Reasoning
Basic relationships between certain regions of space are formulated in natural language
in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts.
We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras
Applying spatial reasoning to topographical data with a grounded geographical ontology
Grounding an ontology upon geographical data has been pro-
posed as a method of handling the vagueness in the domain more effectively. In order to do this, we require methods of reasoning about the spatial relations between the regions within the data. This stage can be computationally expensive, as we require information on the location of
points in relation to each other. This paper illustrates how using knowledge about regions allows us to reduce the computation required in an efficient and easy to understand manner. Further, we show how this system can be implemented in co-ordination with segmented data to reason abou
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