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Intuitionistic Logic according to Dijkstra’s Calculus of Equational Deduction
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Intuitionistic Logic according to Dijkstra’s Calculus of Equational Deduction


Bohórquez, Jaime

Artículo de revista

2008

University of Notre Dame

Estilo de cálculoBuscar en Repositorio UMECIT
Deducción ecuacionalBuscar en Repositorio UMECIT
Lógica intuicionistaBuscar en Repositorio UMECIT
calculational styleBuscar en Repositorio UMECIT
equational deductionBuscar en Repositorio UMECIT
Intuitionistic logicBuscar en Repositorio UMECIT

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.
 
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.
 

https://repositorio.escuelaing.edu.co/handle/001/1910

  • AD - CTG – Informática [76]

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Título: Intuitionistic Logic according to Dijkstra’s Calculus of Equational Deduction.pdf
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