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  1. Categorical Abstract Algebraic Logic: Referential Algebraic Semantics.George Voutsadakis - 2013 - Studia Logica 101 (4):849-899.
    Wójcicki has provided a characterization of selfextensional logics as those that can be endowed with a complete local referential semantics. His result was extended by Jansana and Palmigiano, who developed a duality between the category of reduced congruential atlases and that of reduced referential algebras over a fixed similarity type. This duality restricts to one between reduced atlas models and reduced referential algebra models of selfextensional logics. In this paper referential algebraic systems and congruential atlas systems are introduced, which abstract (...)
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  • Categorical Abstract Algebraic Logic Categorical Algebraization of First-Order Logic Without Terms.George Voutsadakis - 2004 - Archive for Mathematical Logic 44 (4):473-491.
    An algebraization of multi-signature first-order logic without terms is presented. Rather than following the traditional method of choosing a type of algebras and constructing an appropriate variety, as is done in the case of cylindric and polyadic algebras, a new categorical algebraization method is used: The substitutions of formulas of one signature for relation symbols in another are treated in the object language. This enables the automatic generation via an adjunction of an algebraic theory. The algebras of this theory are (...)
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  • Multi‐Term Π‐Institutions and Their Equivalence.José Gil-Férez - 2006 - Mathematical Logic Quarterly 52 (5):505-526.
    The notion of a multi-term π-institution is introduced and a criterion for the equivalence of two multi-term π-institutions in terms of their categories of theories is proved. Moreover, a counterexample that shows that this criterion is false for arbitrary π-institutions is given.
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  • Introduction.Josep Maria Font & Ramon Jansana - 2013 - Studia Logica 101 (4):647-650.
  • Categorical Abstract Algebraic Logic: The Diagram and the Reduction Operator Lemmas.George Voutsadakis - 2007 - Mathematical Logic Quarterly 53 (2):147-161.
    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 the expansion of a first-order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality-free first-order structures are provided in the framework of structure systems. (© 2007 WILEY-VCH (...)
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  • Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity.George Voutsadakis - 2007 - Studia Logica 85 (2):215-249.
    Two classes of π are studied whose properties are similar to those of the protoalgebraic deductive systems of Blok and Pigozzi. The first is the class of N-protoalgebraic π-institutions and the second is the wider class of N-prealgebraic π-institutions. Several characterizations are provided. For instance, N-prealgebraic π-institutions are exactly those π-institutions that satisfy monotonicity of the N-Leibniz operator on theory systems and N-protoalgebraic π-institutions those that satisfy monotonicity of the N-Leibniz operator on theory families. Analogs of the correspondence property of (...)
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  • Categorical Abstract Algebraic Logic: The Largest Theory System Included in a Theory Family.George Voutsadakis - 2006 - Mathematical Logic Quarterly 52 (3):288-294.
    In this note, it is shown that, given a π -institution ℐ = 〈Sign, SEN, C 〉, with N a category of natural transformations on SEN, every theory family T of ℐ includes a unique largest theory system equation image of ℐ. equation image satisfies the important property that its N -Leibniz congruence system always includes that of T . As a consequence, it is shown, on the one hand, that the relation ΩN = ΩN characterizes N -protoalgebraicity inside the (...)
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  • Categorical Abstract Algebraic Logic: Gentzen Π ‐Institutions and the Deduction‐Detachment Property.George Voutsadakis - 2005 - Mathematical Logic Quarterly 51 (6):570-578.
    Given a π -institution I , a hierarchy of π -institutions I is constructed, for n ≥ 1. We call I the n-th order counterpart of I . The second-order counterpart of a deductive π -institution is a Gentzen π -institution, i.e. a π -institution associated with a structural Gentzen system in a canonical way. So, by analogy, the second order counterpart I of I is also called the “Gentzenization” of I . In the main result of the paper, it (...)
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