Categorical Abstract Algebraic Logic: (?,N)-Algebraic Systems

George Voutsadakis

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Categorical Abstract Algebraic Logic: (?,N)-Algebraic Systems

机译：分类抽象代数逻辑：( ?, N）-代数系统

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Algebraic systems play in the theory of algebraizability of π-institutions the role that algebras play in the theory of algebraizable sentential logics. In this same sense, ℐ-algebraic systems are to a π-institution ℐ what $mathcal{S}$ -algebras are to a sentential logic $mathcal{S}$ . More precisely, an (ℐ,N)-algebraic system is the sentence functor reduct of an N′-reduced (N,N′)-full model of a π-institution ℐ. Algebraic systems are formally introduced and their relationship with full models and with bilogical morphisms is investigated.

机译：代数系统在π-机构的可代数理论中扮演着代数在可代数逻辑逻辑理论中扮演的角色。在同样的意义上，ℐ代数系统对π机构ℐ$ mathcal {S} $-代数对句子逻辑$ mathcal {S} $而言。更准确地说，（ℐ，N）代数系统是π机构ℐ的N'约简（N，N'）-完全模型的句子函子约简。正式介绍了代数系统，并研究了它们与完整模型和生物学态射的关系。

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来源
《Applied Categorical Structures》 |2005年第3期|265-280|共16页
作者
George Voutsadakis;
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School of Mathematics and Computer Science Lake Superior State University 650 W. Easterday Avenue Sault Sainte Marie MI 49783 U.S.A.;

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正文语种 eng
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关键词
abstract algebraic logic; deductive systems; institutions; equivalent deductive systems; algebraizable deductive systems; adjunctions; equivalent institutions; algebraizable institutions; Leibniz congruence; Tarski congruence; algebraizable sentential logics; $mathcal{S}$n n -algebras;

机译：抽象代数逻辑;演绎系统;制度;等价演绎系统;可代数演绎系统;附加语;等价制度;可代数制度;Leibniz同余;Tarskis同余;可代数句法;$ mathcal {S} n n-代数;

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专利

1. Categorical Abstract Algebraic Logic: Partially Ordered Algebraic Systems [J] . George Voutsadakis Applied categorical structures . 2006,第1期

机译：分类抽象代数逻辑：部分有序代数系统
2. Categorical Abstract Algebraic Logic: (□,N)-Algebraic Systems [J] . George Voutsadakis Applied categorical structures . 2005,第3期

机译：分类抽象代数逻辑：（□，N）-代数系统
3. Categorical Abstract Algebraic Logic: Referential Algebraic Semantics [J] . George Voutsadakis Studia Logica . 2013,第4期

机译：分类抽象代数逻辑：参照代数语义
4. Completing Categorical Algebras (Extended Abstract) [C] . Stephen L. Bloom, Zoltan Esik Fourth IFIP(International Federation for Information Processing) International Conference on Theoretical Computer Science - TCS 2006; International Federation for Information Processing(IFIP); 209; Sprin . 2006

机译：完成分类代数（扩展摘要）
5. Solving abstract algebraic word problems with a Make a Problem More Specific strategy for high school Algebra 2 students. [D] . Akridge, William. 2009

机译：针对高中代数2学生，使用“使问题更具体”的策略解决抽象代数词的问题。
6. Statistics on microcomputers. A non-algebraic guide to the appropriate use of statistics packages in biomedical research and pathology laboratory practice. 5. Analysis of categorical data. [O] . R A Brown, J S Beck 1989

机译：微型计算机的统计信息。在生物医学研究和病理实验室实践中适当使用统计软件包的非代数指南。 5.分类数据分析。
7. Categorical Abstract Algebraic Logic: Partially Ordered Algebraic Systems [O] . George Voutsadakis, To Don Pigozzi, Kate Pa =lasińska 2005

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8. Technical Report ON SOME CATEGORICAL ALGEBRA ASPECTS OF AUTOMATA THEORY: THE CATEGORICAL PROPERTIES OF TRANSITION SYSTEMS [R] . Yehoshafat Give'on 1966

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Categorical Abstract Algebraic Logic: (?,N)-Algebraic Systems

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