Mathematical linguistics

Mathematical linguistics is the application of mathematics to model phenomena and solve problems in general linguistics and theoretical linguistics. Mathematical linguistics has a significant amount of overlap with computational linguistics.

Discrete mathematics is used in language modeling, including formal grammars, language representation, and historical linguistic trends.

Semantic classes, word classes, natural classes, and the allophonic variations of each phoneme in a language are all examples of applied set theory. Set theory and concatenation theory are used extensively in phonetics and phonology.

In phonotactics, combinatorics is useful for determining which sequences of phonemes are permissible in a given language, and for calculating the total number of possible syllables or words, based on a given set of phonological constraints. Combinatorics on words can reveal patterns within words, morphemes, and sentences.

Context-sensitive rewriting rules of the form a → b / c _ d, used in linguistics to model phonological rules and sound change, are computationally equivalent to finite-state transducers, provided that application is nonrecursive, i.e. the rule is not allowed to rewrite the same substring twice.

Weighted FSTs found applications in natural language processing, including machine translation, and in machine learning. An implementation for part-of-speech tagging can be found as one component of the OpenGrm library.

Optimality theory (OT) and maximum entropy (Maxent) phonotactics use algorithmic approaches when evaluating candidate forms (phoneme strings) for determining the phonotactic constraints of a language.

Trees have several applications in linguistics, including: