Studia Logica

, Volume 71, Issue 1, pp 87-118

First online:

First Order Extensions of Classical Systems of Modal Logic; The role of the Barcan schemas

  • Horacio Arló CostaAffiliated withCarnegie Mellon University

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The paper studies first 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).

First order modal logic Epistemic logic Barcan formulas Logic of likelihoood