Intuitionistic implication without disjunction

Gerard R. Renardel de Lavalette; Alex Hendriks; Dick H.J. de Jongh

doi:10.1093/logcom/exq058

Intuitionistic implication without disjunction

Gerard R. Renardel de Lavalette, Alex Hendriks, Dick H.J. de Jongh

Fundamental Computing

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Abstract

We investigate fragments of intuitionistic propositional logic containing implication but not disjunction. These fragments are finite, but their size grows superexponentially with the number of generators. Exact models are used to characterize the fragments.

Original language	English
Pages (from-to)	375-404
Number of pages	30
Journal	Journal of Logic and Computation
Volume	22
Issue number	3
DOIs	https://doi.org/10.1093/logcom/exq058
Publication status	Published - Jun-2012

Keywords

Intuitionistic logic
logic fragment
implication
exact model
Hilbert algebra
SEMI-LATTICES
LOGIC

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10.1093/logcom/exq058

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title = "Intuitionistic implication without disjunction",

abstract = "We investigate fragments of intuitionistic propositional logic containing implication but not disjunction. These fragments are finite, but their size grows superexponentially with the number of generators. Exact models are used to characterize the fragments.",

keywords = "Intuitionistic logic, logic fragment, implication, exact model, Hilbert algebra, SEMI-LATTICES, LOGIC",

author = "\{Renardel de Lavalette\}, \{Gerard R.\} and Alex Hendriks and Jongh, \{Dick H.J. de\}",

note = "Relation: http://www.rug.nl/fmns-research/bernoulli/index Rights: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science",

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AU - Hendriks, Alex

AU - Jongh, Dick H.J. de

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KW - Intuitionistic logic

KW - logic fragment

KW - implication

KW - exact model

KW - Hilbert algebra

KW - SEMI-LATTICES

KW - LOGIC

U2 - 10.1093/logcom/exq058

DO - 10.1093/logcom/exq058

M3 - Article

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SP - 375

EP - 404

JO - Journal of Logic and Computation

JF - Journal of Logic and Computation

IS - 3

ER -

Intuitionistic implication without disjunction

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Keywords

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