Complexity in Linguistics

Abstract

The topic of language complexity has surfaced in many different contexts and can be measured in many different ways. In this chapter, I discuss notions relevant to the computational and descriptive complexity of language. I introduce the notion of ‘complexity class’ (e.g. P and NP), the corresponding logical distinctions (e.g. definability), and the Cobham-Edmonds thesis identifying the class of practically computable problems with P. Then, I survey how the complexity notions have been applied in the study of syntax and semantics of natural language. This discussion culminates in putting forward Ristad’s Thesis, claiming that our everyday language is semantically bounded by the properties expressible in the existential fragment of second-order logic (belongs to NP). Finally, I discuss, very common in formal semantics, restriction to finite interpretations. This chapter gives, therefore, an additional argument for studying the computational complexity of natural language expressions.