Recent researches have shown that, pocrims (partially ordered commutative residuated integral monoids) and BCK algebras with condition (S) are categorically equivalent, and residuated lattices and bounded BCK lattices with condition (S) are categorically equivalent.
Indication theorem of generalized contradiction is proved,which indicates that generalized contradiction of one limited disturbing fuzzy propositional logic certainly can be downgraded to contradiction of another limited disturbing fuzzy propositional logic.
In addition, this thesis points out that the resource of semantic paradox is in fact "presupposition fallacy", by investigating carefully "context-sensitivity" program as well as analyzing "Situation Semantics " program, the significant representative of "context-sensitivity" program and the typical case of paradox research.
So adopt the mathematics method and go to describe the natural language from the structure angle, introduced the intension concept, possible world might should arrive person who express letter one that extend any the intensions of expression type.
Embarking from view of grand logic, discussion of the philosophical significance of paraconsistent logic is unfolded on the level of non-classical logic, logical truth, problems of contradiction, as well as new pattern of science; and states that the philosophical questions brought by paraconsistent logic is positive.
During that time, the scholars applied European logic and ancient Indian logic to explain the materials of ancient Chinese Mingbian theory, and discovered that there were plenty of logical theories in ancient China.
The study of ancient Chinese logic in the 20th century found the logic that existed in ancient China and the features and the laws of ancient Chinese logic, and has laida solid foundation for the study in this new century.
The research about this theory has found that principle of reason is the real presupposition of argument, while principle of difference, principle of possibility and principle of question are not, as they are only the demands of argument.
After considering, we find that language factors have an especial importance during the formation and the development of Aristotelian logical theory, his logical theory and his language study have a certain origin relation.
The root of Ross paradox is the much difference between the meaning and logical effect of combining the connective "V" with the deontic operator "0" or "P" and that of the combination of the counterparts of the three symbols above in natural language , as people know generally, "either", "should" and "permission".
Basing upon the reconstruction of the development of modern multidimensional debates about logic in the 21st century in China,the author of this dissertation suggests that a pluralist conception of logic is more reasonable.
The theory of descriptions insists that proper names have denotation as well as connotation,and delineates the unique logical status and function of definite descriptions , but Russell抯views that a term抯 meaning is its referal definite descriptions have no meaning necessarilyresult to assault.
Strawson refuted Russell抯 theory of descriptions with taking drastic measures to dealwith an emergency, he thought that Russell抯 theoretical basis that a term抯 meaning isits referral is wrong, and he made a distinguish between meaning and reference, intraducingcontext into the study of meaning .
The purpose of this note is to prove, as Lusztig stated, that the Euler characteristic of the variety of Iwahori subalgebras containing a certain nil-elliptic elementnt istcl wherel is the rank of the associated finite type Lie algebra.
In the present paper we study the remaing nontrivial case, that of a negative central charge-N.
In this note we present a very simple method of proving that some hyperbolic manifoldsM have finite sheeted covers with positive first Betti number.
In all these cases we actually show that Γ=π1(M) has a finite index subgroup which is mapped onto a nonabelian free group.
In the case of 4-dimensional anticommutative algebras a construction is given that links the associated cubic surface and the 27 lines on it with the structure of subalgebras of the algebra.