A SEQUENT SYSTEM WITHOUT IMPROPER DERIVATIONS
Bulletin of the Section of Logic, ISSN: 0138-0680, Vol: 51, Issue: 1, Page: 91-108
2022
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Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
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Article Description
In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper, and others proper. Improper inference rules are more complicated and are often harder to understand than the proper ones. In the present paper, we distinguish between proper and improper derivations by using sequent systems. Specifically, we introduce a sequent system ` for classical propositional logic with only structural rules, and prove that ` does not allow improper derivations in general. For instance, the sequent ⇒ p → q cannot be derived from the sequent p ⇒ q in `. In order to prove the failure of improper derivations, we modify the usual notion of truth valuation, and using the modified valuation, we prove the completeness of `. We also consider whether an improper derivation can be described generally by using `
Bibliographic Details
Uniwersytet Lodzki (University of Lodz)
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