Alan Bush

This dissertation presents a general framework for understanding, applying, comparing, and creating techniques for constructing representational semantics. The work begins with John Etchemendy's positive account of how model-theoretic semantics illuminates the consequence relation for specific languages. Etchemendy uses the term "representational semantics" to identify the approach to logical consequence he advocates. We abstract away from the particulars of Etchemendy's account, and construct a general conceptual framework we call the "representational schema." The representational schema gives a general form for techniques used to construct theories of logical consequence implementing representational semantics. ;We show how the representational schema is capable of subsuming not just modeltheoretic semantics, but also a class of techniques for constructing theories of logical consequence whose central concept can be abstracted from a corollary to Lindenbaum's Lemma; a class we call order-consistency semantics. We use the schema to describe a general methodology for applying representational techniques to construct theories of logical consequence for particular interpreted languages. That methodology is used to apply techniques subsumed by the representational schema to propositional logic, feature logics , and languages in which feature structures are considered as assertions in their own right. We show how the schema helps us to compare and contrast differing techniques of representational semantics across a number of important dimensions including the mode by which they explain the consequence relation; the range of interpreted languages to which they are applicable; their degree of epistemological commitment; and the ease with which they can be used in particular applications. We show how the representational schema serves as a basis for various vectors of extension, and use the schema to construct several new techniques of representational semantics. One reduces the epistemological commitments of the specific model-theoretic technique described by Etchemendy, another gives a model-theoretic technique capable of handling partial models, and a third is an order-consistency technique which does not require the assumption of Lindenbaum's Lemma . Applications and benefits of these extensions are described. tensions are described