3 - A Feature Value Logic with Intensionality, Nonwellfoundedness and Functional and Relational Dependencies

Abstract

This chapter discusses feature value logic with intensionality, nonwellfoundedness, and functional and relational dependencies. In a modal approach to feature logic, it is more appropriate to treat functions and relations as polyadic modalities than to adopt a predicate modal logic approach. The addition of functions and relations to the language not only permits the definition of functional and relational dependencies as used in HPSG, but also allows for the definition of structures other than feature structures. The formal semantics that are given to functional and relational dependencies is the one which most closely matches the informal, intuitive semantics or the use of such dependencies in actual grammatical practice. Formal semantics has some pleasant features. Among these features is the ability to reconstruct the type-token distinction, or to put it another way, the extensionality–intensionality distinction for arbitrary structures and the ability to describe cyclic or nonwellfounded structures of all types. The standard predicate modal logic approach to functions and relations is inadequate to capture the intuitive semantics of functional and relational dependencies as used in the literature. Subsequently, function and relation symbols are existential polyadic polymodal modalities. Thereafter, the interpretation of relation symbols is intensional, whereas the interpretation of function symbols is extensional allowing a type-token distinction for arbitrary objects, including sets.