In the paper, original formal-logical conception of syntactic and semantic： intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics o...In the paper, original formal-logical conception of syntactic and semantic： intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically： in the spirit of some Husserl＇s ideas of pure grammar, Le^niewski-Ajukiewicz＇s theory syntactic/semantic categories and in accordance with Frege＇s ontological canons, Bochefiski＇s famous motto--syntax mirrors ontology and some ideas of Suszko： language should be a linguistic scheme of ontological reality and simultaneously a tool of its cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic （extensional and intensional） categories of expressions of L. From this postulate, three principles of compositionality follow： one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism partial algebra of L into algebraic models of L： syntactic, intensional, and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science.展开更多
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a modu...The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.展开更多
This paper proves that on any tamed closed almost complex four-manifold(M,J)whose dimension of J-anti-invariant cohomology is equal to the self-dual second Betti number minus one,there exists a new symplectic form com...This paper proves that on any tamed closed almost complex four-manifold(M,J)whose dimension of J-anti-invariant cohomology is equal to the self-dual second Betti number minus one,there exists a new symplectic form compatible with the given almost complex structure J.In particular,if the self-dual second Betti number is one,we give an affirmative answer to a question of Donaldson for tamed closed almost complex four-manifolds.Our approach is along the lines used by Buchdahl to give a unified proof of the Kodaira conjecture.展开更多
文摘In the paper, original formal-logical conception of syntactic and semantic： intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically： in the spirit of some Husserl＇s ideas of pure grammar, Le^niewski-Ajukiewicz＇s theory syntactic/semantic categories and in accordance with Frege＇s ontological canons, Bochefiski＇s famous motto--syntax mirrors ontology and some ideas of Suszko： language should be a linguistic scheme of ontological reality and simultaneously a tool of its cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic （extensional and intensional） categories of expressions of L. From this postulate, three principles of compositionality follow： one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism partial algebra of L into algebraic models of L： syntactic, intensional, and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science.
基金supported by National Natural Science Foundation of China (Grant No. 10871016)
文摘The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.
基金supported by PRC Grant NSFC 11701226(Tan),11371309,11771377(Wang),11426195(Zhou),11471145(Zhu)Natural Science Foundation of Jiangsu Province BK20170519(Tan)+1 种基金University Science Research Project of Jiangsu Province 15KJB110024(Zhou)Foundation of Yangzhou University 2015CXJ003(Zhou).
文摘This paper proves that on any tamed closed almost complex four-manifold(M,J)whose dimension of J-anti-invariant cohomology is equal to the self-dual second Betti number minus one,there exists a new symplectic form compatible with the given almost complex structure J.In particular,if the self-dual second Betti number is one,we give an affirmative answer to a question of Donaldson for tamed closed almost complex four-manifolds.Our approach is along the lines used by Buchdahl to give a unified proof of the Kodaira conjecture.
