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From computer algebra to discretized continuous logic

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Roanes-Lozano, E. and Montero, Javier and Hernando, A. and Laita, L. M. (2010) From computer algebra to discretized continuous logic. In XV Congreso español sobre tecnologías y lógica fuzzy : 2010 : Huelva. Universidad de Huelva, Servicio de Publicaciones, Huelva, pp. 169-174. ISBN 978-84-92944-02-6

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Abstract

The aim of this paper is to present a new algebraic approach from computer algebra to a discretized continuous logic. It makes use of a previous model of p-valued logic (where p is a prime number) based on the use of Grobner bases of polynomial ideals. A five-valued logic (i.e., p = 5) with some modal operators has been considered as a compromise between precision and complexity of the polynomials involved. Therefore the continuous truth values are discretized into five intervals corresponding to the likelihood levels: impossible or very unlikely unlikely dubious probably almost sure or absolutely sure. It is therefore posible to obtain the likelihood level of any given logic formula. Moreover, it is possible to perform knowledge extraction and verification of small Rule Based Expert System whose knowledge is represented by this logic. An implementation in the computer algebra system Maple is included.


Item Type:Book Section
Uncontrolled Keywords:Continuous Logic; Computer Algebra; Grobner Bases; Rule Based Expert Systems.
Subjects:Sciences > Mathematics > Logic, Symbolic and mathematical
ID Code:30868
Deposited On:15 Jun 2015 07:51
Last Modified:19 Apr 2016 15:25

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