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Clones and Genoids in Lambda Calculus and First Order Logic

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 نشر من قبل Zhaohua Luo
 تاريخ النشر 2012
  مجال البحث الهندسة المعلوماتية
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 تأليف Zhaohua Luo




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A genoid is a category of two objects such that one is the product of itself with the other. A genoid may be viewed as an abstract substitution algebra. It is a remarkable fact that such a simple concept can be applied to present a unified algebraic approach to lambda calculus and first order logic.



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The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this purpose are various clones over a full subcategory of a category. We show that the syntax of equational logic, lambda calculus and first order logic can be represented as clones or right algebras of clones over the set of positive integers. The semantics is then represented by structures derived from left algebras of these clones.
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