Sentences of natural language may be analyzed as having a function/ argument structure, as was originally observed by Frege. For instance, in Julia weeps, the verb acts as a functor assigning a truth value to entities mentioned in the proper name position. But also, e.g., in Julia weeps bitterly, the adverb may be regarded as denoting a function from verbs to (complex) verbs. Thus, the interpretation of natural language expressions involves a hierarchy of functions — and the task of a categorial grammar is to assign suitable types of function (‘categories’) to linguistic expressions, so as to make the puzzle ‘fit’. This chapter is concerned with some logical aspects of the categorial mode of description.
KeywordsNatural Language Relative Clause Type Change Regular Language Natural Deduction
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