Categorical Abstract Algebraic Logic: Equivalential π-Institutions
AbstractThe 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.
How to Cite
VOUTSADAKIS, George. Categorical Abstract Algebraic Logic: Equivalential π-Institutions. The Australasian Journal of Logic, [S.l.], v. 6, aug. 2008. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1790>. Date accessed: 18 july 2019. doi: https://doi.org/10.26686/ajl.v6i0.1790.