A coding method for a sequent calculus of propositional logic
type: Item
instance of: scholarly article
title: A coding method for a sequent calculus of propositional logic
zbMATH Open document ID: 1156.03010
author: Romas Alonderis
published in: Lithuanian Mathematical Journal
publication date: 2008-09-22T00:00:00Z
review text: Given a sequent of propositional calculus, one can construct its deduction tree to see if the sequent is derivable and how. Drawbacks of this procedure are that subformulas must be copied over and over again, and the tree can expand rapidly because it has many branches. (The author gives an example of a formula with four letters that has 64 branches in its deduction tree.) But from a sequent \(\to F\), one can read off \(F\)'s main connective and so what inference rule is to be used, with two premises or one, and which subformulas belong in the antecedent or succedent of the premise sequent(s). One can repeat this process for new sequents, and read off how many branches there are and what all the leaves are. The author's aim in this paper is to code the above information in a neat and handy way, and get all the leaves without constructing the tree. His instruction for coding is precise and natural, and he gives a number of examples for illustration and as applications.
Mathematics Subject Classification ID: 03B05
Mathematics Subject Classification ID: 03F07
zbMATH DE Number: 5345632
zbMATH Keywords: propositional logic
zbMATH Keywords: sequent calculus
zbMATH Keywords: coding of proofs
MaRDI profile type: Publication
full work available at URL: s10986-008-9008-6
OpenAlex ID: W2089782082
DOI: 10.1007/S10986-008-9008-6
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description: scientific article; zbMATH DE number 5345632