Interval-Set Algebra for Qualitative Knowledge Representation
نویسنده
چکیده
The notion of interval sets is introduced as a new kind of sets, represented by a pair of sets, namely, the lower and upper bounds. The interval-set algebra may be regarded as a counterpart of the interval-number algebra. It provides a useful tool to represent qualitative information. Operations on interval sets are also defined, based on the corresponding set-theoretic operations on their members. In addition, basic properties of interval-set algebra are examined, and the relationships between interval sets, rough sets and fuzzy sets
منابع مشابه
Reasoning about Qualitative Temporal Information
Interval and point algebras have been proposed for representing qualitative temporal information about the relationships between pairs of intervals and pairs of points, respectively. In this paper, we address two related reasoning tasks that arise in these algebras: Given (possibly indefinite) knowledge of the relationships between some intervals or points, (1) find one or more scenarios that a...
متن کاملA Probabilistic Logic of Qualitative Time
Representing and reasoning over dynamic processes can benefit from using a qualitative representation of time when precise timing information is unavailable. Allen’s interval algebra provides a framework to do so. However, a more precise model can be obtained by modelling uncertainty in the process. In this paper we propose an extension of Allen’s algebra with uncertainty, using probability the...
متن کاملThe Temporal Reasoning Systems
We describe two domain-independent temporal reasoning systems called TimeGraph I and II which can be used in AI-applications as tools for eeciently managing large sets of relations in the Point Algebra, in the Interval Algebra, and metric information such as absolute times and durations. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the sear...
متن کاملOn 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 alway...
متن کاملOn the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$
We consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$. After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of the repre...
متن کامل