On the formal semantics of IF-like logics

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In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Independence Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of th...

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Autores principales:	Figueira, S., Gorín, D., Grimson, R.
Formato:	Artículo publishedVersion
Publicado:	2010
Materias:	Compositional semantics Flattening operator Full abstraction Independence friendly logic Regular formulas Signaling Valuation Bound variables Classical logic Formal Semantics Abstracting Formal methods Game theory Semantics
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00220000_v76_n5_p333_Figueira http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00220000_v76_n5_p333_Figueira_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_00220000_v76_n5_p333_Figueira_oai
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spelling	I28-R145-paper_00220000_v76_n5_p333_Figueira_oai2020-10-19 Figueira, S. Gorín, D. Grimson, R. 2010 In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Independence Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of these logics but a defect in the way in which the compositional semantics given by Hodges for the regular fragment was generalized to arbitrary formulas. We fix this by proposing an alternative formalization, based on a variation of the classical notion of valuation. Basic metatheoretical results are proven. We present these results for Hodges' slash logic (from which these can be easily transferred to other IF-like logics) and we also consider the flattening operator, for which we give novel game-theoretical semantics. © 2009 Elsevier Inc. All rights reserved. Fil:Figueira, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Gorín, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_00220000_v76_n5_p333_Figueira info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Comput. Syst. Sci. 2010;76(5):333-346 Compositional semantics Flattening operator Full abstraction Independence friendly logic Regular formulas Signaling Valuation Bound variables Classical logic Compositional semantics Flattening operator Formal Semantics Full abstraction Abstracting Formal methods Game theory Signaling Semantics On the formal semantics of IF-like logics info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00220000_v76_n5_p333_Figueira_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic	Compositional semantics Flattening operator Full abstraction Independence friendly logic Regular formulas Signaling Valuation Bound variables Classical logic Compositional semantics Flattening operator Formal Semantics Full abstraction Abstracting Formal methods Game theory Signaling Semantics
spellingShingle	Compositional semantics Flattening operator Full abstraction Independence friendly logic Regular formulas Signaling Valuation Bound variables Classical logic Compositional semantics Flattening operator Formal Semantics Full abstraction Abstracting Formal methods Game theory Signaling Semantics Figueira, S. Gorín, D. Grimson, R. On the formal semantics of IF-like logics
topic_facet	Compositional semantics Flattening operator Full abstraction Independence friendly logic Regular formulas Signaling Valuation Bound variables Classical logic Compositional semantics Flattening operator Formal Semantics Full abstraction Abstracting Formal methods Game theory Signaling Semantics
description	In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Independence Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of these logics but a defect in the way in which the compositional semantics given by Hodges for the regular fragment was generalized to arbitrary formulas. We fix this by proposing an alternative formalization, based on a variation of the classical notion of valuation. Basic metatheoretical results are proven. We present these results for Hodges' slash logic (from which these can be easily transferred to other IF-like logics) and we also consider the flattening operator, for which we give novel game-theoretical semantics. © 2009 Elsevier Inc. All rights reserved.
format	Artículo Artículo publishedVersion
author	Figueira, S. Gorín, D. Grimson, R.
author_facet	Figueira, S. Gorín, D. Grimson, R.
author_sort	Figueira, S.
title	On the formal semantics of IF-like logics
title_short	On the formal semantics of IF-like logics
title_full	On the formal semantics of IF-like logics
title_fullStr	On the formal semantics of IF-like logics
title_full_unstemmed	On the formal semantics of IF-like logics
title_sort	on the formal semantics of if-like logics
publishDate	2010
url	http://hdl.handle.net/20.500.12110/paper_00220000_v76_n5_p333_Figueira http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00220000_v76_n5_p333_Figueira_oai
work_keys_str_mv	AT figueiras ontheformalsemanticsofiflikelogics AT gorind ontheformalsemanticsofiflikelogics AT grimsonr ontheformalsemanticsofiflikelogics
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On the formal semantics of IF-like logics

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