Tomorrow’s colloquium in the Stanford Linguistics Department (3:30 in Margaret Jacks Hall, if you’re local and interested):
A set-theoretic typology of phonological map interaction, by Eric Baković, UC San Diego (with Lev Blumenfeld, Carleton University). Beginning of the abstract:
Theories of generative phonology assume that, in general, morphemes have unitary underlying representations and that systematic variations in the surface pronunciation of morphemes in different morphological contexts result from the application of a complex, context-sensitive transformation – a phonological grammar – to those underlying representations. A phonological grammar is thus a complex map from underlying representations to surface representations. Theories differ on the details of what the phonological grammar is comprised of, but it is commonly assumed that it can be broken down into a set of simpler maps – intuitively, individual phonological processes – that make particular changes in particular contexts.
The question we ask in this work is: what is the set of possible interactions among the individual maps that constitute a phonological grammar?
The simple maps — the terminology is from mathematics, where map is short for mapping, of one set of objects to another — are what’s known in standard generative phonology as rules (a label that’s open to several misunderstandings).
The background for Eric’s presentation is the idea of UDRA — Universally Determined Rule Application — according to which interactions between the individual maps in a phonological grammar are determined by universal principles. UDRA is known to be too strong a hypothesis, so the question is what limited sorts of parochiality are available to particular phonological grammars.
Eric’s abstract continues:
We start from the observation that pairs of maps interact to the extent that their inputs (= the sets of substrings that match a map’s structural description) overlap with each other and/or with each other’s outputs (= the sets of substrings that match a map’s structural change). This observation is not new, but save for some early work on formal inclusion relations between these components of phonological rules (the Elsewhere Condition and the Proper Inclusion Precedence Principle), its consequences have not been adequately explored.
The present work fills this gap in our understanding of phonological grammars by fleshing out the full typology of predicted pairwise map interaction types. Formal analysis reveals this typology to be relatively small, consisting of seven interaction types: (counter)feeding, self-destructive feeding, mutual feeding, merger, (counter)bleeding, convergent mutual bleeding, and divergent mutual bleeding. We present this typology and our formal analysis of it in detail, and also offer formal characterizations of the notions ‘underapplication’ and ‘overapplication’, familiar from the literature on phonological opacity, which cross-classify map interaction types.
(There will of course be examples.)
A personal note. A long time ago (30 years ago) I published a paper on this topic in a very obscure offset-printed journal (Innovations in Linguistics Education, put out for a few years by the Indiana University Linguistics Club): “Rule interactions: Another gloss on K&K” (ILE, 1987). K&K is Michael J. Kenstowicz & Charles W. Kissebeth’s textbook Generative phonology: Description and practice (Academic Press, 1979). The “another gloss” in the title is a reference to a 1985 ILE paper of mine, “Elementary phonology from an advanced point of view: A gloss on K&K” (the links are to copies of the full papers).