Consequence Relations, Finitary Closure Operators and Scott’s Information Systems

Jonatan Gomez

Peter Aczel showed that there is a conection betweeen Scott Information Systems and Consequence Relations. This connections was done using closure systems. I defined and used Finitary Closure Operators (FCOs) to do Denotational Semantic and I showed that Scott’s Domains and FCOs are equivalent structures. This paper shows the following facts:

1. Closure Systems are induced by Finitary Closure Operators (FCOs)

2. Scott’s Information System and FCOs are equivalent structures.

3. Consequence Relations are Scott’s Information System.

REFERENCES:

Aczel, P. ”Schematic Consequence”in ”What is a Logical System”, edited by Dov Gabbay, OUP, (1994).

Gomez, J. ”Denotational Semantic Using Closure Operators”, Master of Sciences Thesis, Universidad Nacional de Colombia, (1999).

Address: Universidad Nacional de Colombia, Departamento Ingenieria de Sistemas, Ciudad Universitaria, Bogota, Colombia

E-mail: jgomezp@ing.unal.edu.co