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# Using Model Theory for Grammatical Inference: a Case Study from Phonology

; Proceedings of The 13th International Conference on Grammatical Inference, PMLR 57:66-78, 2017.

#### Abstract

This paper examines the characterization and learning of grammars defined by conjunctions of negative and positive literals (CNPL) where the literals correspond to structures in an enriched model theory of strings. CNPL logic represents an intermediate between conjunctions of negative literals (CNL) and a propositional-style logic, both of which have been well-studied in terms of the language classes they describe. Model-theoretic approaches to formal language theory have traditionally assumed that each position in a string belongs to exactly one unary relation. Using enriched models (which do no satisfy this assumption) presents a new avenue for investigation with potential applications in several fields including linguistics, planning and control, and molecular biology. We demonstrate the value of such structures and CNPL logic with a particular learning problem in phonology.