Recursion in Language: Is It Indirectly Constrained?

Abstract

Recursion is a key aspect of formal theories of language. In this chapter we have presented a new perspective on recursion in language, claiming that recursion in language is indirectly constrained. After discussing some aspects of the relation between linguistic theory and mathematical linguistics, we show that this perspective arises from the properties of grammars that are beyond context-free grammars with context-sensitivity that is mild in a sense and that the derivation proceeds from structures to structures. Viewing the generation process inductively, we then show that for each index of recursion, there is a form (we call this a canonical form) that can be generated. However, corresponding to the canonical form, there are variants of the form, called here as non-canonical forms that exhibit gaps in the sense that for a given index of recursion, beyond two levels of embedding, not all non-canonical forms can be generated. This property emerges from the formal architecture of the system and not from any particular linguistic or processing constraint. We call this property Indirectly Constrained Recursion (ICR), suggesting a new perspective on recursion in language. ICR is a formal structural constraint and not a linguistic or processing constraint. In linguistic theories constraints on recursion are usually expressed either in terms of some linguistic constraints or in terms of processing constraints. ICR arises from the properties of the kinds of formal systems considered here. Linguistic constraints and processing constraints are then to be considered as additional constraints. The linguistic phenomena referred to in this chapter are well-known. Hence, the main contribution of this chapter is the presentation of a new perspective on recursion as described above.KeywordsDependencies:nestedCrossedGrammars:context-freeContext-freeContext-sensitivePhrase structureTransformationalTree-adjoiningMulti-component tree-adjoiningLanguages context-freeMildly context-sensitiveExtraposition from NPCanonical formsNon-canonical formsScrambling or liberation