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dc.contributor.author
Celani, Sergio Arturo
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dc.contributor.author
Montangie, Lidia Daniela
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dc.date.available
2021-09-23T13:08:52Z
dc.date.issued
2019-11
dc.identifier.citation
Celani, Sergio Arturo; Montangie, Lidia Daniela; Algebraic semantics of the { → , □ } -fragment of Propositional Lax Logic; Springer; Soft Computing; 24; 2; 11-2019; 813-823
dc.identifier.issn
1433-7479
dc.identifier.uri
http://hdl.handle.net/11336/141317
dc.description.abstract
In this paper, we will study a particular subvariety of Hilbert algebras with a modal operator □ , called Lax Hilbert algebras. These algebras are the algebraic semantic of the { □ , → } -fragment of a particular intuitionistic modal logic, called Propositional Lax Logic (PLL), which has applications to the formal verification of computer hardware. These algebras turn to be a generalization of the variety of Heyting algebras with a modal operator studied, under different names, by Macnab (Algebra Univ 12:5–29, 1981), Goldblatt (Math Logic Q 27(31–35):495–529, 1981; J Logic Comput 21(6):1035–1063, 2010) and by Bezhanishvili and Ghilardi (Ann Pure Appl Logic 147:84–100, 2007). We shall prove that the set of fixpoints of a Lax Hilbert algebra 〈 A, □ 〉 is a Hilbert algebra such that its dual space is homeomorphic to the subspace of reflexive elements of the dual space of A. We will define the notion of subframe of a Hilbert space 〈 X, K〉 , and we will prove that there is a 1–1 correspondence between subframes of 〈 X, K〉 and binary relations Q⊆ X× X such that 〈 X, K, Q〉 is a Lax Hilbert space. In addition, we will define the notion of subframe variety and we will prove that any variety of Hilbert algebras is a subframe variety.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
HILBERT ALGEBRAS
dc.subject
MODAL OPERATORS
dc.subject
TOPOLOGICAL REPRESENTATION
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Algebraic semantics of the { → , □ } -fragment of Propositional Lax Logic
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2021-06-07T16:57:57Z
dc.journal.volume
24
dc.journal.number
2
dc.journal.pagination
813-823
dc.journal.pais
Alemania
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dc.description.fil
Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo Consolidado de Matemática Pura y Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina
dc.description.fil
Fil: Montangie, Lidia Daniela. Universidad Nacional del Comahue; Argentina
dc.journal.title
Soft Computing
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00500-019-04536-9
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00500-019-04536-9
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