Cut Elimination, Identity Elimination, and Interpolation in Super-Belnap Logics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00477770" target="_blank" >RIV/67985807:_____/17:00477770 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11225-017-9746-8" target="_blank" >http://dx.doi.org/10.1007/s11225-017-9746-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11225-017-9746-8" target="_blank" >10.1007/s11225-017-9746-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cut Elimination, Identity Elimination, and Interpolation in Super-Belnap Logics

Popis výsledku v původním jazyce

We develop a Gentzen-style proof theory for super-Belnap logics (extensions of the four-valued Dunn–Belnap logic), expanding on an approach initiated by Pynko. We show that just like substructural logics may be understood proof-theoretically as logics which relax the structural rules of classical logic but keep its logical rules as well as the rules of Identity and Cut, super-Belnap logics may be seen as logics which relax Identity and Cut but keep the logical rules as well as the structural rules of classical logic. A generalization of the cut elimination theorem for classical propositional logic is then proved and used to establish interpolation for various super-Belnap logics. In particular, we obtain an alternative syntactic proof of a refinement of the Craig interpolation theorem for classical propositional logic discovered recently by Milne.

Název v anglickém jazyce

Cut Elimination, Identity Elimination, and Interpolation in Super-Belnap Logics

Popis výsledku anglicky

We develop a Gentzen-style proof theory for super-Belnap logics (extensions of the four-valued Dunn–Belnap logic), expanding on an approach initiated by Pynko. We show that just like substructural logics may be understood proof-theoretically as logics which relax the structural rules of classical logic but keep its logical rules as well as the rules of Identity and Cut, super-Belnap logics may be seen as logics which relax Identity and Cut but keep the logical rules as well as the structural rules of classical logic. A generalization of the cut elimination theorem for classical propositional logic is then proved and used to establish interpolation for various super-Belnap logics. In particular, we obtain an alternative syntactic proof of a refinement of the Craig interpolation theorem for classical propositional logic discovered recently by Milne.

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

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Studia Logica

ISSN

0039-3215

e-ISSN

—

Svazek periodika

105

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

35

Strana od-do

1255-1289

Kód UT WoS článku

000415716400009

EID výsledku v databázi Scopus

2-s2.0-85027872839