Fitch-Style Modal Necessity as a Substructural Sequent-Style System
Abstract: The question of defining a Jaśkowski-Fitch natural deduction system for modal logic has been settled since the very introduction of such formalisms in the middle of the last century. In contrast, a sequent-style formulation of this approach has only been discussed since the turn of this century but exclusively from the point of view of type theories. In this paper we propose a substructural sequent-style deductive system, based on previous ideas by Borghuis and Clouston, which captures Fitch-style for modal logic in a faithful way, meaning that the features of the original diagrammatic proofs are enforced by the sequent rules. This answers the question of what is a sequent-style version of Fitch-style natural deduction in the case of the necessity fragment of minimal modal logic S 4.
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Digital revista |
| Language: | English |
| Published: |
Instituto Politécnico Nacional, Centro de Investigación en Computación
2023
|
| Online Access: | http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1405-55462023000100315 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| id |
oai:scielo:S1405-55462023000100315 |
|---|---|
| record_format |
ojs |
| spelling |
oai:scielo:S1405-554620230001003152023-06-13Fitch-Style Modal Necessity as a Substructural Sequent-Style SystemMiranda-Perea,Favio E.Estrada Zavaleta,XimenaGonzález Huesca,Lourdes del Carmen Natural deduction fitch-style modal necessity substructural logics sequents Abstract: The question of defining a Jaśkowski-Fitch natural deduction system for modal logic has been settled since the very introduction of such formalisms in the middle of the last century. In contrast, a sequent-style formulation of this approach has only been discussed since the turn of this century but exclusively from the point of view of type theories. In this paper we propose a substructural sequent-style deductive system, based on previous ideas by Borghuis and Clouston, which captures Fitch-style for modal logic in a faithful way, meaning that the features of the original diagrammatic proofs are enforced by the sequent rules. This answers the question of what is a sequent-style version of Fitch-style natural deduction in the case of the necessity fragment of minimal modal logic S 4.info:eu-repo/semantics/openAccessInstituto Politécnico Nacional, Centro de Investigación en ComputaciónComputación y Sistemas v.27 n.1 20232023-03-01info:eu-repo/semantics/articletext/htmlhttp://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1405-55462023000100315en10.13053/cys-27-1-4542 |
| institution |
SCIELO |
| collection |
OJS |
| country |
México |
| countrycode |
MX |
| component |
Revista |
| access |
En linea |
| databasecode |
rev-scielo-mx |
| tag |
revista |
| region |
America del Norte |
| libraryname |
SciELO |
| language |
English |
| format |
Digital |
| author |
Miranda-Perea,Favio E. Estrada Zavaleta,Ximena González Huesca,Lourdes del Carmen |
| spellingShingle |
Miranda-Perea,Favio E. Estrada Zavaleta,Ximena González Huesca,Lourdes del Carmen Fitch-Style Modal Necessity as a Substructural Sequent-Style System |
| author_facet |
Miranda-Perea,Favio E. Estrada Zavaleta,Ximena González Huesca,Lourdes del Carmen |
| author_sort |
Miranda-Perea,Favio E. |
| title |
Fitch-Style Modal Necessity as a Substructural Sequent-Style System |
| title_short |
Fitch-Style Modal Necessity as a Substructural Sequent-Style System |
| title_full |
Fitch-Style Modal Necessity as a Substructural Sequent-Style System |
| title_fullStr |
Fitch-Style Modal Necessity as a Substructural Sequent-Style System |
| title_full_unstemmed |
Fitch-Style Modal Necessity as a Substructural Sequent-Style System |
| title_sort |
fitch-style modal necessity as a substructural sequent-style system |
| description |
Abstract: The question of defining a Jaśkowski-Fitch natural deduction system for modal logic has been settled since the very introduction of such formalisms in the middle of the last century. In contrast, a sequent-style formulation of this approach has only been discussed since the turn of this century but exclusively from the point of view of type theories. In this paper we propose a substructural sequent-style deductive system, based on previous ideas by Borghuis and Clouston, which captures Fitch-style for modal logic in a faithful way, meaning that the features of the original diagrammatic proofs are enforced by the sequent rules. This answers the question of what is a sequent-style version of Fitch-style natural deduction in the case of the necessity fragment of minimal modal logic S 4. |
| publisher |
Instituto Politécnico Nacional, Centro de Investigación en Computación |
| publishDate |
2023 |
| url |
http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1405-55462023000100315 |
| work_keys_str_mv |
AT mirandapereafavioe fitchstylemodalnecessityasasubstructuralsequentstylesystem AT estradazavaletaximena fitchstylemodalnecessityasasubstructuralsequentstylesystem AT gonzalezhuescalourdesdelcarmen fitchstylemodalnecessityasasubstructuralsequentstylesystem |
| _version_ |
1769607146004021248 |