Handbook of logic in artificial intelligence and logic programming (vol. 3)
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Computing Circumscription Revisited: A Reduction Algorithm
Journal of Automated Reasoning
Knowledge Representation Techniques (Studies in Fuzziness and Soft Computing)
Knowledge Representation Techniques (Studies in Fuzziness and Soft Computing)
Second Order Quantifier Elimination: Foundations, Computational Aspects and Applications
Second Order Quantifier Elimination: Foundations, Computational Aspects and Applications
Approximation Spaces in Rough-Granular Computing
Fundamenta Informaticae - Understanding Computers' Intelligence Celebrating the 100th Volume of Fundamenta Informaticae in Honour of Helena Rasiowa
A Correspondence Framework between Three-Valued Logics and Similarity-Based Approximate Reasoning
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
Nearness of Objects: Extension of Approximation Space Model
Fundamenta Informaticae - Special Issue on Concurrency Specification and Programming (CS&P)
Satisfiability and Meaning of Formulas and Sets of Formulas in Approximation Spaces
Fundamenta Informaticae - Concurrency Specification and Programming (CS&P 2004)
Tolerance Approximation Spaces
Fundamenta Informaticae
A Reduction Result for Circumscribed Semi-Horn Formulas
Fundamenta Informaticae
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This paper focuses on approximate reasoning based on the use of approximation spaces. Approximation spaces and the approximated relations induced by them are a generalization of the rough set-based approximations of Pawlak. Approximation spaces are used to define neighborhoods around individuals and rough inclusion functions. These in turn are used to define approximate sets and relations. In any of the approaches, one would like to embed such relations in an appropriate logical theory which can be used as a reasoning engine for specific applications with specific constraints. We propose a framework which permits a formal study of the relationship between properties of approximations and properties of approximation spaces. Using ideas from correspondence theory, we develop an analogous framework for approximation spaces. We also show that this framework can be strongly supported by automated techniques for quantifier elimination.