On Decidability of a Logic for Order of Magnitude Qualitative Reasoning with Bidirectional Negligibility
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.
Keywordsmulti-modal logic qualitative reasoning order-of-magnitude reasoning bidirectional negligibility knowledge representation decidability
Unable to display preview. Download preview PDF.
- 5.Golińska-Pilarek, J., Mora, A., Muñoz-Velasco, E.: An ATP of a Relational Proof System for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance. In: Ho, T.-B., Zhou, Z.-H. (eds.) PRICAI 2008. LNCS (LNAI), vol. 5351, pp. 128–139. Springer, Heidelberg (2008)CrossRefGoogle Scholar
- 8.Orłowska, E., Golińska-Pilarek, J.: Dual Tableaux: Foundations, Methodology, Case Studies. Trends in Logic 36. Springer (2011)Google Scholar