In [8] Bennett, Isli and Cohn put out the following challenge to researchers working with theories based on composition tables (CT): give a general characterization of theories and relational constraint languages for which a complete proof procedure can be specified by a CT. For theories based on CTs, they make the distinction between a weak, consistency-based interpretation of the CT, and a stronger extensional definition. In this paper, we take up a limited aspect of the challenge, namely, we characterize a subclass of formalisms for which the weak interpretation can be related in a canonical way to a structure based on a total ordering, while the strong interpretations have the property of aleph-zero categoricity (all countable models are isomorphic). Our approach is based on algebraic, rather than logical, methods. It can be summarized by two keywords: relation algebra and weak representation.
CITATION STYLE
Ligozat, G. (2001). When tables tell it all: Qualitative spatial and temporal reasoning based on linear orderings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2205, pp. 60–75). Springer Verlag. https://doi.org/10.1007/3-540-45424-1_5
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