A Concatenation Operation to Derive Autosegmental Graphs

Abstract

Autosegmental phonology represents words with graph structures. This paper introduces a way of reasoning about autosegmental graphs as strings of concatenated graph primitives. The main result shows that the sets of autosegmental graphs so generated obey two important, putatively universal, constraints in phonological theory provided that the graph primitives also obey these constraints. These constraints are the Obligatory Contour Principle and the No Crossing Constraint. Thus, these constraints can be understood as being derived from a finite basis under concatenation. This contrasts with (and complements) earlier analyses of autosegmental representations, where these constraints were presented as axioms of the grammatical system. Empirically motivated examples are provided.

The local nature of tone-association patterns

“…One might claim that human learners cannot observe ARs directly – they only perceive linear strings of TBUs. Even if this is true, Jardine & Heinz (2015) have shown how to derive ARs from strings, resolving this potential problem. There are thus ways of learning autosegmental grammars from string input.…”

“…An AR is a kind of graph (Goldsmith 1976, Coleman & Local 1991, Jardine & Heinz 2015), where a graph is defined as a set of elements or nodes and a set of binary relations or edges over those elements. We can represent an AR as a set of labelled nodes with undirected edges representing association and directed edges representing precedence on each tier (marked in (13b) with arrows; cf.…”

“…Pulleyblank (1986) and Odden (1986) have argued respectively against full specification and the OCP as universals, but they will suffice for the tone patterns discussed here, and the results of this paper do not depend on whether or not these properties are universal. 3 Formal definitions of all of the above properties can be found in Goldsmith (1976), Coleman & Local (1991), Kornai (1995), Jardine (2014) and Jardine & Heinz (2015).…”

The computational nature of phonological generalizations

“…Closer to issues in phonological theory, Kornai (1995) shows how autosegmental representations can processed by finite-state automata for recognition and generation. Similarly, Jardine and Heinz (2015a) show that autosegmental representations have important string-like properties and can be thought of as the concatenation of finitely many autosegmental primitives. Jardine (2014) shows how Strictly Local autosegmental representations can be defined (and how in certain circumstances the No Crossing Constraint is a Strictly Local constraint).…”

On the Logical Complexity of Autosegmental Representations

“…We can then talk about strings and their corresponding ARs. Jardine and Heinz (2015) define such a relationship in terms of concatenation, but they do not address how this relationship connects to complexity. As discussed in §3.1, natural language phonotactics are largely describable with FO-definable stringsets.…”