Algebraic logic
Algebraic logic
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DOI：
10.1007/978-94-017-0452-6_3
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
H. Madarász
中科院分区：
文献类型：
--
作者：
H. Madarász
Algebraic logic can be divided into two main parts. Part I studies algebras which are relevant to logic (s), eg algebras which were obtained from logics (one way or another). Since Part I studies algebras, its methods are, basically, algebraic. One could say that Part I belongs to'Algebra Country'. Continuing this metaphor, Part 11 deals with studying and building the bridge between Algebra Country and Logic Country. Part 11 deals with the methodology of solving logic problems by (i) translating them to algebra (the process of algebraization),(ii) solving the algebraic problem (this really belongs to Part I), and (iii) translating the result back to logic. There is an emphasis here on step (iii), because without such a methodological emphasis one could be tempted to play the'enjoyable games'(i) and (ii), and then forget about the'boring duty'of (iii). Of course, this bridge can also be used backwards, to solve algebraic problems with logical methods. We will give some simple examples for this in the present work.Accordingly, the present work consists of two parts, too. Parts land 11 of the Paper deal with the corresponding parts of algebraic logic. More specifically, Part I deals with the algebraic theory in general, and with algebras of sets of sequences, or algebras of relations, in particular. Part 11 deals with the methodology of algebraization of logics and logical problems, equivalence theorems between properties of logics and properties of (classes of) algebras, and in particular, discusses concrete results about logics obtained via this methodology of algebraization. Since Part 11 deals with general connections between logics and algebras, a general definition of what we understand by a logic or logical system is needed. Of course, such a definition has to be broad enough to be widely applicable and narrow enough to support interesting theorems. The first Section of Part 11 is devoted to finding such adefinition.
