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Information Journal Paper

Title

Continuous Logic

Pages

  89-120

Abstract

 continuous logic is generalization of first order logic to a many valued logic with an infinitary truth value set. Many of the results of classic logic and it's model theory have been generalized to continuous logic. continuous logic not only has many uses in the mathematical analysis and in the model theory of mathematical analysis structures, but also has created new attitudes in classical model theory. Firstly, the present paper study the development of continuous logic from Ł ukasiewicz logic. Then we have a review on some of the most important basic results of continuous logic, including the completeness of the proof system and the compactness theorem. Finally, according to the concept of continuity with respect to the truth value set, we will introduce a kind of continuous logic that is based on continuous t-norm based fuzzy logics. This will lead to the introduction of two kinds of continuous logics based on Gö del logic and product logic. Then we developed some of the results of continuous logic sucontinuous logic is generalization of first order logic to a many valued logic with an infinitary truth value set. Many of the results of classic logic and it's model theory have been generalized to continuous logic. continuous logic not only has many uses in the mathematical analysis and in the model theory of mathematical analysis structures, but also has created new attitudes in classical model theory. Firstly, the present paper study the development of continuous logic from Ł ukasiewicz logic. Then we have a review on some of the most important basic results of continuous logic, including the completeness of the proof system and the compactness theorem. Finally, according to the concept of continuity with respect to the truth value set, we will introduce a kind of continuous logic that is based on continuous t-norm based fuzzy logics. This will lead to the introduction of two kinds of continuous logics based on Gö del logic and product logic. Then we developed some of the results of continuous logic such as the compactness theorem for these two logics. h as the compactness theorem for these two logics.

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    • Cite

    APA: Copy

    Khatami, Seyed Mohammad Amin, & Por Mahdiyan, Masood. (2019). Continuous Logic. MANTEQ-PAZHUHI (LOGICAL STUDIES), 10(1 ), 89-120. SID. https://sid.ir/paper/216435/en

    Vancouver: Copy

    Khatami Seyed Mohammad Amin, Por Mahdiyan Masood. Continuous Logic. MANTEQ-PAZHUHI (LOGICAL STUDIES)[Internet]. 2019;10(1 ):89-120. Available from: https://sid.ir/paper/216435/en

    IEEE: Copy

    Seyed Mohammad Amin Khatami, and Masood Por Mahdiyan, “Continuous Logic,” MANTEQ-PAZHUHI (LOGICAL STUDIES), vol. 10, no. 1 , pp. 89–120, 2019, [Online]. Available: https://sid.ir/paper/216435/en

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