Fuzzy sets, uncertainty, and information
Fuzzy sets, uncertainty, and information
Knowledge compilation and theory approximation
Journal of the ACM (JACM)
Tolerance approximation spaces
Fundamenta Informaticae - Special issue: rough sets
Fuzzy sets and binary-proximity-based rough sets
Information Sciences: an International Journal - From rough sets to soft computing
Tractable Reasoning in Artificial Intelligence
Tractable Reasoning in Artificial Intelligence
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Computing strongest necessary and weakest sufficient conditions of first-order formulas
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
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
Dynamics of Approximate Information Fusion
RSEISP '07 Proceedings of the international conference on Rough Sets and Intelligent Systems Paradigms
Towards Approximate BGI Systems
CEEMAS '07 Proceedings of the 5th international Central and Eastern European conference on Multi-Agent Systems and Applications V
Agents in approximate environments
Games, Actions and Social Software
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
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The relation of similarity is essential in understanding and developing frameworks for reasoning with vague and approximate concepts. There is a wide spectrum of choice as to what properties we associate with similarity and such choices determine the nature of vague and approximate concepts defined in terms of these relations. Additionally, robotic systems naturally have to deal with vague and approximate concepts due to the limitations in reasoning and sensor capabilities. Halpern [1] introduces the use of subjective and objective states in a modal logic formalizing vagueness and distinctions in transitivity when an agent reasons in the context of sensory and other limitations. He also relates these ideas to a solution to the Sorities and other paradoxes. In this paper, we generalize and apply the idea of similarity and tolerance spaces [2,3,4,5], a means of constructing approximate and vague concepts from such spaces and an explicit way to distinguish between an agent's objective and subjective states. We also show how some of the intuitions from Halpern can be used with similarity spaces to formalize the above-mentioned Sorities and other paradoxes.