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2016 Algebraic Logic Perspective on Prucnal’s Substitution
Alex Citkin
Notre Dame J. Formal Logic 57(4): 503-521 (2016). DOI: 10.1215/00294527-3659423

Abstract

A term td(p,q,r) is called a ternary deductive (TD) term for a variety of algebras V if the identity td(p,p,r)r holds in V and (c,d)θ(a,b) yields td(a,b,c)td(a,b,d) for any AV and any principal congruence θ on A. A connective f(p1,,pn) is called td-distributive if td(p,q,f(r1,,rn)) f(td(p,q,r1),,td(p,q,rn)). If L is a propositional logic and V is a corresponding variety (algebraic semantic) that has a TD term td, then any admissible in L rule, the premises of which contain only td-distributive operations, is derivable, and the substitution rtd(p,q,r) is a projective L-unifier for any formula containing only td-distributive connectives. The above substitution is a generalization of the substitution introduced by T. Prucnal to prove structural completeness of the implication fragment of intuitionistic propositional logic.

Citation

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Alex Citkin. "Algebraic Logic Perspective on Prucnal’s Substitution." Notre Dame J. Formal Logic 57 (4) 503 - 521, 2016. https://doi.org/10.1215/00294527-3659423

Information

Received: 30 September 2012; Accepted: 30 January 2014; Published: 2016
First available in Project Euclid: 13 August 2016

zbMATH: 06663938
MathSciNet: MR3565535
Digital Object Identifier: 10.1215/00294527-3659423

Subjects:
Primary: 03B55, 03B60
Secondary: 03G25, 03G27

Rights: Copyright © 2016 University of Notre Dame

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Vol.57 • No. 4 • 2016
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