Artificial Intelligence - Special issue: Qualitative reasoning about physical systems II
A Logic for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance
Current Topics in Artificial Intelligence
PRICAI '08 Proceedings of the 10th Pacific Rim International Conference on Artificial Intelligence: Trends in Artificial Intelligence
Order of magnitude qualitative reasoning with bidirectional negligibility
CAEPIA'05 Proceedings of the 11th Spanish association conference on Current Topics in Artificial Intelligence
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Qualitative Reasoning (QR) is an area of research within Artificial Intelligence that automates reasoning and problem solving about the physical world. QR research aims to deal with representation and reasoning about continuous aspects of entities without the kind of precise quantitative information needed by conventional numerical analysis techniques. Order-of-magnitude Reasoning (OMR) is an approach in QR concerned with the analysis of physical systems in terms of relative magnitudes. In this paper we consider the logic OMRN for order-of-magnitude reasoning with the bidirectional negligibility relation. It is a multi-modal logic given by a Hilbert-style axiomatization that reflects properties and interactions of two basic accessibility relations (strict linear order and bidirectional negligibility). Although the logic was studied in many papers, nothing was known about its decidability. In the paper we prove decidability of OMRN by showing that the logic has the strong finite model property.