Looking at probabilistic conditionals from an institutional point of view

Authors:
Christoph Beierle;Gabriele Kern-Isberner
Affiliations:
Praktische Informatik VIII – Wissensbasierte Systeme, Fachbereich Informatik, FernUniversität Hagen, Hagen, Germany;Praktische Informatik VIII – Wissensbasierte Systeme, Fachbereich Informatik, FernUniversität Hagen, Hagen, Germany
Venue:
WCII'02 Proceedings of the 2002 international conference on Conditionals, Information, and Inference
Year:
2002

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Abstract

We show how probabilistic logic and probabilistic conditional logic can be formalized in the framework of institutions, thereby supporting the study of structural properties of both syntax and semantics of these logics. By using the notions of institution morphism and institution embedding, the relationships between probabilistic propositional logic, probabilistic conditional logic, and the underlying two-valued propositional logic are investigated in detail, telling us, for instance, precisely how to interpret probabilistic conditionals as probabilistic facts or in a propositional setting and vice versa.