Clausal proof nets and discontinuity

We consider the task of theorem proving in Lambek calculi and their generalisation to "multimodal residuation calculi". These form an integral part of categorial logic, a logic of signs stemming from categorial grammar, on the basis of which language processing is essentially theorem provi...

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Detalles Bibliográficos
Autor: Morrill, Glyn|||0000-0002-5528-4384
Tipo de recurso: informe técnico
Fecha de publicación:1994
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/96810
Acceso en línea:https://hdl.handle.net/2117/96810
Access Level:acceso abierto
Palabra clave:Theorem proving
Lambek calculi
Multimodal residuation calculi
Categorial logic
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
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spelling Clausal proof nets and discontinuityMorrill, Glyn|||0000-0002-5528-4384Theorem provingLambek calculiMultimodal residuation calculiCategorial logicÀrees temàtiques de la UPC::Informàtica::Informàtica teòricaWe consider the task of theorem proving in Lambek calculi and their generalisation to "multimodal residuation calculi". These form an integral part of categorial logic, a logic of signs stemming from categorial grammar, on the basis of which language processing is essentially theorem proving. The demand of this application is not just for efficient processing of some or other specific calculus, but for methods that will be generally applicable to categorial logics. It is proposed that multimodal cases be treated by dealing with the highest common factor of all the connectives as linear (propositional) validity. The prosodic (sublinear) aspects are encoded in labels, in effect the term-structure of quantified linear logic. The correctness condition on proof nets ("long trip condition") can be implemented by SLD resolution in linear logic with unification on labels/terms limited to one-way matching. A suitable unification strategy is obtained for calculi of discontinuity by normalisation of the ground goal term followed by recursive decent and redex pattern-matching on the head term.19941994-03-0120162016-11-18reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/96810reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/968102026-05-27T15:37:01Z
dc.title.none.fl_str_mv Clausal proof nets and discontinuity
title Clausal proof nets and discontinuity
spellingShingle Clausal proof nets and discontinuity
Morrill, Glyn|||0000-0002-5528-4384
Theorem proving
Lambek calculi
Multimodal residuation calculi
Categorial logic
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
title_short Clausal proof nets and discontinuity
title_full Clausal proof nets and discontinuity
title_fullStr Clausal proof nets and discontinuity
title_full_unstemmed Clausal proof nets and discontinuity
title_sort Clausal proof nets and discontinuity
dc.creator.none.fl_str_mv Morrill, Glyn|||0000-0002-5528-4384
author Morrill, Glyn|||0000-0002-5528-4384
author_facet Morrill, Glyn|||0000-0002-5528-4384
author_role author
dc.subject.none.fl_str_mv Theorem proving
Lambek calculi
Multimodal residuation calculi
Categorial logic
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
topic Theorem proving
Lambek calculi
Multimodal residuation calculi
Categorial logic
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
description We consider the task of theorem proving in Lambek calculi and their generalisation to "multimodal residuation calculi". These form an integral part of categorial logic, a logic of signs stemming from categorial grammar, on the basis of which language processing is essentially theorem proving. The demand of this application is not just for efficient processing of some or other specific calculus, but for methods that will be generally applicable to categorial logics. It is proposed that multimodal cases be treated by dealing with the highest common factor of all the connectives as linear (propositional) validity. The prosodic (sublinear) aspects are encoded in labels, in effect the term-structure of quantified linear logic. The correctness condition on proof nets ("long trip condition") can be implemented by SLD resolution in linear logic with unification on labels/terms limited to one-way matching. A suitable unification strategy is obtained for calculi of discontinuity by normalisation of the ground goal term followed by recursive decent and redex pattern-matching on the head term.
publishDate 1994
dc.date.none.fl_str_mv 1994
1994-03-01
2016
2016-11-18
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/96810
url https://hdl.handle.net/2117/96810
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
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eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
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