Abstract:
To study the characterizations of a special theory-Boolean theory in the propositional logic system L*. Some necessary and sufficient conditions for a theory to be Boolean are obtained from two aspects of syntactics and semantics, respectively. By means of Boolean theory a congruence relation on F(S) is defined and it is proved that the corresponding quotient algebra is a Boolean algebra.Moreover, the minimal closed Boolean theory TH(L) is given.
