Possible worlds semantics: A research program that cannot fail?

Studia Logica 43 (4):379 - 393 (1984)
Abstract
Providing a possible worlds semantics for a logic involves choosing a class of possible worlds models, and setting up a truth definition connecting formulas of the logic with statements about these models. This scheme is so flexible that a danger arises: perhaps, any (reasonable) logic whatsoever can be modelled in this way. Thus, the enterprise would lose its essential tension. Fortunately, it may be shown that the so-called incompleteness-examples from modal logic resist possible worlds modelling, even in the above wider sense. More systematically, we investigate the interplay of truth definitions and model conditions, proving a preservation theorem characterizing those types of truth definition which generate the minimal modal logic
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