Propositional Vector Logic System and Its Adequacy Theorem

With the paradigm of holistic thinking and multiple perspectives, an overall new understanding of logic is obtained for reasoning in collective intelligent systems (CIS). Based on the hypothesis of multiple resolutions of reasoning in CIS, the logical state of a proposition is generalized into an n - dimensional vector whose element Is cither 1 or 0. In contrast with classical logic with binary truth - values, a prepositional vector logic system is constructed by introducing new connectives, new axioms, and new rules. Adequate sets of connectives are provided. The soundness theorem and the adequacy theorem for the vector logic system arc shown.