Double-sided Effect in OT: Sequential Grounding and Local Conjunction

Abstract

In a standard SPE-style rewrite rule scheme, the positioning of the environmental dash ("__") directly expresses both adjacency and linear precedence relations between the focus and the determinant. For example, all of the three rules in (1) involve A-to-B alternation, but differ with each other in the focus (A) - determinant (X, Y) relation: in (1a), A becomes B when preceded by X; in (1b), A becomes B when followed by Y; and in (1c), A becomes B when double -sided (preceded by X and followed by Y). (1) a. A → B / X __ b. A → B / __ Y c. A → B / X __ Y Thus, in this model, both adjacency and linear precedence relations are treated as properties of a rule. This view has been carried over to subsequent work in some guise or other (see, e.g. Howard 1972, Cho 1991, Archangeli and Pulleyblank (A&P) 1994). The question to be addressed here is how these various focus -determinant relations are expressed if there are no rules (see McCarthy 1995b for a recent treatment of this issue). In this paper, I would like to consider this question from the perspective of Optimality Theory (henceforth OT) (Prince and Smolensky 1993, McCarthy and Prince (M&P) 1993). Specifically, I consider the three types of focus-determinant relations seen in (1) with respect to the phenomenon of vowel raising. We find that the variation of vowel raising among Basque, Old High German, and Woleaian parallels the variation illustrated in (1): in many dialects of Basque, a low vowel raises to a mid vowel when preceded by a high vowel (de Rijk 1970, Hualde 1991) ( =1a); in Old High German, a low vowel raises to a mid vowel when followed by a high vowel (Voyles 1992) ( =1b); and in Woleaian (spoken in Woleai Island of Micronesia), a low vowel raises to a mid vowel when double-sided by high vowels (Howard 1972, Sohn 1975, Poser 1982) ( =1c). I argue that all of these cases are accounted for by allowing constraints to make reference to the adjacency and linear precedence information. Formally, I propose the following two notions: Sequential Grounding (Smolensky 1993), a syntagmatic extension of Grounded Conditions (A &P 1994), and Local Conjunction (Smolensky 1993, 1995), a UG-operation which conjoins two constraints (details of these notions are explained in section 2.2.2.). This paper is organized as follows. Section 2 provides data and an analysis of the double -sided raising in Woleaian, introducing Sequential Grounding (Smolensky 1993) and Local Conjunction (Smolensky 1993, 1995). I show that Local Conjunction of two Sequential Grounding constraints accounts for the fact that one adjacent high vowel on either side is not sufficient to trigger the raising, but there must be a high vowel on each side. Section 3 gives brief analyses of Basque and Old High German. I demonstrate that reranking of the constraints proposed for the double -sided raising in Woleaian accounts for the other cases of raising (Basque and Old High German). Finally in section 4, the summary of the analyses and conclusion are provided.