Open AccessCategorical Abstract Algebraic Logic: Equivalential π-Institutions
Author(s) -
George Voutsadakis
Publication year - 2008
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v6i0.1790
Subject(s) - equivalence (formal languages) , mathematics , parameterized complexity , categorical variable , algebra over a field , logical equivalence , algebraic number , pure mathematics , context (archaeology) , cover (algebra) , discrete mathematics , combinatorics , mathematical analysis , mechanical engineering , engineering , paleontology , statistics , biology
The theory of equivalential deductive systems, as introduced by Prucnal and Wrónski and further developed by Czelakowski, is abstracted to cover the case of logical systems formalized as π-institutions. More precisely, the notion of an N-equivalence system for a given π-institution is introduced. A characterization theorem for N-equivalence systems, previously proven for N-parameterized equivalence systems, is revisited and a “transfer theorem” for N-equivalence systems is proven. For a π-institution I having an N-equivalence system, the maximum such system is singled out and, then, an analog of Herrmann’s Test, characterizing those N-protoalgebraic π-institutions having an N-equivalence system, is formulated. Finally, some of the rudiments of matrix theory are revisited in the context of π-institutions, as they relate to the existence of N-equivalence systems.