Notre Dame Journal of Formal Logic

Intuitionistic Logic according to Dijkstra's Calculus of Equational Deduction

Jaime Bohórquez V.


Dijkstra and Scholten have proposed a formalization of classical predicate logic on a novel deductive system as an alternative to Hilbert's style of proof and Gentzen's deductive systems. In this context we call it CED (Calculus of Equational Deduction). This deductive method promotes logical equivalence over implication and shows that there are easy ways to prove predicate formulas without the introduction of hypotheses or metamathematical tools such as the deduction theorem. Moreover, syntactic considerations (in Dijkstra's words, "letting the symbols do the work") have led to the "calculational style," an impressive array of techniques for elegant proof constructions. In this paper, we formalize intuitionistic predicate logic according to CED with similar success. In this system (I-CED), we prove Leibniz's principle for intuitionistic logic and also prove that any (intuitionistic) valid formula of predicate logic can be proved in I-CED.

Article information

Notre Dame J. Formal Logic Volume 49, Number 4 (2008), 361-384.

First available in Project Euclid: 17 October 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03F50: Metamathematics of constructive systems
Secondary: 03B20: Subsystems of classical logic (including intuitionistic logic)

intuitionistic logic calculational style equational deduction


Bohórquez V., Jaime. Intuitionistic Logic according to Dijkstra's Calculus of Equational Deduction. Notre Dame J. Formal Logic 49 (2008), no. 4, 361--384. doi:10.1215/00294527-2008-017.

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