A Unification-Based Semantic Interpretation for Coordinate Constructs

A UNIFICATION-BASED SEMANTIC INTERPRETATION FOR COORDINATE CONSTRUCTS Jong C. Park University of Pennsylvania Computer and Information Science 200 South 33rd Street Philadephia, PA 19104-6389 USA Internet: park@line, cis. upenn, edu Abstract This paper shows that a first-order unification- based semantic interpretation for various coordi- nate constructs is possible without an explicit use of lambda expressions if we slightly modify the standard Montagovian semantics of coordination. This modification, along with partial execution, completely eliminates the lambda reduction steps during semantic interpretation. 1 Introduction Combinatory Categorial Grammar (CCG) has been offered as a theory of coordination in nat- ural language (Steedman [1990]). It has usually been implemented in languages based on first or- der unification. Moore [1989] however has pointed out that coordination presents problems for first- order unification-based semantic interpretation. We show that it is possible to get over the problem by compiling the lambda reduction steps that are associated with coordination in the lexicon. We show how our first-order unification handles the following examples of coordinate constructs. (1.1) Harry walks and every farmer walks. (1.2) A farmer walks and talks. (1.3) A farmer and every senator talk. (1.4) Harry finds and a woman cooks a mushroom. (1.5) Mary gives every dog a bone and some policeman a flower. We will first start with an illustration of why standard Montagovian semantics of coordination cannot be immediately rendered into a first-order 209 unification strategy. The lexicon must contain multiple entries for the single lexical item "and", since only like categories are supposed to conjoin. For example, the lexical entry for "and" in (1.1) specifies the constraint that the lexical item should expect on both sides sentences to give a sentence. Moore [1989] predicts that a unification-based semantic interpretation for sentences which in- volve for example noun phrase coordination won't be possible without an explicit use of lambda expressions, though there are cases where some lambda expressions can be eliminated by di- rectly assigning values to variables embedded in a logical-form expression. The problematic exam- ple is shown in (1.6), where proper noun subjects are conjoined. (1.6) john and bill walk. The argument is that if we do not change the se- mantics of "john" from j to AP.P(j), where P is a second order variable for property in the Montago- vian sense 1 , then the single predicate AX. walk(X) should accommodate two different constants j and b in a single variable X at the same time. Since the unification simply blocks in this case, the ar- gument goes, we need to use higher order lambda expressions such as AP.P(j) or AP.P(b), which when conjoined together, will yield semantics for e.g. "john and bill" as ,~P.(P(j) ~ P(b)) . Combined finally with the predicate, this will re- sult in the semantics (1.7), after lambda reduction. (1.7) walk(j) & walk(b) 1Montague [1974]. )~pVp(j) to be exact, taking in- tensionality into account. The semantics of the predi- cate "walks" will then be (^AX.walk(X)). Although Moore did not use quantified noun phrases to illustrate the …

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