Exploring Jaśkowski’s Discussive Logic: Proof Analysis and Related Remarks

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00641211" target="_blank" >RIV/67985807:_____/25:00641211 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10992-025-09808-4" target="_blank" >https://doi.org/10.1007/s10992-025-09808-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10992-025-09808-4" target="_blank" >10.1007/s10992-025-09808-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Exploring Jaśkowski’s Discussive Logic: Proof Analysis and Related Remarks

Popis výsledku v původním jazyce

This paper presents a comprehensive proof-theoretic analysis of Jaśkowski’s discussive (or discursive) logic, working with a set of connectives including classical negation and disjunction, as well as so-called (right-)discussive conjunction and discussive implication. By employing established techniques two labelled frameworks are introduced: sequent and natural deduction systems. The paper explores the ability of the proposed calculi to accurately represent Jaśkowski’s discussive logic, particularly in light of its paraconsistent nature, and establishes cut-admissibility and normalization theorems. Additionally, the introduced sequent calculus – shown to allow terminating proof search – is employed to prove the embedding of discussive logic within modal logic S5. Finally, it is proved that the natural deduction calculus translates into the corresponding sequent system, with soundness and completeness established for both calculi. Concluding remarks highlight the potential for expanding this study and suggest directions for future research.

Název v anglickém jazyce

Exploring Jaśkowski’s Discussive Logic: Proof Analysis and Related Remarks

Popis výsledku anglicky

This paper presents a comprehensive proof-theoretic analysis of Jaśkowski’s discussive (or discursive) logic, working with a set of connectives including classical negation and disjunction, as well as so-called (right-)discussive conjunction and discussive implication. By employing established techniques two labelled frameworks are introduced: sequent and natural deduction systems. The paper explores the ability of the proposed calculi to accurately represent Jaśkowski’s discussive logic, particularly in light of its paraconsistent nature, and establishes cut-admissibility and normalization theorems. Additionally, the introduced sequent calculus – shown to allow terminating proof search – is employed to prove the embedding of discussive logic within modal logic S5. Finally, it is proved that the natural deduction calculus translates into the corresponding sequent system, with soundness and completeness established for both calculi. Concluding remarks highlight the potential for expanding this study and suggest directions for future research.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Philosophical Logic

ISSN

0022-3611

e-ISSN

1573-0433

Svazek periodika

54

Číslo periodika v rámci svazku

September 2025

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

59

Strana od-do

935-993

Kód UT WoS článku

001570387100001

EID výsledku v databázi Scopus

2-s2.0-105016132480