Assertive graphs (AGs) modify Peirce’s Alpha part of Exis- tential Graphs (EGs) and are used to reason about assertions without any ad hoc sign of assertion. This paper presents an extension of propo- sitional AGs to Beta by lines. Absence of polarities necessitate Beta- AGs to resort to two kinds of lines: standard lines (a certain method of asserting), and barbed lines (a general method of asserting). A new set of rules of transformations for Beta-AGs is presented that derive theorems of quantificational intuitionistic logic. Beta-AGs offer a new system to analyse assertions through quantificational diagrams.
Beta Assertive Graphs
Francesco Bellucci
;Ahti-Veikko Pietarinen
2020
Abstract
Assertive graphs (AGs) modify Peirce’s Alpha part of Exis- tential Graphs (EGs) and are used to reason about assertions without any ad hoc sign of assertion. This paper presents an extension of propo- sitional AGs to Beta by lines. Absence of polarities necessitate Beta- AGs to resort to two kinds of lines: standard lines (a certain method of asserting), and barbed lines (a general method of asserting). A new set of rules of transformations for Beta-AGs is presented that derive theorems of quantificational intuitionistic logic. Beta-AGs offer a new system to analyse assertions through quantificational diagrams.File in questo prodotto:
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