Titlebook: Cylindric-like Algebras and Algebraic Logic; Hajnal Andréka,Miklós Ferenczi,István Németi Book 2013 Springer-Verlag Berlin Heidelberg 2013

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Introductions as logic, mathematics, computer science, artificial intelligence, linguistics and even relativity theory. In some of the applications one has to transcend (a little) the original definition of CAs but .. For example, the emphasis shifted to relativized CAs and to adding extra operations such as, e

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Varieties of Two-Dimensional Cylindric Algebrasmensional diagonal-free cylindric algebras and with varieties of two-dimensional cylindric algebras with the diagonal. It is well known that two-dimensional diagonal-free cylindric algebras correspond to the two variable equality-free fragment of classical first-order logic FOL, whereas two-dimensio

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Completions and Complete Representationsdered is this: to what extent can we use an abstract mathematical language to express and reason about relations? Going back at least as far as Augustus de Morgan [Mor,60], a relation can be . explicitly, as a set of tuples of some fixed length. This allows us to focus on the mathematical aspects of

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Amalgamation, Interpolation and Epimorphisms in Algebraic Logic natural interface between universal algebra and logic (in our present context a variant of first order logic). Indeed, in algebraic logic amalgamation properties in classes of algebras are proved to be equivalent to interpolation results in the corresponding logic. In algebra, the properties of epi

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Neat Reducts and Neat Embeddings in Cylindric Algebrass is due to Leon Henkin, and one can find that the discussion of this notion is comprehensive and detailed in [Hen-Mon-Tar,85] (closer to the end of the book). This notion proved useful in at least two respects. Analyzing the number of variables appearing in proofs of first order formulas [Hir-Hod,0

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Completions, Complete Representations and Omitting Typesfields as algebraic geometry and algebraic topology, where the main constructions and theorems are algebraic in nature, but the main intuitions underlying them are respectively geometric and topological. The main intuitions underlying algebraic logic are, of course, those of formal logic. Investigat