Local applications of logics via model-theoretic interpretations

Abstrakt

This paper analyses the notion of ’interpretation’, which is often

tied to the semantic approach to logic, where it is used when referring to

truth-value assignments, for instance. There are, however, other uses of the

notion that raise interesting problems. These are the cases in which interpreting

a logic is closely related to its justification for a given application.

Thus, the paper aims to present an understanding of interpretations that

supports the model-theoretic characterization of validity to the detriment

of the proof-theoretic one. This is done by making use of the hierarchy of

ST-related logics. Finally, a localist conception of logic is defended as the

natural view stemming from the model-theoretic approach.