UMass Amherst LINGUIST 610 - Common Nouns and Adjectives in Predicate Position

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Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 1 Common Nouns and Adjectives in Predicate Position1 (1) The Lexicon of Our System at Present a. Proper Names: [[ Barack ]] = Barack b. Intransitive Verbs: [[ smokes ]] = [ λx : x ∈ De . IF x smokes THEN T ELSE F ] c. Transitive Verbs: [[ likes ]] = [ λx : x ∈ De . [ λy : y ∈ De . IF x likes y THEN T ELSE F ] ] d. Logical Connectives [[ orS ]] = [ λx : x ∈ Dt . [ λy : y ∈ Dt . IF x = T or y = T THEN T ELSE F ] ] [[ andVP ]] = [ λg ∈ D<et> : [ λf ∈ D<et> : [ λx ∈ De : IF f(x) = T and g(x) = T THEN T, ELSE F ] ] ] (2) Question: Adjectives and ‘Common Nouns’? But what about adjectives like male and so-called ‘common nouns’ like politician? What sort of entries should they receive? (3) Our Methodology for Answering Question (2) a. Find some (restricted) class of sentences where these lexical items appear. b. Develop lexical entries for those lexical items that will capture the truth-conditions of those sentences...(and work out from there to other constructions…) (4) Predicative Uses of Adjectives and Common Nouns Following the methodology in (3), the restricted class of sentences we’ll work with are those where adjectives and common nouns seem to function as a ‘main predicate’. a. Barack is male. b. Barack is a politican. 1 These notes are based on the material in Heim & Kratzer (1998: 61-63).Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 2 Why are we starting here? As we’ll see, the semantics we develop for sentences like (4) will be applicable to other places where we find common Ns and As! (5) The Questions We Have to Answer a. What is the extension of male? b. What is the extension of politician? c. What is the extension of is? d. What is the extension of a? (6) A Space-Saving Measure for our Lambda Formulas As compact as it is, the formulae we’re going to write in our lambda notation are only going to get bigger. For that reason, let’s use the following abbreviating convention. Old Notation: [ λx : x ∈ De . IF ϕ(x) THEN T ELSE F ] New Notation: [ λx : x ∈ De . ϕ(x) ] Examples [ λx : x ∈ De . IF x smokes THEN T ELSE F ] = [ λx : x ∈ De . x smokes ] [ λx : x ∈ De . [ λy : y ∈ De . IF x likes y THEN T ELSE F ] ] = [ λx : x ∈ De . [ λy : y ∈ De . x likes y ] ] [ λxt : [ λyt : IF x = T or y = T THEN T ELSE F ] ] = [ λxt : [ λyt : x = T or y = T ] ] 1. The Semantics of the English Copula Let’s start off with the sentence in (4a), Barack is male. In order for our system to be able to interpret this sentence, we need a lexical entry for the copula is and a lexical entry for the adjective male. (8) The Semantics of the Copula: The Leading Idea For the purposes of our class, let’s assume that the copula is in English essentially has no real meaning, that it is semantically vacuous. • The idea here is that the copula appears in a sentence for purely syntactic reasons (e.g. in order to express the tense suffix, which can’t go on the noun) • Since it’s only there for syntactic reasons, the copula itself doesn’t really contribute to the sentence’s meaning…Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 3 (9) Some Motivation for ‘The Leading Idea’ a. It’s Tradition! Grammarians have long considered ‘copulas’ to be semantically empty. o In Elementary School, we learn to call is a ‘helping verb’. (It doesn’t really mean anything, it just ‘helps’ adjectives and nouns to be predicates.) o The technical term ‘copula’ comes from a Latin word meaning ‘joiner’. b. Typological There are many languages that lack copulas, and get along fine without them. (This suggests that the copula in an English sentence doesn’t really add anything to the meaning of the sentence…) Lillooet (Salish; British Columbia) emh-ál’qwem’ [ ti=pelalhtsítcw=a ] good.looking DET=stranger=DET The stranger is good looking. (10) Question: How do we represent in our system the idea that the coupla (is) is ‘semantically vacuous’, …that it doesn’t contribute anything to the meaning of the sentence? (11) Naïve Answer: What if we just don’t give is a lexical entry? Then is won’t mean anything in our system! PROBLEM: If is doesn’t have any lexical entry, then our system won’t be able to compute the meaning of sentences that contain is. (12) Better Answer: How about we give is a lexical entry, but one that effectively adds nothing to the meaning of the larger phrase? …that is, we treat the meaning of the copula as an identity function! a. [[ is ]] = [ λf : f ∈ D<e,t> . f ] The function from <et> functions to <et> functions, which takes an <et> function f and simply returns f.Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 4 2. The Semantics of Adjectives (13) Our Goal: Derive the Following T-Conditional Statement “ S ” is T iff Barack is male. NP VP N V AP Barack is A male (14) Let’s Work Out The Types! a. Types We Already Know (i) S type t (ii) NP, N, Barack type e (iii) V type <et,et> (see (12)) S t NP e VP N V <et,et> AP Barack is A male b. Deducing the Types of VP, AP (i) The VP must be of type <e,t> • The extension of the VP must take the extension of the subject as argument and return the extension of the sentence. (ii) The AP must be of type <e,t> • Since VP is a branching node, its meaning must be derived via FA • Thus, [[VP]] = [[V]]([[AP]]) • However, [[V]] is of type <et,et>, and so it only takes <et> functions as argument. • Thus, [[AP]] is of type <et>.Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 5 (iii) The A and ‘male’ must be of type <et> • Since AP is a non-branching node, [[AP]] = [[A]] • Since A is a non-branching node, [[A]] = [[male]] • Thus, [[AP]], [[A]] and [[male]] are all of type <e,t> But what kind of <e,t> function is the extension of “male”? (15) Some Reasoning, Part 1 The


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