Royal Skousen

Analogical Modeling and morphological change: the case of the adjectival negative prefix in English

This article examines the usefulness of Skousens Analogical Modeling (AM) for explaining morphological change. In contrast to previous accounts of analogy, AM constitutes a general unified model of language that accounts for both sporadic and systematic changes. AM also provides explicit constraints on analogy that allow explanation of how morphological changes begin, which forms most likely serve as patterns for analogy, and which forms are most likely to change. AM is then tested on the case of the adjectival negative prefix in English ( in -, un -, dis -, etc.), using the Middle and Early Modern English portions of the Helsinki corpus as a basis for prediction. AM was given the task of using forms containing negative prefixes for one time period to predict the prefixes that adjectives would take in the subsequent time period. For each of the roughly seventy-year periods in the corpus, AM was able to predict valid prefixes about 90 percent of the time.

Natural statistics in language Modelling

Abstract Language speakers have the ability to estimate frequencies of occurrence, predict which outcome is the most frequent, and use language as if the statistical relationships between various linguistic variables have been determined. Within a psychologically plausible theory of analogical modeling, natural statistics would allow speakers to make such judgments without requiring them to posit highly complex statistical distributions or to directly calculate probabilities mathematically.

Systems of Rules

We define a system S of rules {R 1,R 2, ..., R i , ...} by partitioning the contextual space of a base rule R.

Measuring the Certainty of Probabilistic Rules

We begin by defining a general measure of certainty for discrete probabilistic rules. A discrete probabilistic rule is a statement about behavior that is composed of three parts: (1) a set of conditions c called the context or environment of the rule; (2) a countable set of possible outcomes Ω = {ω1,ω2,...,ω j ,...}; (3) a probability function P that assigns a probability P j to each outcome ω j in Ω.

Analyzing the Effect of a Variable

Very often we can analyze rule contexts in terms of one or more contextual variables, v1,v2,... vk. We will let V stand for this set of variables. In the general case we assume that there are no restrictions on the possible co-occurrence of variables. We will assume that the contextual space of the correct description S* is accurately described by the set V of k variables. One way to derive S* is in terms of a sequence of the k variables. We start with no variables; that is, we start with the single-rule system S 0,which has essentially no contextual specification. We choose one of the k variables (say v1), which produces a system S(v 1 ) with m 1 rules. Then we choose from among the remaining k –1 variables a second variable (say v2), which along with vl produces a system S(v1v2) with m1•m2 rules. In other words, system S(v1v2) is derived by splitting up each of the ml rules of S(v 1 ) into m2 rules. In this same way we continue to select one variable at a time until we have chosen all k of the variables and have produced system S(v1v2...vk) with ml•m2...m k rules (that is, system S*).

Analogical Analyses of Continuous Variables

Thus far we have only dealt with categorical variables. In this chapter we apply our procedures — with some minor adaptation — to variables that are ordered or are numerically scaled.

Problems with Structuralist Descriptions

There are two different types of problems that arise when we seek to describe behavior by means of rule systems. The first type deals with problems that occur in learning a system of rules. The second type occurs when we try to use a system of rules to predict behavior. In this section we will discuss the first type.

A Natural Test for Homogeneity

In this chapter, unlike the previous one, we assume that all contexts have a fmite number of occurrences. We will, however, still retain our assumption of perfect memory throughout this chapter. We follow the same analogical procedure outlined in the previous chapter to predict behavior except that local homogeneity must be determined statistically rather than probabilistically. In order to determine the local homogeneity of a supracontext, we define a natural estimate of certainty.

Maximum Likelihood Statistics

In this chapter we use maximum likelihood estimates of p ij , p i+ , p +j, and pj|i, to estimate the certainty and uncertainty for a system of rules. In actual fact we never know the probability function for any given probabilistic rule. Instead, we can only observe frequencies of occurrence: frequency of outcome