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Tautologies and Logical Equivalence in Intuitionistic Propositional Logic without Implication

Kort, S (2015) Tautologies and Logical Equivalence in Intuitionistic Propositional Logic without Implication. Bachelor's Thesis, Mathematics.

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Abstract

Intuitionistic Propositional Logic, or IPL, is based on the idea that a formula "A" is valid when there is a proof for it and invalid when there is a proof for "not A". As long as a formula has not been proven or disproven the truth value remains unknown. This means that the law of excluded middle, "A or not A", is not a tautology. In this thesis we will look at a fragment of IPL, namely IPL without implication. The questions we would like to answer are: When is a formula a tautology in IPL without implication? How many formulas exist that are not logically equivalent in IPL without implication? We will investigate IPL in the possible world semantics with the use of Kripke models. When implication is excluded as a connective, every model can be simplified without changing the truth value of formulas. These simplified models are aptly called "simple". The largest of these simple models will prove very useful when determining whether a formula is a tautology. When the number of possible atoms is finite, the number of simple models is finite. This means that the number of formulas that are not logically equivalent is also finite and it leads to an upper bound for the number of formulas.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:02
Last Modified: 15 Feb 2018 08:02
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/12440

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