A Note on Comparing Semantics for Conditionals

Christoph Beierle, Gabriele Kern-Isberner

In this paper, we will study semantics that have been used for conditionals in the area of knowledge representation and reasoning: A purely qualitative semantics based on the popular system-of-spheres semantics of Lewis, an ordinal semantics making use of rankings, and a possibilistic semantics. As a common framework for the corresponding logics, we will use institutions which provide formal rigidity based on category theory, but leaves enough abstract freedom to formalize and compare quite different logics. We will show that the conditional semantics mentioned above are logically similar, yet each semantics allows semantical subtleties.

Subjects: 11. Knowledge Representation; 3.5 Qualitative Reasoning

Submitted: Feb 12, 2006

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