From Mathfuzzlog
| Authors: |
|
| Title: |
Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space |
| Journal: |
Fuzzy Sets and Systems |
| Volume |
158 |
| Number |
|
| Pages: |
2591-2604 |
| Year: |
2007 |
Abstract
A maximal consistent theory is a maximal theory with respect to its consistency. The present paper is divided into two parts. The first one is devoted to characterize the maximality of a consistent theory in the formal deductive system L* (which is a logic system equivalent to the nilpotent minimum logic). It is proved that each maximal consistent theory in this logic must be the deductive closure of a collection of simple compound formulas. Hence, it follows that there is a one-to-one correspondence between the set of all maximal consistent theories and the set of evaluations e assigning to each propositional variable p its truth degree e(p) ∈ {0, 1 2 , 1}. The Satisfiability Theorem and Compactness Theorem of L* are obtained. The second part is to investigate the topological structure of the set of all maximal consistent theories over L*, and the results show that this topological space is a Cantor space
