From computer algebra to discretized continuous logic

Autores: Eugenio Roanes Lozano , Francisco Javier Montero de Juan , Antonio Hernando , Luis María Laita de la Rica
Localización: XV Congreso Español sobre Tecnologías y Lógica Fuzzy ESTYLF 2010: Huelva [Recurso electrónico] / coord. por Antonio Peregrín Rubio , 2010, ISBN 978-84-92944-02-6, págs. 169-174
Idioma: inglés
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Resumen
- 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 Gröbner 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.