Implicit and Explicit Stances in Logic
Johan van Benthem

Abstract:
We identify a pervasive contrast in modeling styles in logic between
what may be called more 'implicit' and more 'explicit' approaches. The
former change the meaning of logical constants and consequence to
accommodate new topics entering the field, while explicit approaches
extend classical logical systems with vocabulary. We discuss the
contrast in intuitionistic vs. epistemic logic, default reasoning,
logics of questions, information dynamics and games, and then define
the stances more sharply. New technical issues arise concerning
dualities and merges between the two styles of logical
analysis. Finally, we discuss what the contrast means for an
understanding of logic as a repertoire of natural stances.

Keywords: implicit, explicit, intuitionistic logic, epistemic;  logic, dynamic semantics, non-monotonic logic,;  translation, logic of gaes, logic as games