Paradigmatic Morphology

PARADIGMATIC MORPHOLOGY Jonathan Calder University of Edinburgh Centre for Cognitive Science 2 Buccleuch Place Edinburgh Scotland EH8 9LW ABSTRACT We present a notation for the declarative statement of morphological relationships and lexieal rules, based on the traditional notion of Word and Paradigm (cf Hockett 1954). The phenomenon of blocking arises from a generalized version of Kiparsky's (1973) Elsewhere Condition, stated in terms of ordering by subsumption over paradigms. Orthographic constraints on morphemic alternation are described by means of string equations (Siekmann 1975). We indicate some criticisms to be made of our approach from both linguistic and computational perspectives and relate our approach to others such as Finite-State Morphology (Koskenniemi 1983), DATR (Gazdar and Evans 1989) and object-oriented morphophonemics (de Smedt 1984, Daelemans 1988). Finally, we discuss the questions of whether a system involving string equations allows a reduction to finite-state techniques. I Introduction A common assumption in linguistics is that the phonological, morphological and orthographic statements are most appropriately phrased in a fundamentally procedural way, (see for example Hoeksma and Janda 1988). Morphological analysis under the rubric of finite-state morphology (Koskenniemi 1983) has arguably tended to support the view that morphological alternation is best described by stating procedures for the destructive alteration of orthographic units. At the very least, it appears to have led to the view that morphological descriptions should be restricted to those with an immediate interpretation in terms of the operations of finite-state transducers. In this paper, we present a notation for the declarative statement of morphological relationships and lexieal rules, based on the traditional notion of Word and Paradigm (WP, Hockett 1954, see also Anderson 1982). The phenomenon of blocking arises from a generalized version of Kiparsky's (1973) Elsewhere Condition, stated in terms of ordering by subsumption over paradigms. Orthographic constraints on morphemic alternation are described by means of string equations (Siekmann 1975). We will first give a brief introduction to string equations and the other formal devices used in our model, namely lexical entries and rules, grammatical properties and paradigms. We give example paradigms and show how our interpretation of paradigms leads to the phenomenon of blocking. We will then indicate some criticisms to be made of our approach from both linguistic and computational perspectives. We discuss relations between our proposals and the approaches of Finite-State Morphology (FSM, Koskenniemi 1983), DATR (Gazdar and Evans 1989) and object-oriented morphophonemies (de Smedt 1985, Daelemans 1988). One important question in the light of current work in morphology is whether a system involving string equations allows a reduction to finite-state techniques. We review some possible answers to this question. 2 Components of the Model 2.1 String Equations and String Unification This introduction is based on Siekmann (1975). A string a is a sequence of elements drawn from a finite alphabet C combined by the associative operator +, representing the concatenation of strings. - 58 - A string specification or string form is a sequence possibly containing variables drawn from the set of variables V, disjoint from C. Omission of …

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