1,094 research outputs found
On the Decidability of Connectedness Constraints in 2D and 3D Euclidean Spaces
We investigate (quantifier-free) spatial constraint languages with equality,
contact and connectedness predicates as well as Boolean operations on regions,
interpreted over low-dimensional Euclidean spaces. We show that the complexity
of reasoning varies dramatically depending on the dimension of the space and on
the type of regions considered. For example, the logic with the
interior-connectedness predicate (and without contact) is undecidable over
polygons or regular closed sets in the Euclidean plane, NP-complete over
regular closed sets in three-dimensional Euclidean space, and ExpTime-complete
over polyhedra in three-dimensional Euclidean space.Comment: Accepted for publication in the IJCAI 2011 proceeding
Modal logic of planar polygons
We study the modal logic of the closure algebra , generated by the set
of all polygons in the Euclidean plane . We show that this logic
is finitely axiomatizable, is complete with respect to the class of frames we
call "crown" frames, is not first order definable, does not have the Craig
interpolation property, and its validity problem is PSPACE-complete
Qualitative constraint satisfaction problems: An extended framework with landmarks
Dealing with spatial and temporal knowledge is an indispensable part of almost all aspects of human activity. The qualitative approach to spatial and temporal reasoning, known as Qualitative Spatial and Temporal Reasoning (QSTR), typically represents spatial/temporal knowledge in terms of qualitative relations (e.g., to the east of, after), and reasons with spatial/temporal knowledge by solving qualitative constraints. When formulating qualitative constraint satisfaction problems (CSPs), it is usually assumed that each variable could be "here, there and everywhere".1 Practical applications such as urban planning, however, often require a variable to take its value from a certain finite domain, i.e. it is required to be 'here or there, but not everywhere'. Entities in such a finite domain often act as reference objects and are called "landmarks" in this paper. The paper extends the classical framework of qualitative CSPs by allowing variables to take values from finite domains. The computational complexity of the consistency problem in this extended framework is examined for the five most important qualitative calculi, viz. Point Algebra, Interval Algebra, Cardinal Relation Algebra, RCC5, and RCC8. We show that all these consistency problems remain in NP and provide, under practical assumptions, efficient algorithms for solving basic constraints involving landmarks for all these calculi. © 2013 Elsevier B.V
Dwelling on ontology - semantic reasoning over topographic maps
The thesis builds upon the hypothesis that the spatial arrangement of topographic
features, such as buildings, roads and other land cover parcels, indicates how land is
used. The aim is to make this kind of high-level semantic information explicit within
topographic data. There is an increasing need to share and use data for a wider range of
purposes, and to make data more definitive, intelligent and accessible. Unfortunately,
we still encounter a gap between low-level data representations and high-level concepts
that typify human qualitative spatial reasoning. The thesis adopts an ontological
approach to bridge this gap and to derive functional information by using standard
reasoning mechanisms offered by logic-based knowledge representation formalisms. It
formulates a framework for the processes involved in interpreting land use information
from topographic maps. Land use is a high-level abstract concept, but it is also an
observable fact intimately tied to geography. By decomposing this relationship, the
thesis correlates a one-to-one mapping between high-level conceptualisations
established from human knowledge and real world entities represented in the data.
Based on a middle-out approach, it develops a conceptual model that incrementally
links different levels of detail, and thereby derives coarser, more meaningful
descriptions from more detailed ones. The thesis verifies its proposed ideas by
implementing an ontology describing the land use ‘residential area’ in the ontology
editor Protégé. By asserting knowledge about high-level concepts such as types of
dwellings, urban blocks and residential districts as well as individuals that link directly
to topographic features stored in the database, the reasoner successfully infers instances
of the defined classes. Despite current technological limitations, ontologies are a
promising way forward in the manner we handle and integrate geographic data,
especially with respect to how humans conceptualise geographic space
A Logic for Choreographies
We explore logical reasoning for the global calculus, a coordination model
based on the notion of choreography, with the aim to provide a methodology for
specification and verification of structured communications. Starting with an
extension of Hennessy-Milner logic, we present the global logic (GL), a modal
logic describing possible interactions among participants in a choreography. We
illustrate its use by giving examples of properties on service specifications.
Finally, we show that, despite GL is undecidable, there is a significant
decidable fragment which we provide with a sound and complete proof system for
checking validity of formulae.Comment: In Proceedings PLACES 2010, arXiv:1110.385
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