2,731 research outputs found
Relation algebras and their application in temporal and spatial reasoning
Abstract Qualitative temporal and spatial reasoning is in many cases based on binary relations such as before, after, starts, contains, contact, part of, and others derived from these by relational operators. The calculus of relation algebras is an equational formalism; it tells us which relations must exist, given several basic operations, such as Boolean operations on relations, relational composition and converse. Each equation in the calculus corresponds to a theorem, and, for a situation where there are only nitely many relations, one can construct a composition table which can serve as a look up table for the relations involved. Since the calculus handles relations, no knowledge about the concrete geometrical objects is necessary. In this sense, relational calculus is pointless. Relation algebras were introduced into temporal reasoning by Allen [1] and into spatial reasoning by Egenhofer and Sharm
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
Case Adaptation with Qualitative Algebras
This paper proposes an approach for the adaptation of spatial or temporal
cases in a case-based reasoning system. Qualitative algebras are used as
spatial and temporal knowledge representation languages. The intuition behind
this adaptation approach is to apply a substitution and then repair potential
inconsistencies, thanks to belief revision on qualitative algebras. A temporal
example from the cooking domain is given. (The paper on which this extended
abstract is based was the recipient of the best paper award of the 2012
International Conference on Case-Based Reasoning.
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
Counterpart semantics for a second-order mu-calculus
We propose a novel approach to the semantics of quantified μ-calculi, considering models where states are algebras; the evolution relation is given by a counterpart relation (a family of partial homomorphisms), allowing for the creation, deletion, and merging of components; and formulas are interpreted over sets of state assignments (families of substitutions, associating formula variables to state components). Our proposal avoids the limitations of existing approaches, usually enforcing restrictions of the evolution relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of
Temporal Data Modeling and Reasoning for Information Systems
Temporal knowledge representation and reasoning is a major research field in Artificial
Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to
model and process time and calendar data is essential for many applications like appointment
scheduling, planning, Web services, temporal and active database systems, adaptive
Web applications, and mobile computing applications. This article aims at three complementary
goals. First, to provide with a general background in temporal data modeling
and reasoning approaches. Second, to serve as an orientation guide for further specific
reading. Third, to point to new application fields and research perspectives on temporal
knowledge representation and reasoning in the Web and Semantic Web
Convolution, Separation and Concurrency
A notion of convolution is presented in the context of formal power series
together with lifting constructions characterising algebras of such series,
which usually are quantales. A number of examples underpin the universality of
these constructions, the most prominent ones being separation logics, where
convolution is separating conjunction in an assertion quantale; interval
logics, where convolution is the chop operation; and stream interval functions,
where convolution is used for analysing the trajectories of dynamical or
real-time systems. A Hoare logic is constructed in a generic fashion on the
power series quantale, which applies to each of these examples. In many cases,
commutative notions of convolution have natural interpretations as concurrency
operations.Comment: 39 page
- …