Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 1 The Semantics of Movement and Relative Clauses 1 1. The Basic Problem Syntacticians have long recognized a category of structures dubbed ‘movement structures’. The structures in (1) all contain examples of ‘movement’. (1) Examples of Movement a. Topicalization: John, Bill likes b. Relativization: the man [ who Bill likes ] c. Wh-Questions: Who does Bill like? (2) The Key Properties of Movement Structures a. There is a portion of the sentence that seems to be missing something (e.g. the sequence Bill likes in (1a-c), which is missing a direct object ) b. The element ‘missing’ from that part of the sentence appears at the beginning of the sentence (e.g. the element John or who in (1a-c)) (3) The Overarching Question for This Unit How can we augment our semantic system so that such structures can be interpreted? (4) Our Starting Place • We’ll begin by examining topicalization structures like (1a), since they differ from a simple declarative sentence (e.g. Bill likes John) only in the presence of movement. • Having developed a semantics for sentences like (1a), we’ll see how those basic ideas can also be employed to develop a semantics for relative clauses like (1b). But before we can do any of that, we need to precisely lay out our assumptions about the syntactic structure of sentences like (1a). 1 These notes are based on the material in Heim & Kratzer (1998: 86-115, 239-245).Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 2 2. The Syntax of Movement Structures The assumptions in (5)-(8) have been standard for about 30 years, and are probably familiar to you from earlier classes (or LING 601). (5) Assumption 1: The Moved Phrase C-Commands The Material that Follows it S’ DP S John DP VP Bill V likes (6) Assumption 2: All DPs – Including Non-Pronominals – Bear Indices a. Syntax of Movement Structure S’ DP1 S John DP2 VP Bill V likes b. Irrelevance of Indices to Non-Pronominals If DPi is not headed by a pronoun, then [[ DPi ]]g = [[ DP ]] (7) Assumption 3: Movement Leaves ‘Traces’ The ‘missing material’ in the movement structure is actually a phonologically empty element referred to as a ‘trace’. S’ DP1 S John DP2 VP Bill V t likesSeth Cable Semantics and Generative Grammar Fall 2011 Ling610 3 (8) Assumption 4: Traces Are Coindexed with Moved Phrase Like DPs, traces also bear indices. However, they necessarily bear the same index as the moved phrase. S’ DP1 S John DP2 VP Bill V t1 likes The following assumption, critical for our semantic account, will probably be new to you… (9) Assumption 5: Index Copying The index of the moved phrase is copied as a sister to the sister of the moved phrase. S’’ DP1 S’ John 1 S DP2 VP Bill V t1 likes (10) The Main Upshot The structure of (1a) will be assumed to be that in (9), which – except for ‘index copying’ – is pretty much what syntacticians have thought since the early 1980s. (11) A Quick Note on ‘Index Copying’ • This syntactic assumption was introduced by Heim & Kratzer 1998. • Since its introduction, it has gained much ground with semanticists, and with ‘semantically-minded’ syntacticians…Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 4 3. Working Towards a Semantics of Movement Now that we have a syntactic structure for (1a), let’s start to work out its compositional semantics… … we’ll begin with a plausible assumption regarding the T-conditional statement for (1a) that our semantics should derive… (12) Assumed T-Conditional Statement “John, Bill likes” is T iff Bill likes John. (13) Working Out the Types S’’ DP1 S’ John 1 S DP2 VP Bill V t1 likes [[ S’’ ]] :: Type t [[ John ]] :: Type e Therefore… [[ S’ ]] :: Type <e,t > (14) Working Out the Extension of S’ a. Starting T-Conditional Statement: [[ S’’ ]] = T iff Bill likes John. b. Key Consequence of the Types Deduced in (13) [[ S’’ ]] = [[ S’ ]] (John) c. Key Deductive Step [[ S’ ]] (John) = T iff Bill likes John. d. Key Generalization [[ S’ ]] is an <et> function will takes an entity x as argument and gives back T iff John likes x.Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 5 (15) Deduced Extension for S’ [[ S’ ]] = [ λxe : Bill likes x ] So, clearly, we want a semantics for movement structures that will deliver the equation in (15)… but how do we do this?... (16) Key Observation: A Parallelism in Structure [[ S’ ]] = [[ [ 1 [ Bill likes t1 ] ]] = [ [ λxe : Bill likes x ] ]] • There are two key syntactic pieces to S’ (i) The index ‘1’ (ii) The trace bearing index 1 • There are two key syntactic parts to the extension of S’ (i) The lambda operator ‘λxe’ (ii) The variable x bound by the lambda operator • Even more interesting…these two pieces seem to correspond to each other nicely… (17) Working Hypothesis Regarding Movement Structures a. The index in S’ is interpreted as the lambda operator in the extension of S’ b. The trace in S’ is interpreted as the bound variable in the extension of S’ So, let’s now work to formally implement the hypotheses in (17a) and (17b)… … Doing so, however, will require us to introduce some new notation and a new semantic rule.Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 6 3. Formally Implementing Our Hypothesis (18) First Ingredient: Modified Variable Assignments Let g be a variable assignment, let n be an index, and let a be some entity. We will write ‘g (n / a)’ to mean ‘the variable assignment which is exactly like g, except that it maps the index n to the entity a. (19)