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Categorical abstract algebraic logic categorical algebraization of first-order logic without terms

✍ Scribed by George Voutsadakis

Publisher
Springer
Year
2004
Tongue
English
Weight
200 KB
Volume
44
Category
Article
ISSN
0933-5846

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Categorical abstract algebraic logic: Th
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## Abstract Czelakowski introduced the Suszko operator as a basis for the development of a hierarchy of non‐protoalgebraic logics, paralleling the well‐known abstract algebraic hierarchy of protoalgebraic logics based on the Leibniz operator of Blok and Pigozzi. The scope of the theory of the Leibn

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## Abstract The notion of an __ℐ__ ‐matrix as a model of a given __π__ ‐institution __ℐ__ is introduced. The main difference from the approach followed so far in Categorical Abstract Algebraic Logic (CAAL) and the one adopted here is that an __ℐ__ ‐matrix is considered modulo the entire class of mo

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## Abstract Equivalent deductive systems were introduced in [4] with the goal of treating 1‐deductive systems and algebraic 2‐deductive systems in a uniform way. Results of [3], appropriately translated and strengthened, show that two deductive systems over the same language type are equivalent if

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## Abstract The study of structure systems, an abstraction of the concept of first‐order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of