An implementation of a dual tableaux system for order-of-magnitude qualitative reasoning

Logic programming has been used as a natural framework to automate deduction in the logic of order-of-magnitude reasoning. Specifically, we introduce a Prolog implementation of the Rasiowa–Sikorski proof system associated with the relational translation Re(OM) of the multi-modal logic of order-of-magnitude qualitative reasoning OM.

[1]  E. Orlowska.  Relational interpretation of modal logics , 1988 .

[2]  Philippe Dague.  Numeric Reasoning with Relative Orders of Magnitude , 1993, AAAI.

[3]  Andrea Formisano,et al.  A Prolog tool for relational translation of modal logics: a front-end for relational proof systems , 2005 .

[4]  Manuel Ojeda-Aciego,et al.  A Multimodal Logic Approach to Order of Magnitude Qualitative Reasoning with Comparability and Negligibility Relations , 2005, Fundam. Informaticae.

[5]  Siddarth Subramanian and Raymond J. Mooney.  Multiple-Fault Diagnosis Using General Qualitative Models with Fault Modes , 1994 .

[6]  Maarten Marx,et al.  The Computational Complexity of Hybrid Temporal Logics , 2000, Log. J. IGPL.

[7]  Klaus Stein,et al.  Coarse Qualitative Descriptions in Robot Navigation , 2000, Spatial Cognition.

[8]  Chris Bailey-Kellogg,et al.  Qualitative Spatial Reasoning Extracting and Reasoning with Spatial Aggregates , 2004, AI Mag..

[9]  Ewa Orlowska,et al.  Relational Semantics for Nonclassical Logics: Formulas are Relations , 1994 .

[10]  R. Sikorski,et al.  The mathematics of metamathematics , 1963 .

[11]  Beata Konikowska,et al.  Rasiowa-Sikorski deduction systems in computer science applications , 2002, Theor. Comput. Sci..

[12]  P. Pandurang Nayak,et al.  Order of Magnitude Reasoning using Logarithms , 1992, KR.

[13]  Ewa Orlowska,et al.  Logics of similarity and their dual tableaux. A survey , 2008 .

[14]  Frank Wolter,et al.  All Finitely Axiomatizable Tense Logics of Linear Time Flows Are CoNP-complete , 2005, Stud Logica.

[15]  F. Wolter,et al.  Qualitative spatiotemporal representation and reasoning: a computational perspective , 2003 .

[16]  Manuel Ojeda-Aciego,et al.  Relational Approach to Order-of-Magnitude Reasoning , 2006, Theory and Applications of Relational Structures as Knowledge Instruments.

[17]  Núria Agell,et al.  Relative and absolute order-of-magnitude models unified , 2005, Annals of Mathematics and Artificial Intelligence.

[18]  Andrea Formisano,et al.  An Environment for Specifying Properties of Dyadic Relations and Reasoning About Them II: Relational Presentation of Non-classical Logics , 2006, Theory and Applications of Relational Structures as Knowledge Instruments.

[19]  Brandon Bennett,et al.  Modal Logics for Qualitative Spatial Reasoning , 1996, Log. J. IGPL.

[20]  Olivier Raiman,et al.  Order of Magnitude Reasoning , 1986, Artif. Intell..

[21]  Joanna Golinska-Pilarek,et al.  Tableaux and Dual Tableaux: Transformation of Proofs , 2007, Stud Logica.

[22]  Andrew B. Whinston,et al.  A Set-Theoretical Foundation of Qualitative Reasoning and its Application to the Modeling of Economics and Business Management Problems , 2003, Inf. Syst. Frontiers.

[23]  Angel Mora,et al.  An ATP of a Relational Proof System for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance , 2008, PRICAI.

[24]  Michael L. Mavrovouniotis,et al.  Reasoning with Orders of Magnitude and Approximate Relations , 1987, AAAI.