A Note on Extensions: Admissible Rules via Semantics

J.P. Goudsmit

doi:10.1007/978-3-642-35722-0_15

A Note on Extensions: Admissible Rules via Semantics

J.P. Goudsmit

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

Abstract

Any intermediate logic with the disjunction property admits the Visser rules if and only if it has the extension property. This equivalence restricts nicely to the extension property up to n. In this paper we demonstrate that the same goes even when omitting the rule ex falso quod libet, that is, working over minimal rather than intuitionistic logic. We lay the groundwork for providing a basis of admissibility for minimal logic, and tie the admissibility of the Mints-Skura rule to the extension property in a stratified manner.

Original language	English
Title of host publication	Symposium on Logical Foundations in Computer Science 2013
Editors	S Artemov, A Nerode
Place of Publication	Berlin/Heidelberg
Publisher	Springer
Pages	206-218
Number of pages	13
DOIs	https://doi.org/10.1007/978-3-642-35722-0_15
Publication status	Published - 5 Jan 2013

Access to Document

10.1007/978-3-642-35722-0_15

http://www.phil.uu.nl/preprints/lgps/authors/goudsmit/note-on-extensions/pdf

Cite this

@inbook{92d19735e50f4b17b42b6b2850f26f85,

title = "A Note on Extensions: Admissible Rules via Semantics",

abstract = "Any intermediate logic with the disjunction property admits the Visser rules if and only if it has the extension property. This equivalence restricts nicely to the extension property up to n. In this paper we demonstrate that the same goes even when omitting the rule ex falso quod libet, that is, working over minimal rather than intuitionistic logic. We lay the groundwork for providing a basis of admissibility for minimal logic, and tie the admissibility of the Mints-Skura rule to the extension property in a stratified manner.",

author = "J.P. Goudsmit",

note = "Logical Foundations of Computer Science",

year = "2013",

month = jan,

day = "5",

doi = "10.1007/978-3-642-35722-0_15",

language = "English",

pages = "206--218",

editor = "S Artemov and A Nerode",

booktitle = "Symposium on Logical Foundations in Computer Science 2013",

publisher = "Springer",

}

TY - CHAP

T1 - A Note on Extensions: Admissible Rules via Semantics

AU - Goudsmit, J.P.

N1 - Logical Foundations of Computer Science

PY - 2013/1/5

Y1 - 2013/1/5

N2 - Any intermediate logic with the disjunction property admits the Visser rules if and only if it has the extension property. This equivalence restricts nicely to the extension property up to n. In this paper we demonstrate that the same goes even when omitting the rule ex falso quod libet, that is, working over minimal rather than intuitionistic logic. We lay the groundwork for providing a basis of admissibility for minimal logic, and tie the admissibility of the Mints-Skura rule to the extension property in a stratified manner.

AB - Any intermediate logic with the disjunction property admits the Visser rules if and only if it has the extension property. This equivalence restricts nicely to the extension property up to n. In this paper we demonstrate that the same goes even when omitting the rule ex falso quod libet, that is, working over minimal rather than intuitionistic logic. We lay the groundwork for providing a basis of admissibility for minimal logic, and tie the admissibility of the Mints-Skura rule to the extension property in a stratified manner.

U2 - 10.1007/978-3-642-35722-0_15

DO - 10.1007/978-3-642-35722-0_15

M3 - Chapter

SP - 206

EP - 218

BT - Symposium on Logical Foundations in Computer Science 2013

A2 - Artemov, S

A2 - Nerode, A

PB - Springer

CY - Berlin/Heidelberg

ER -

A Note on Extensions: Admissible Rules via Semantics

Abstract

Access to Document

Fingerprint

Cite this