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Horacio Arl o Costa First Order Extensions of Classical Systems of Modal

Summary: Horacio Arl o Costa First Order Extensions of
Classical Systems of Modal
The role of the Barcan schemas
Abstract. The paper studies rst order extensions of classical systems of modal logic
(see (Chellas, 1980, part III)). We focus on the role of the Barcan formulas. It is shown
that these formulas correspond to fundamental properties of neighborhood frames. The
results have interesting applications in epistemic logic. In particular we suggest that the
proposed models can be used in order to study monadic operators of probability (Kyburg,
1990) and likelihood (Halpern-Rabin, 1987).
Keywords: First order modal logic, Epistemic logic, Barcan formulas, Logic of likelihoood.
1. Introduction
The eld known today as epistemic logic is almost fty years old. The
philosopher Georg von Wright proposed the study of the logics of knowledge
and belief in a celebrated essay published in 1951 (von Wright, 1951). Eleven
years later Jaakko Hintikka wrote an important book in the eld (Hintikka,
1962). Hintikka's essay remains one of the best sources for understanding
the nature of the enterprise in spite of the considerable amount of work
done in this area during the last four decades. Hintikka was keenly aware of
the special foundational problems that a ect this branch of modal logic and


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University


Collections: Mathematics