State-of-affairs Semantics for Positive Free Logic

Journal of Philosophical Logic 35 (2):183-208 (2006)
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Abstract
In the following the details of a state-of-affairs semantics for positive free logic are worked out, based on the models of common inner domain - outer domain semantics. Lambert's PFL system is proven to be weakly adequate (i.e., sound and complete) with respect to that semantics by demonstrating that the concept of logical truth definable therein coincides with that one of common truth-value semantics for PFL. Furthermore, this state-of-affairs semantics resists the challenges stemming from the slingshot argument since logically equivalent statements do not always have the same extension according to it. Finally, it is argued that in such a semantics all statements of a certain language for PFL are state-of-affairs-related extensional as well as salva extensione extensional, even though their salva veritate extensionality fails
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