Reasoning about negligibility and proximity
نویسنده
چکیده
In this paper, we consider the binary relations of negligibility, comparability and proximity in the set of all hyperreals. Associating with them the binary predicates N , C and P and the operators [N ], [C] and [P ], we consider a first-order theory based on these predicates and a modal logic based on these operators. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal
منابع مشابه
Logic-based order of magnitude qualitative reasoning for closeness via proximity intervals: a first approach
Qualitative reasoning is an area of AI which provides solutions to problems where the quantitative information either is not available or can not be used; in particular, order of magnitude qualitative reasoning assumes different qualitative classes and relations such as negligibility and closeness. In this paper, we focus mainly on the very important notion of closeness from the logical point o...
متن کاملQualitative reasoning based on fuzzy relative orders of magnitude
—This paper proposes a fuzzy set-based approach for handling relative orders of magnitude stated in terms of closeness and negligibility relations. At the semantic level, these relations are represented by means of fuzzy relations controlled by tolerance parameters. A set of sound inference rules, involving the tolerance parameters, is provided, in full accordance with the combination/projectio...
متن کاملOrder of Magnitude Qualitative Reasoning with Bidirectional Negligibility
In this paper, we enrich the logic of order of magnitude qualitative reasoning by means of a new notion of negligibility which has very useful properties with respect to operations of real numbers. A complete axiom system is presented for the proposed logic, and the new negligibility relation is compared with previous ones and its advantages are presented on the basis of an example.
متن کاملA Multimodal Logic Approach to Order of Magnitude Qualitative Reasoning with Comparability and Negligibility Relations
Non-classical logics have proven to be an adequate framework to formalize knowledge representation. In this paper we focus on a multimodal approach to formalize order-of-magnitude qualitative reasoning, extending the recently introduced system MQ, by means of a certain notion of negligibility relation which satisfies a number of intuitively plausible properties, as well as a minimal axiom syste...
متن کاملAn ATP of a Relational Proof System for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance
We introduce an Automatic Theorem Prover (ATP) of a dual tableau system for a relational logic for order of magnitude qualitative reasoning, which allows us to deal with relations such as negligibility, non-closeness and distance. Dual tableau systems are validity checkers that can serve as a tool for verification of a variety of tasks in order of magnitude reasoning, such as the use of qualita...
متن کامل