7,775 research outputs found
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
Model Checking Spatial Logics for Closure Spaces
Spatial aspects of computation are becoming increasingly relevant in Computer
Science, especially in the field of collective adaptive systems and when
dealing with systems distributed in physical space. Traditional formal
verification techniques are well suited to analyse the temporal evolution of
programs; however, properties of space are typically not taken into account
explicitly. We present a topology-based approach to formal verification of
spatial properties depending upon physical space. We define an appropriate
logic, stemming from the tradition of topological interpretations of modal
logics, dating back to earlier logicians such as Tarski, where modalities
describe neighbourhood. We lift the topological definitions to the more general
setting of closure spaces, also encompassing discrete, graph-based structures.
We extend the framework with a spatial surrounded operator, a propagation
operator and with some collective operators. The latter are interpreted over
arbitrary sets of points instead of individual points in space. We define
efficient model checking procedures, both for the individual and the collective
spatial fragments of the logic and provide a proof-of-concept tool
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
Towards Autopoietic Computing
A key challenge in modern computing is to develop systems that address
complex, dynamic problems in a scalable and efficient way, because the
increasing complexity of software makes designing and maintaining efficient and
flexible systems increasingly difficult. Biological systems are thought to
possess robust, scalable processing paradigms that can automatically manage
complex, dynamic problem spaces, possessing several properties that may be
useful in computer systems. The biological properties of self-organisation,
self-replication, self-management, and scalability are addressed in an
interesting way by autopoiesis, a descriptive theory of the cell founded on the
concept of a system's circular organisation to define its boundary with its
environment. In this paper, therefore, we review the main concepts of
autopoiesis and then discuss how they could be related to fundamental concepts
and theories of computation. The paper is conceptual in nature and the emphasis
is on the review of other people's work in this area as part of a longer-term
strategy to develop a formal theory of autopoietic computing.Comment: 10 Pages, 3 figure
Specifying and Verifying Properties of Space - Extended Version
The interplay between process behaviour and spatial aspects of computation
has become more and more relevant in Computer Science, especially in the field
of collective adaptive systems, but also, more generally, when dealing with
systems distributed in physical space. Traditional verification techniques are
well suited to analyse the temporal evolution of programs; properties of space
are typically not explicitly taken into account. We propose a methodology to
verify properties depending upon physical space. We define an appropriate
logic, stemming from the tradition of topological interpretations of modal
logics, dating back to earlier logicians such as Tarski, where modalities
describe neighbourhood. We lift the topological definitions to a more general
setting, also encompassing discrete, graph-based structures. We further extend
the framework with a spatial until operator, and define an efficient model
checking procedure, implemented in a proof-of-concept tool.Comment: Presented at "Theoretical Computer Science" 2014, Rom
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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