The logic of tune - A proof-theoretic analysis of intonation

This paper presents a proof-theoretic sign-based grammar founded on non-associative non-commutative linear logic which models a compositional theory of the 'information packaging' meaning of intonational contours. Cross-language comparison reveals that in expressing information packaging, different languages exploit word order and prosody in different ways: one single informational construct can be realized by drastically different structural means across languages. Thus for languages such as English and Dutch it can be argued that, roughly speaking, information packaging is structurally realized by means of alternative intonational contours of identical strings, while languages such as Catalan and Turkish have a constant prosodic structure and realize information packaging by means of string order permutations. Such cross-linguistic generalizations suggest that information packaging involves syntax as well as prosody, so that any attempt to reduce informational aspects to either syntax (for Catalan or Turkish) or prosody (for English or Dutch) must be inadequate from a cross-linguistic point of view. The present paper proposes to treat the different structural realizations of information packaging by means of a both intonationally/syntactically and semantically/informationally interpreted sign-based version of the non-associative Lambek calculus, the 'pure logic of residuation'. The signs, the grammatical resources of this formalism, are form-meaning units which reflect the fact that the dimensions of form and meaning contribute to well-formedness in an essentially parallel way. The proof-theoretic categorial engine of the formalism represents phonological head/non-head dependencies in terms of a doubling of the pure logic of residuation which is enriched with unary modal operators, where the unary brackets that come with these operators function as demarcations of specific intonational domains.