From Computer Algebra to Discretized Continuous Logic

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. Palabras Clave: Continuous Logic, Computer Algebra, Gröbner Bases, Rule Based Expert Systems.