Towards the minimum set of primitive relations in temporal logic
Information Processing Letters
On relations between intervals
Information Processing Letters
Maintaining knowledge about temporal intervals
Communications of the ACM
Parametrized abstract objects for linguistic information processing
EACL '85 Proceedings of the second conference on European chapter of the Association for Computational Linguistics
The completeness of a natural system for reasoning with time intervals
IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 1
Probabilistic temporal networks: A unified framework for reasoning with time and uncertainty
International Journal of Approximate Reasoning
AI'10 Proceedings of the 23rd Canadian conference on Advances in Artificial Intelligence
Categorical methods in qualitative reasoning: the case for weak representations
COSIT'05 Proceedings of the 2005 international conference on Spatial Information Theory
| Hi-index | 0.00 |
Ladkin and Maddux [LaMa87] showed how to interpret the calculus of time intervals defined by Allen [All83] in terms of representations of a particular relation algebra, and proved that this algebra has a unique countable representation up to isomorphism. In this paper, we consider the algebra An of n-intervals, which coincides with Allen's algebra for n=2, and prove that An has a unique countable representation up to isomorphism for all n2 1. We get this result, which implies that the first order theory of An is decidable, by introducing the notion of a weak representation of an interval algebra, and by giving a full classification of the connected weak representations of An. We also show how the topological properties of the set of atoms of An can be represented by a n-dimensional polytope.