Seyed Mohammad Amin Khatami; Esfandiar Eslami
Abstract
In the early 19th century, the ''principle of bivalence'' of the Aristotelian logic was challenged. Of course, Aristotle himself was questioned the applicability of this principle to propositions concerning future contingents, and he answered it via something like as modalities of possibility. However, ...
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In the early 19th century, the ''principle of bivalence'' of the Aristotelian logic was challenged. Of course, Aristotle himself was questioned the applicability of this principle to propositions concerning future contingents, and he answered it via something like as modalities of possibility. However, Aristotle did not abandon the principle and it has not received much attention till the Renaissance. From Renaissance to the early 19th century, some philosophical considerations to this issue were developed. Rejecting the principle of bivalence implies alternative accounts of various kinds of logics such as many-valued logics in the context of logic. In this article, we first survey the development of many-valued logics by reviewing motivational ideas behind many-valued logics together with examining the aims and scopes of some of these logics. Then, we devote the rest of the paper to study various aspects of "truth value sets" and "interpretation of logical connectives" in many-valued logics to obtain a more comprehensive view on these logics.
Seyed Mohammad Amin Khatami; masood por mahdiyan
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 ...
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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 Łukasiewicz 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 Gödel logic and product logic. Then we developed some of the results of continuous logic such as the compactness theorem for these two logics.
