Semántica categórica para subexponenciales en SELL

CARLOS ERNESTO RAMÍREZ^*

Universidad del Valle, Departamento de Matemáticas, Cali, Colombia.

Resumen. La semántica categórica ha permitido establecer de forma precisa y formal el significado de los términos y conectivos de distintas lógicas. En particular, los trabajos de distintos autores empezando por de Paiva y Hyland [3] han permitido abordar desde el enfoque categórico la semántica de la lógica lineal, tanto clásica como intuicionista. Uno de los aspectos más relevantes consiste en intentar dar una interpretación categórica al operador exponencial !. Mellies [11] y Bierman [4] finalmente han mostrado que esta interpretación corresponde a un composición entre adjuntos monoidales. Con la aparición de SELL, ahora se cuenta con una familia de subexponenciales ajustados dentro de una estructura de preorden. Lo que se pretende en este trabajo es obtener una interpretación categórica para esta familia de subexponenciales, inspirados en la misma noción de adjuntos monoidales, pero que respete la estructura de preorden asignada para la familia de exponenciales.

Palabras Claves: Lógica lineal, categorías monoidales, categorías enriquecidas, semántica categórica.
MSC2010: 03F52, 18C50.

Categorical semantics for subexponentials in SELL

Abstract. Categorical semantics have established formal and accurately the meaning of the terms and connectives of different logics. In particular, the work of various authors, starting with de Paiva and Hyland [3], have allowed to look at the semantics of linear logic, both classical and intuitionists, from a categorical point of view. One of the most important task is to try to give a categorical interpretation to the exponential operator !. Mellies [11] and Bierman [4] have finally shown that this interpretation corresponds to a composition between monoidal adjoints. With the emergence of SELL, now we have a family of subexponential, adjusted within a preorder structure. The intention in this work is to obtain a categorical interpretation for this family of subexponentials, inspired by the very notion of monoidal adjoints, but preserving the preorder structure assigned to the exponential family.

Keywords: Linear logic, monoidal categories, enriched categories, categorical semantic.

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^*E-mail: carlos.ernesto.ramirez@correounivalle.edu.co.
Recibido: 12 de septiembre de 2013, Aceptado: 10 de febrero de 2014.
Para citar este artículo: C. E. Ramírez, Semántica categórica para subexponenciales en SELL, Rev. Integr. Temas Mat. 32 (2014), no. 1, 39-54.