The two value weak model for first order logic with generalized quantifier Q is generalized to be valued in complete weak complemented lattices.

The traditional model for utterance understanding is the code model based on the two-valued logic, which, however, cannot interpret how conversational implicature is inferred from utterance.

From the syntactical point of view, the concept of the syntactic truth degree of formulas is proposed in two-valued propositional logic system.