David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 74 (1-2):275 - 311 (2003)
A category theoretic generalization of the theory of algebraizable deductive systems of Blok and Pigozzi is developed. The theory of institutions of Goguen and Burstall is used to provide the underlying framework which replaces and generalizes the universal algebraic framework based on the notion of a deductive system. The notion of a term -institution is introduced first. Then the notions of quasi-equivalence, strong quasi-equivalence and deductive equivalence are defined for -institutions. Necessary and sufficient conditions are given for the quasi-equivalence and the deductive equivalence of two term -institutions, based on the relationship between their categories of theories. The results carry over without any complications to institutions, via their associated -institutions. The -institution associated with a deductive system and the institution of equational logic are examined in some detail and serve to illustrate the general theory.
|Keywords||Algebraic Logic Multi-sorted Behavioral Logic Behavioral Algebraizability Behavioral Leibniz Operator Behavioral Leibniz Hierarchy Multi-sorted π-Institutions Behavioral Leibniz Congruence Systems Behavioral Categorical Leibniz Hierarchy|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
George Voutsadakis (2013). Categorical Abstract Algebraic Logic: Referential Algebraic Semantics. Studia Logica 101 (4):849-899.
Similar books and articles
Tatjana L. Plotkin, Sarit Kraus & Boris I. Plotkin (1998). Problems of Equivalence, Categoricity of Axioms and States Description in Databases. Studia Logica 61 (3):347-366.
M. Spinks & R. Veroff (2008). Constructive Logic with Strong Negation is a Substructural Logic. II. Studia Logica 89 (3):401 - 425.
Romà J. Adillon & Ventura Verdú (2000). On a Contraction-Less Intuitionistic Propositional Logic with Conjunction and Fusion. Studia Logica 65 (1):11-30.
Steffen Lewitzka (2007). Abstract Logics, Logic Maps, and Logic Homomorphisms. Logica Universalis 1 (2):243-276.
Alexej P. Pynko (1995). Algebraic Study of Sette's Maximal Paraconsistent Logic. Studia Logica 54 (1):89 - 128.
George Voutsadakis (2005). Categorical Abstract Algebraic Logic: Models of Π-Institutions. Notre Dame Journal of Formal Logic 46 (4):439-460.
Marius Petria & Răzvan Diaconescu (2006). Abstract Beth Definability in Institutions. Journal of Symbolic Logic 71 (3):1002 - 1028.
George Voutsadakis (2007). Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity. Studia Logica 85 (2):215 - 249.
W. J. Blok & J. Rebagliato (2003). Algebraic Semantics for Deductive Systems. Studia Logica 74 (1-2):153 - 180.
George Voutsadakis (2003). Categorical Abstract Algebraic Logic Metalogical Properties. Studia Logica 74 (3):369 - 398.
Added to index2009-01-28
Total downloads6 ( #292,803 of 1,696,808 )
Recent downloads (6 months)2 ( #250,888 of 1,696,808 )
How can I increase my downloads?