Roussanka Loukanova: An overview of applications of logic to computational linguistics

The strata of language representation in computational linguistics and human language processing (e.g., phonology, phonetics, morphology, syntax, semantics, pragmatics, discourse) rely on mathematical models and methods. We begin with a brief historical overview of the areas shaped by such layers of representation and corresponding methods.

We present Chomsky's criteria for adequacy and related developments in syntactic theories. On the other hand, by considering model-theoretic approaches to language theory, Barwise and Perry (1983) differentiated semantic universals of human languages that serve as criteria for adequateness of theories of meaning. We present these universals by pointing to corresponding tasks in computational linguistics.

We overview major computational approaches to computational syntax, semantics, and syntax-semantics interfaces. To provide background for the forthcoming lectures and seminars, we introduce linguistic concepts, such as words vs. phrases, head of a phrase, compositionality, underspecification.

We consider contributions from the theories of formal languages, formal grammar, first-order logic (FOL), and higher-order logic (HOL). FOL is a valuable and sophisticated area in logic and its applications. During the series, we will be returning to FOL to point to some tasks and problems in its applications to linguistics. We will also point to logics used as semantic representations in syntactic theories and syntactic approaches.