Representing and Accessing [Textual] Digital Information (COMS/INFO 630), Spring 2006Lecture 22: TAG Adjunction Trees and Feature Based TAGs4/20/06 Lecturer: Lillian LeeScribes: Nicolas Hamatake (nh39), Min Park (mp257)1 Overview and ReviewIn today’s lecture we continue our discussion of Tree Adjoining Grammars (TAG’s) in attempting to analyze a phrase that has the same syntactic structure for different semantic interpretations. Recall that toward the end of last lecture, we took note that for TAG’s, parse trees are based on individual lexical items that compose associated information. Is it possible then, to use TAG’s to also model idioms that have non-compositional meaning?Idioms are ‘fixed’ phrases with non-compositional meanings, and few modifications (if any) are allowed. We introduced the following idiom as a concrete example to guide our discussion today:Bob kicked the bucket. Interpretation of this phrase is not unique. There is at least the literal interpretation, but also an idiomatic one. Either Bob kicked—with his foot—a pail (literal); or, Bob died (idiomatic).Notice that only a few idiomatic modifications of this phrase are imaginable. For example, Bob kicked the red bucket, etc., is not idiomatic (within reason). Still, Bob kicked the proverbial bucket would be an idiomatic modification of the phrase. Today we continue exploring the difficulty that arises from idiomatic phrases.2 Ambiguity in Analyses of Idiomatic Phrases2.1 Idiomatic and Non-Idiomatic Syntactic AnalysesConsider the following simplified non-idiomatic syntactic analysis of (1.1): S NP VP V NP | kicked DET N | | the bucketwhere Det denotes determiners—words such as the, that, and so forth. What are the compositional semantics here? We could imagine that a compositional semantic analysis would be easily derived via writing a TAG with an initial tree for kicked, kα1. This initial tree for “kicked” will require two arguments: a subject and an object. Thus for a compositional semantic analysis, we have the logical form:Kicked(Bob,bucket) which is just a function (Kicked()), which has two arguments for the subject and object analogous to the two non-terminal leaf nodes in kickedα.For the case of the idiomatic syntactic analysis of (1.1), the appropriate logical form would be: Died(Bob) which is a function of one argument instead of two. We now have two different logical forms, (1.2) and (1.3), for our phrase (1.1).What is each of their corresponding syntactic analyses? Should they be different from each other? If they are different, the implication would be that grammar is able to reflect their difference in meaning.2.2 Syntactic Analyses2.2.1 Idiom as One Lexical Item: No.First, one might attempt a syntactic analysis where the idiom is treated as a single lexical item: S NP VP | | Bob kicked-the-bucketInitially, this seems to make sense, given the non-compositional semantics of the phrase. However, treating ‘kicked-the-bucket’ as one word would not allow for any modification such as ‘kicked-the-proverbial-bucket’ which is still idiomatic. Thus, we need a place in our analysis for a modifier as in the case with the non-idiomatic analysis (unless we decided to have a separate tree for the modified case). In this sense, we need the ‘same’ syntactic analysis for both the idiomatic and non-idiomatic case. Clearly we are faced with ambiguities in having the ‘same’ syntax for divergent semantics. Is there some way to capture these ambiguities? Where exactly does the vagueness arise? 1 Given in the following page.Page 2 of 102.2.2 Same Syntax for Two Meanings: Where does the Ambiguity Arise?First consider using TAG’s to represent the literal interpretation of (1.1).: S kα NP VP V NP | kickedkα is the initial tree for kicked, which takes two arguments.: NP | BobBαBαis the tree for Bob, one of the arguments for kα: NP tbα DET N | | the buckettbα is the simplified tree for the bucket, the other argument for kαStarting with the initial tree kαwe can write the derivation tree for (1.1) using TAG’s as: kα (1) (2.2)B tbα αWe will claim that it is possible to immediately observe the logical form of (1.1) from this derivation tree. Recall (1.2), Kicked(Bob,bucket), the logical form for the non-idiomatic syntactic analysis of (1.1). The nodes Bα(1) and tbα(2.2) correspond to the arguments, while kα corresponds to the function Kicked.Page 3 of 10Secondly, consider using TAG’s to represent the idiomatic interpretation of (1.1).: S diedα NP VP V NP | kicked DET N | | the bucketdiedα is another initial tree, which takes one argument.Starting with the initial treediedα, we can also write the derivation tree for (1.1) using TAG’s as: |(1)diedBααAgain, we can ‘read off’ the logical form for this syntactic analysis, Died(Bob), immediately from this derivation tree.By using TAG’s, we have shown that the derived tree itself is not the source of ambiguity since both derivations lead to the same tree; however, the semantics has become clear in the derivation process. That is, the derivation process is the source of vagueness as represented by the fact that we have two plausible derivation trees.3 Modification for Idioms: Adjunction3.1 Adjunction Trees to Allow for Modification We return to our problem presented in section 2.2.1 where we attempted a syntactic analysis of (1.1) treating kicked-the-bucket as one lexical item. The problem was that this analysis would not allow for any (idiomatic) modification of the phrase. To allow for modification of an idiom, consider having the following adjunction tree. Since it will modify bucket , its root (under simplified analysis) must be N and so should its