Research On Cognitive Predicates Based On Friedman-Sheard Theory

Modal is a very important category in logic.It is usually characterized by sentence operators,and thus many branches of logic have been derived.Cognitive logic is one of them.Modal predicate is a new research field which combines axiomatic truth theory with modal logic.Its main idea is to change the operator in modal operator logic into predicate,and to solve the inconsistency of predicate theory through the contradiction-free truth predicate provided by axiomatic truth theory.Therefore,cognitive predicate is the predicative expression of "cognitive" mode.This paper studies three cognitive predicate theories,MPK,MPB and MPBT,which based on the single-agent cognitive systems S5,K45 and KD45,using the non-contradictory truth predicate provided by the theory of Friedman-Sheard.Through the comparison of the three,the philosophical implications are discussed.This paper intends to show that predicating the basic system of cognitive logic is feasible,which not only has the support of logical technology,but also has the philosophical explanation.It is hoped that through the study of cognitive predicates,the application of predicate methods in other branches of generalized modal logic will be promoted.The first part mainly shows some basic theories which needed to study cognitive predicates,including Peano arithmetic theory,Friedman-Sheard theory,MFS and some basic theorems needed to be used.The second part is about the study of the MPK,which mainly includes two aspects:syntax and semantics.For syntax,this paper mainly studies MPK’s axioms,inference rules and some syntactic properties.In semantics,we focus on the knowledge modification semantics,and prove the consistency of MPK and its preservation of the corresponding properties of modal axioms.Finally,the relationship between MPK and MFS is discussed.The third part: MPB and MPBT are studied,and their syntax and semantics are discussed respectively.For MPB,it is proved that it can maintain consistency without true predicate,the semantic model for MPB is given,and it is proved to be a sound and complete theory.For MPBT,it is mainly proved to be a sub-theory of MPK,and the preservation of its corresponding properties in modal axioms is also discussed.In the fourth part,we study some philosophical meaning on the three modal theories.The epistemological connotations embodied in the three theories are studied,and the epistemological explanations of the consistency differences between the theories are given through the comparison of syntax and semantics.