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From what I read in a a thoughtful answer here, Leben's theory, as a precursor to Autosegmental Phono, posited a so-called "tone pattern diacritic" plus underspecification of tone features. Accordingly, tone was assigned into the segmental matrix "through" the tonal matrix. This approach contrasts with that of Goldsmith's Autosegmental Phono, which implies a "full and equal partnership between tones and segments".

This makes me wonder what kind of "unit" segmental and feature matrices are. So far as I understand (and please tell me if I am wrong), Leben's theory denied the segment and suprasegment, apparently opting for matrices. But how is the identity of a segment as a unit distinct from the identity of a matrix as a unit?

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The concept of "segment" and "matrix" overlapped in linguistics for a brief period, up to the late 70's when the "matrix" was buried by autosegmental phonology. The current state of the art is that "matrix" plays no role at all, and a "segment" has no formal role, though there is a way of reconstructing the concept (a "segment" is whatever is dominated by a root node). Affricates, consonant+glide sequences, and NC sequences among other things have caused all sorts of qualms about "segment" in phonology. In the historical transition to where we are, Leben's dissertation is an important first step is deconstructing the "matrix" a.k.a. segment.

In generative phonology, the "feature matrix" was taken to be what a "segment" is, mathematically speaking. In The sound pattern of English, ch. 8 section 2, Chomsky and Halle give their explication of segments, which "consist of feature columns", and which are graphically represented as a stack of features enclosed in brackets, i.e. a matrix. The main claim is that a segment is a combination of phonetic features, and they are not atomic units. In the appendix on formalism p. 391, they define "unit", "matrix" and "rule", though if you read that appendix you will understand why nobody cites it.

Various terms have been used to refer to the collection of features defining a segment: feature complex, feature bundle (originally from Bloomfield, I believe), feature matrix. In pre-autosegmental days there were two interpretations of the "matrix" in an utterance with multiple segments, such as "Buy hotdog buns". One is that there is an ordered sequence matrices, one for each segment; the other is that there is one big matrix containing an ordered series of feature-specification columns (see Clements 1985 p 226 for a small example, and Leben's dissertation sect 1.4.1). Given the full-specification assumption (that every segment has some value for every feature), these two modes of representation are interchangeable. The most popular convention was that each segment is a feature matrix.

There are two related questions about features in connection with matrices in pre-autosegmental generative phonology: are the featural elements of a segment ordered, and are they value-attribute pairs, or just values? The way matrices are typically presented in papers suggests that within the segment, there is no ordering to the features, thus [+cons,-son,-cont] is not distinct from [+cons,-cont,-son] or any of the other permutations: features are "simultaneous" within the segment; this also implies that features are pairings of name and specification. An alternative interpretation of the representation is that a segment is an ordered collection of values only, e.g. [+,-,-,+...] where value 1 refers to "consonantal", value 2 refers to "sonorant" and so on. The "matrix of unordered value-attribute pairs" can be easily translated into a "matrix of ordered values" – provided that the set of features is part of universal grammar. This was the claims for the phonetic features of SPE, but there are also diacritic features, and it was noted in SPE (fn 1 p. 390) that there is an unlimited set of diacritic features. In light of the fact that the total set of features is not fixed and varies between languages, a segment has to be interpreted as being composed of a collection of value-attribute pairs, in which case the feature specifications would be unordered (ordering would be superfluous).

Segments are obviously ordered: [æsk] is distinct from [sæk]. Under the theory where a segment is a feature matrix (unordered set of value-attribute pairs), there is ordering between matrices. It would be appropriate to mention here that there is a bit of divergence between general mathematical conventions and linguistic concepts. A segment looks like a column vector (m x 1 matrix), but the elements of a column vector are ordered. Note, though, that if diacritic features are expelled from the theory and segments are composed of a universal set of features (people basically ignored non-phonetic features), then there is considerable freedom to re-interpret representations, in terms of content and structure. A string like [æsk] could be an ordered sequence of three matrices of value-attribute pairs (the most common representation), or it could be an ordered sequence of values of the 23 features, with segments being computed from a sequence of plus and minus values in the same way that a sequence of 1s and 0s can be interpreted as a sequence of numbers in computer memory. Because the completely unstructured representation is difficult for people to parse, it was not a popular option, and graphic metaphors tend to determine theoretical interpretation -- an utterance is a sequence of matrices, where each matrix is a segment, and the content of each matrix is an unordered set of value-attribute pairs.

Now on to Leben. Leben retained most of the SPE formal system, but he added a division into two kinds of matrices. His starting point is the observation from SPE that every morpheme "falls into many categories", such as "noun"... and that "nasality" etc. is just another kind of category, where the word "inn" is a member of the categories "initial non-tense vowel", "noun" (I will interject that the former claim, that "initial non-tense vowel" is a category, is based on a bizarre epistemology). SPE did not actually have two matrices, one for morphemic features and one for segmental features, and they were unclear as to the lexical locus of non-phonetic features (e.g. are nons specified [+Noun] on every segment, the first segment, the last, can it contrast?), and indeed they had a convention spreading morphemic features to ever segment within a morpheme. Leben created the two-matrix representational theory so that "Noun, Past" etc were in "matrix two" which is one of the elements of a morpheme – and then he placed tone features in M2, for some languages. So Leben did not actually deny the segment, he factored out tone (and nasality, in Guarani) and made it be a morphemic feature, which was nevertheless converted into a semi-standard SPE segmental matrix representation. (His theory of surface contour tones was totally non-orthodox, however).

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  • You wrote that "if you read that appendix you will understand why nobody cites it" -- but I don't. Is it because of the quality of the description? – Teusz Sep 17 '16 at 11:02
  • Also, what are "diacritic features" in SPE? I assume this is prosodic phenomena like stress (well for English, but also presumably tone). Is that true? – Teusz Sep 17 '16 at 11:51
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    The reason why nobody cites the appendix is that it is totally opaque: IMO it is not necessary for formal linguistic writing to be impenetrable. Diacritic features are arbitrary features with no phonetic, syntactic, morphological or semantic correlates. They are used to identify members of word classes, for example "verbs with ablaut pattern 3 in the past tense", or in Spanish "verbs which paradigmatically diphthongize stressed e, o to ie, ue. – user6726 Sep 17 '16 at 21:49
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In working out a theory of monostratal phonology (see Eliminating intermediary forms ...), I had to confront the problem of "hyperreduced" pronunciations, in which speech has become just a mutter, with whole syllables missing. In conventional generative phonology, one can append extra rule applications onto the end of ordinary derivations, with the segments that don't show up in the surface pronunciation eliminated by various phonological rules of assimilation and deletion. But this requires assuming additional intermediate derivational forms. In a monostratal theory, which does not tolerate intermediate derivational forms, another way must be found.

I worked out a phonetic representation, which I call a "change matrix", which gives only a sequence of changes of state for each significant articulatory organ. This is a feature matrix in which neighboring columns of feature specifications must be distinct. There are no alphabetic segments at all, but vertical columns of the matrix correspond to what would be written as segments in alphabetic phonetic representations. In this theory, it is impossible to distinguish between what would be segment deletions and complete assimilations in ordinary alphabetic phonetics.

This is probably very similar to the "asegmental" idea in Natural Phonology, which is referred to in the following quote from Donegan and Stampe.

Donegan and Stampe (1978, 1979 and subsequent talks) have claimed that if each process operates over rhythmically delimited strings which include both the causal and the affected elements and which are defined solely in terms of the phonetic features of that string, then direct reference to phonemes or even segments per se can be avoided – without such superstructures as “autosegmental tiers” (Goldsmith 1990), “long components” (Harris 1944), “prosodies” (Firth 1948), or “gestures” (Browman and Goldstein 1986). In an asegmental phonology like that which we have proposed, every feature is its own “tier” or “autosegment”. Successive segments are differentiated from each other only by some feature difference or, as in the case of geminates or long vowels, by syllable positions or prosodic associations. (This accounts automatically for much of what the Obligatory Contour Principle (Goldsmith 1979) has been used to explain.) Hypotheses of Natural Phonology.

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