Combinators and Structurally Free Logic
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Combinators and Structurally Free Logic
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| Id. |
46485120 |
| Idioma |
inglés
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| Titulo |
Combinators and Structurally Free Logic |
| Autor(es) |
J. Michael Dunn
Robert K. Meyer
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| Localización |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.7520
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| Versión |
1.0 |
| Estado |
Final
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| Descripción |
A "Kripke-style" semantics is given for combinatory logic using frames with a ternary accessibility relation, much as in the Routley-Meyer semantics for relevance logic. We prove by algebraic means a completeness theorem for combinatory logic, by proving a representation theorem for "combinatory posets." A philosophical interpretation is given of the models, showing that an element of a combinatory poset can be understood simultaneously as a set of states and as a set of (untyped) actions on states. This double interpretation allows for one such element to be applied to another (including itself). Application turns out to be modeled the same way as "fusion" in relevance logic. We also introduce "dual combinators" that apply from the right. We then explore relationships to some well-known substructural logics, showing that each can be embedded into the structurally free, non-associative Lambek calculus, with the embedding taking a theorem # to a statement of the form # # #, where # i...
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| Tipo |
application/postscript
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| Palabras clave |
combinatory logic
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| Tipo de recurso |
Texto Narrativo
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| Tipo de Interactividad |
Expositivo
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| Nivel de Interactividad |
muy bajo
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| Audiencia |
Estudiante
Profesor
Autor
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| Estructura |
Atomic |
| Coste |
no
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| Copyright |
sí
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Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| Formatos |
application/postscript
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| Requerimientos técnicos |
Browser: Any
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| Relación |
[IsBasedOn] http://www3.oup.co.uk/igpl/Volume_05/Issue_04/ps/dunn.ps.gz
[References] 10.1.1.116.2392
[References] 10.1.1.50.9674
[References] 10.1.1.57.1260
[References] 10.1.1.22.6179
[References] 10.1.1.117.3217
[References] 10.1.1.42.9498
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| Fecha de contribución |
27-oct-2009 |
| Contacto |
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