A POLYNOMIAL MODEL FOR MULTIVALUED LOGICS WITH A TOUCH OF ALGEBRAIC-GEOMETRY AND COMPUTER ALGEBRA

In this paper, a polynomial model (residue class ring) for a given p-v alued propositional Logic (p prime), is constructed. This will allow t he study of logical deductions using Computer Algebra techniques (Grab ner Bases). Also, an interesting interpretation of \= and Kleene's sty le --> and their relation from the point of view of Algebraic Geometry (in terms of algebraic varieties) will be given. Only modest requirem ents about the good behaviour of the Logic will be assumed. This appro ach makes it possible to move a step forward and treat Knowledge Based Systems (KBSs) based on multi-valued Logics. (C) 1998 IMACS/Elsevier Science B.V.