 Another arena for the interaction between the proof-theoretic and the model-theoretic perspectives has to do with the definition of the logical vocabulary. For example, one can hold a “moderate” inferentialist view which defines the meanings of logical connectives through their semantics (i.e. truth conditions) but demands that the meaning of a connective be determined by inference rules. Carnap has famously shown that the classical inference rules allow non-standard interpretations of the logical expressions (Carnap 1943). Much recent work in the field has been devoted to the exact nature and extent of Carnap’s categoricity problem (Raatikainen 2008, Murzi and Hjortland 2009, Woods 2012, Garson 2013, Peregrin 2014, Bonnay and Westerståhl 2016. See also the entry on  sentence connectives in formal logic).