Deduction Theorem

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Geoff Sutcliffe - One of the best experts on this subject based on the ideXlab platform.

Xu Yang - One of the best experts on this subject based on the ideXlab platform.

  • four valued propositional logic system fl
    Systems Man and Cybernetics, 2002
    Co-Authors: Qin Keyun, Zheng Pei, Wu Jianle, Xu Yang
    Abstract:

    This paper presents a four valued propositional logic system FL by using the method of free algebra. In this system, the truth values of formulae can be incomparable. The semantical and syntactical problems of FL are discussed. The soundness Theorem, Deduction Theorem and adequacy Theorem are given.

  • L -valued propositional logic L vpl
    Information Sciences, 1999
    Co-Authors: Xu Yang, Qin Ke-yun, Liu Jun, Song Zhen-ming
    Abstract:

    In this paper, two types of gradational L-type lattice-valued propositional logic L"v"p"l, with truth values in a lattice implication algebra are introduced and some fundamental questions of them such as semantics, syntax and compactness are investigated, and where the L-type @a-Soundness Theorem, (@a, @b)-Completeness Theorem, (@a, @b)-Consistent Theorem and (@a, @b, @q)-Deduction Theorem are also proved.

Marianne Brown - One of the best experts on this subject based on the ideXlab platform.

Yanhong She - One of the best experts on this subject based on the ideXlab platform.

  • On the rough consistency measures of logic theories and approximate reasoning in rough logic
    International Journal of Approximate Reasoning, 2014
    Co-Authors: Yanhong She
    Abstract:

    This paper is mainly devoted to establishing a kind of graded reasoning method in the context of rough logic. To this end, a weak form of Deduction Theorem in rough logic is firstly obtained, then, based upon the weak Deduction Theorem and the notion of rough truth degree, a new kind of graded reasoning method in rough logic is presented. Moreover, to embody the idea of rough approximations, the notions of graded rough upper consequence and graded rough lower consequence are also proposed, which can be treated as the logical counterpart of rough upper and lower approximation, respectively. Compared with the existing graded reasoning method, the proposed method in the present paper does not employ the notion of rough similarity degree, and hence their fundamental starting points are different, however, they are also closely related, accordingly, a comparative study is performed between these two different graded reasoning methods. Lastly, based on the proposed graded reasoning method, the notions of rough (upper, lower) consistency degree are also proposed and their properties are investigated in detail.

Ernst Zimmermann - One of the best experts on this subject based on the ideXlab platform.

  • A Predicate Logical Extension of a Subintuitionistic Propositional Logic
    Studia Logica, 2002
    Co-Authors: Ernst Zimmermann
    Abstract:

    We develop a predicate logical extension of a subintuitionistic propositional logic. Therefore a Hilbert type calculus and a Kripke type model are given. The propositional logic is formulated to axiomatize the idea of strategic weakening of Kripke's semantic for intuitionistic logic: dropping the semantical condition of heredity or persistence leads to a nonmonotonic model. On the syntactic side this leads to a certain restriction imposed on the Deduction Theorem. By means of a Henkin argument strong completeness is proved making use of predicate logical principles, which are only classically acceptable.

  • A subintuitionistic logic and some of its methods
    Lecture Notes in Computer Science, 2002
    Co-Authors: Ernst Zimmermann
    Abstract:

    We develop a predicate logical extension of a subintuitionistic propositional logic. Therefore a Hilbert type calculus and a Kripke type model are given. The propositional logic is formulated to axiomatize the idea of strategic weakening of Kripke's semantic for intuitionistic logic: dropping the semantical condition of heredity or persistence leads to a nonmonotonic model. On the syntactic side this leads to a certain restriction imposed on the Deduction Theorem. By means of a Henkin argument strong completeness is proved making use of predicate logical principles, which are only classically acceptable. Semantic tableaux and an embedding into modal logic are defined straightforward.