Studies On Calculus Theory And Reasoning Of Propositional Universal Logic

How to deal with various uncertainties and evolution become the key problems for further development of AI. The well-developed classical mathematical logic is the rigid logic and can only solve problems of certainty. How to make classical mathematical logic more flexible to contain various uncertainties and evolution is a new challenge that logics faces. Under this situation, all kinds of non-classical and modern logic are much proposed. Based on studies of general law of logics, Professor Huacan He proposed a universal logic principle frame which can contain many logical modalities and reasoning modes. It established a theoretical basis for the studies of complex uncertainty problems and evolution process.This thesis is a theoretical research on universal logic. Centered on the calculus of propositional universal logic, its semantics, syntax and reasoning are deeply studied. The main results and main innovations in this thesis are as following:1. The generalized tautologies theory is introduced into the propositional universal logic, and that theories for some fixed value of h and k are described, hence, some important results are obtained: when c∈[0.75, 1], if the semantic is explained by I_h=c, there are only three different generalized tautologies in F(S), that is, accessible 0-tautology, 0⁺-tautology and tautology; when h=1, k=0.5, if the semantic is explained by I_h=1,k=0.5, there are only five different generalized tautologies in F(S), that is, accessible 0-tautology, 0⁺-tautology,accessible (1/2)-tautology, (1/2)⁺-tautology and tautology in F(S); when h=0.75, k=0.5, if the semantic is explained by I_h=0.75,k=0.5, the accessible tautologies exist for each rational number in F(S), and they are difference each other.2. When h∈ (0,1], the propositional calculus deductive system UL_{h∈(0,1])} of universal logic is built up based on the 0-level universal AND operators as logic conjunction and 0-level universal IMPLICATION as logic implication. And its soundness and completeness are proved.3. When h∈(0,1], k∈ (0,1), based on the 1-level universal AND as logic conjunction,...