<OT> New Posting: ROA-939

[roa at ruccs.rutgers.edu]

ROA 939-1207

A Comparison of Lexicographic and Linear Numeric Optimization Using Violation Difference Ratios

Bruce Tesar <tesar at rutgers.edu>

Direct link: http://roa.rutgers.edu/view.php3?roa=939


Abstract:
Optimality Theory (henceforth OT) (Prince and Smolensky
1993/2004) is based upon lexicographic optimization. It
differs in this respect from Harmonic Grammar (henceforth
HG) (Legendre et al. 1990a, Legendre et al. 1990b), which
is based upon linear numeric optimization. Differences between
the two have been discussed in several places, including
(Legendre et al. 2006, Pater et al. 2007a, Prince and Smolensky
1993/2004).

Patterns which are achievable in HG but not in OT can be
called cumulative interactions. Extensive discussion and
exemplification of cumulative interactions is provided in
(Pater et al. 2007a) (henceforth PBP). An important point
of PBP is that HG cannot realize every possible pattern:
only some linguistic patterns which are not achievable in
OT can be achieved via cumulative interactions. In part
of their paper, PBP examine some undesirable cumulative
interactions, in particular ones that occur when linear
numeric optimization is used in the context of 'global'
optimization models, in which the optimal candidate(s) in
a competition is decided via a single optimization in which
all candidates are simultaneously competing. PBP ultimately
propose a variant of Harmonic Serialism (Prince and Smolensky
1993/2004), called Local Harmonic Serialism, to prevent
the undesired interactions. Local Harmonic Serialism draws
in part on recent work by McCarthy (McCarthy 2006b, McCarthy
2007). Harmonic Serialism uses 'local' optimization, in
which the optimal candidate is determined via a series of
optimizations, each of which consists only of candidates
that differ in a specific localized property (see PBP for
further discussion).

In this paper, I focus exclusively on 'global' optimization
models, providing further investigation into the similarities
and differences between OT and HG in that context. The relation
is viewed with respect to violation differences: the difference
(as a quantity) in the number of violations assessed to
two candidates in a comparison. When two constraints conflict
on a candidate comparison, we can examine the violation
difference ratio of those constraints: the relative size
of the differences in the number of violations for the constraint
s. The relation between violation difference ratios for
different candidate comparisons can predict potential for
cumulative interactions.

The major points of the present work are listed in (1).

(1)	Major points of this paper.

a. Many cases permitting OT and HG to diverge can be understood
in terms of disproportional constraint violation differences:
the violation difference ratios for conflicting constraints
differs across candidate comparisons.

b. Failure to exhibit cumulative interaction is not limited
to instances of 'Anything Goes' competitions; there are
competitions which are not 'Anything Goes', but do exhibit
proportional violation differences, and do not permit cumulative
interactions.

c. Efforts to avoid cumulative interactions in some comparisons
can introduce cumulative interactions into other comparisons.

d. Imposing a fixed bound on the number of violations a
constraint can assess does not eliminate typologically problemati
c patterns in HG, it only limits the number of variations.

Many parts of this paper are summary and synthesis of insights
originally presented elsewhere, especially in (Legendre
et al. 2006, Pater et al. 2007a, Prince and Smolensky 1993/2004,
Prince 2002), with a few new observations along the way.
I make particularly extensive use of the investigation in
PBP; many of the examples are either taken from or adapted
from PBP. The construct of violation difference ratios makes
it possible to tie together many of these prior insights
in a particularly understandable way.

Comments: 
Keywords: harmonic grammar, typology
Areas: Phonology,Formal Analysis
Type: Manuscript

Direct link: http://roa.rutgers.edu/view.php3?roa=939