The general problem this research addresses is the nature of multi-dimensional linguistic composition. Natural language expressions display properties in a variety of dimensions: they have properties linking them to the physical world; they are syntactically categorized; they support pragmatic and semantic interpretation. The properties of basic expressions may be assumed to be finitely stipulated or listed, as in a dictionary or its mental counterpart. The properties of complex expressions cannot be assumed to be encodable this way, but must be derivable in a way that depends both on the correlative properties of their component parts and on their mode of combination. This question of linguistic composition arises with regard to each dimension; moreover, it arises in a generalized form across dimensions, since composition in one dimension may affect or depend on composition in another. Although there are a variety of solutions to this problem instantiated in existing grammatical architectures, the question deserves to be studied more sys- tematically, since the interrelation of properties of different kinds forms the basis of the unbounded creative character of natural language and its expressive power. The investigation here views linguistic composition as a problem of resource-sensitive grammatical inference in a system of labeled deduction: the component parts of an utterance are taken to be a structured set mf premises from which a coherent global structure for the utterance is sought within a particular system of deductive postulates. This point of view connects directly with two recent trends in logic: the rise of interest in substructural logics and the investigation of labeled deduction. The research will exploit the results in these areas for applications to the study of grammatical architecture and the dynamic flow of grammatical information within and across different dimensions in the course of composition. The principal research goals are: 1) to gain insight into the nature of multidimensional composition through the construction and systematic study of appropriate models based on logical principles; 2) to connect these insights to the analysis of a broad range of linguistic phenomena; and S) to show that the resulting framework offers a unifying perspective on current grammatical theories. The expected results of the research include a monograph describing the range and power of the known landscape of grammatical logics and a computer implementation of such a system with robust empirical coverage of English.
