80 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
On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi
Qualitative calculi play a central role in representing and reasoning about
qualitative spatial and temporal knowledge. This paper studies distributive
subalgebras of qualitative calculi, which are subalgebras in which (weak)
composition distributives over nonempty intersections. It has been proven for
RCC5 and RCC8 that path consistent constraint network over a distributive
subalgebra is always minimal and globally consistent (in the sense of strong
-consistency) in a qualitative sense. The well-known subclass of convex
interval relations provides one such an example of distributive subalgebras.
This paper first gives a characterisation of distributive subalgebras, which
states that the intersection of a set of relations in the subalgebra
is nonempty if and only if the intersection of every two of these relations is
nonempty. We further compute and generate all maximal distributive subalgebras
for Point Algebra, Interval Algebra, RCC5 and RCC8, Cardinal Relation Algebra,
and Rectangle Algebra. Lastly, we establish two nice properties which will play
an important role in efficient reasoning with constraint networks involving a
large number of variables.Comment: Adding proof of Theorem 2 to appendi
Answer Set Programming Modulo `Space-Time'
We present ASP Modulo `Space-Time', a declarative representational and
computational framework to perform commonsense reasoning about regions with
both spatial and temporal components. Supported are capabilities for mixed
qualitative-quantitative reasoning, consistency checking, and inferring
compositions of space-time relations; these capabilities combine and synergise
for applications in a range of AI application areas where the processing and
interpretation of spatio-temporal data is crucial. The framework and resulting
system is the only general KR-based method for declaratively reasoning about
the dynamics of `space-time' regions as first-class objects. We present an
empirical evaluation (with scalability and robustness results), and include
diverse application examples involving interpretation and control tasks
Reasoning mechanism for cardinal direction relations
In the classical Projection-based Model for cardinal directions [6], a two-dimensional Euclidean space relative to an arbitrary single-piece region, a, is partitioned into the following nine tiles: North-West, NW(a); North, N(a); North-East, NE(a); West, W(a); Neutral Zone, O(a);East, E(a); South-West, SW(a); South, S(a); and South-East,SE(a). In our Horizontal and Vertical Constraints Model [9], [10] these cardinal directions are decomposed into sets corresponding to horizontal and vertical constraints. Composition is computed for these sets instead of the typical individual cardinal directions. In this paper, we define several whole and part direction relations followed by showing how to compose such relations using a formula introduced in our previous paper [10]. In order to develop a more versatile reasoning system for direction relations, we shall integrate mereology, topology, cardinal directions and include their negations as well. © 2010 Springer-Verlag
Allen's Interval Algebra Makes the Difference
Allen's Interval Algebra constitutes a framework for reasoning about temporal
information in a qualitative manner. In particular, it uses intervals, i.e.,
pairs of endpoints, on the timeline to represent entities corresponding to
actions, events, or tasks, and binary relations such as precedes and overlaps
to encode the possible configurations between those entities. Allen's calculus
has found its way in many academic and industrial applications that involve,
most commonly, planning and scheduling, temporal databases, and healthcare. In
this paper, we present a novel encoding of Interval Algebra using answer-set
programming (ASP) extended by difference constraints, i.e., the fragment
abbreviated as ASP(DL), and demonstrate its performance via a preliminary
experimental evaluation. Although our ASP encoding is presented in the case of
Allen's calculus for the sake of clarity, we suggest that analogous encodings
can be devised for other point-based calculi, too.Comment: Part of DECLARE 19 proceeding
Quantized spin waves in the metallic state of magnetoresistive manganites
High resolution spin waves measurements have been carried out in
ferromagnetic (F) La(1-x)(Sr,Ca)xMnO3 with x(Sr)=0.15, 0.175, 0.2, 0.3 and
x(Ca)=0.3. In all q-directions, close to the zone boundary, the spin wave
spectra consist of several energy levels, with the same values in the metallic
and the x\approx 1/8 ranges. Mainly the intensity varies, jumping from the
lower energy levels determined in the x\approx 1/8 range to the higher energy
ones observed in the metallic state. On the basis of a quantitative agreement
found for x(Sr)=0.15 in a model of ordered 2D clusters, the spin wave anomalies
of the metallic state can be interpreted in terms of quantized spin waves
within the same 2D clusters, embedded in a 3D matrix.Comment: 4 pages, 5 figure
Tractable Fragments of Temporal Sequences of Topological Information
In this paper, we focus on qualitative temporal sequences of topological
information. We firstly consider the context of topological temporal sequences
of length greater than 3 describing the evolution of regions at consecutive
time points. We show that there is no Cartesian subclass containing all the
basic relations and the universal relation for which the algebraic closure
decides satisfiability. However, we identify some tractable subclasses, by
giving up the relations containing the non-tangential proper part relation and
not containing the tangential proper part relation. We then formalize an
alternative semantics for temporal sequences. We place ourselves in the context
of the topological temporal sequences describing the evolution of regions on a
partition of time (i.e. an alternation of instants and intervals). In this
context, we identify large tractable fragments
Positions, Regions, and Clusters: Strata of Granularity in Location Modelling
Abstract. Location models are data structures or knowledge bases used in Ubiquitous Computing for representing and reasoning about spatial relationships between so-called smart objects, i.e. everyday objects, such as cups or buildings, containing computational devices with sensors and wireless communication. The location of an object is in a location model either represented by a region, by a coordinate position, or by a cluster of regions or positions. Qualitative reasoning in location models could advance intelligence of devices, but is impeded by incompatibilities between the representation formats: topological reasoning applies to regions; directional reasoning, to positions; and reasoning about set-membership, to clusters. We present a mathematical structure based on scale spaces giving an integrated semantics to all three types of relations and representations. The structure reflects concepts of granularity and uncertainty relevant for location modelling, and gives semantics to applications of RCC-reasoning and projection-based directional reasoning in location models
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