Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 1 Pronouns and Variable Assignments 1 1. Putting this Unit in Context (1) What We’ve Done So Far This Unit • Expanded our semantic theory so that it includes (the beginnings of) a theory of how the presuppositions of a sentence are derived. • Expanded our theory so that it includes (the beginnings of) a theory of how the implicatures of a sentence are derived. (2) Implicatures and Context • We’ve seen that implicatures are crucially related to context. Implicatures are inferences drawn from (i) the asserted content of the sentence, and (ii) features of the context, particularly the assumption that the speaker is following the ‘Gricean Conversational Maxims’ • Thus, context clearly has an effect on the informational content of a sentence, through its affect on the implicatures of the sentence. But, it turns out, implicatures aren’t the only thing affected by context… (3) Truth-Conditions and Context In this part of the unit, we will see that context also affects the truth-conditions (asserted content) of a sentence… a. Key Example: Pronouns (i) In a context where I am pointing at Barack Obama, “He smokes” is T iff Barack Obama smokes. (ii) In a context where I am pointing at Joe Biden, “He smokes” is T iff Joe Biden smokes. b. Conclusion: The T-conditions of “He smokes” varies from context to context. c. Our Goal for This Unit: Augment our extensional semantics so that it captures the way in which the T-conditions of certain sentences (e.g. those containing pronouns) depend upon features of the context. 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. Pronouns and the Basic Problem of Their Context Dependency (4) Overarching Question • How should / could our semantic system model the meanings of pronouns? • What should our interpretation function “[[ . ]]” yield as the extension of a pronoun? Our Methodology (Again): Let’s consider the T-conditions of sentences that contain pronouns and lexical items whose extensions we already know, and from those try to deduce a lexical entry for the pronoun that will derive those T-conditions… (5) First Core Fact The extension of a pronoun seems to be an entity. • In a context where the speaker is pointing at Barack: [[ He smokes ]] = T iff Barack smokes. • CONCLUSION: [[He]] = Barack (in this context) (6) Second Core Fact The extension of a pronoun can vary across contexts. • In a context where the speaker is pointing at Joe: [[ He doesn’t drink ]] = T iff Joe doesn’t drink. • CONCLUSION: [[He]] = Joe (in this context) (7) The Challenge The property in (6) poses a serious problem for our account (as it is currently structured). • How do we write a lexical entry for [[ he ]] which reflects the fact that its value varies depending on the context? • We can’t just write [[he]] = Barack or Joe or Barney or John… for every x in De • Not only does such an entry just look ugly, it doesn’t do the crucial work of relating the extension of the pronoun to the specific context it’s used in… … all such an entry says is that “he” can refer to those entities… it doesn’t tell us when it can refer to those entities….Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 3 (8) A Syntactic Side-Note Following decades of work in syntactic theory, we will assume that pronouns are DPs. Thus, their structure is as follows: DP D he. 3. Variable Assignments: The Basic Idea (9) The Challenge (Restated) How can we augment our semantic interpretation function “[[ . ]]” so that it somehow represents properties of the context? (10) The Solution (First Pass) • We will represent contextual information via special superscripts on “[[ . ]]” • We will start with that contextual information which concerns the interpretation of pronouns. • We will represent that information with a special superscript, which we will call the ‘variable assignment’. • For now, we take variable assignments to be single specific entities taken from De (11) Some ‘Lingo’ [[ XP ]]g = ‘the extension of XP relative to the variable assignment g’ (‘the extension of XP in a context where we’re talking about g’) (12) Pronoun Rule, First Pass [PR] If X is a pronoun (he, she, it, him, her, his, etc.), then [[X]]g = g Illustration a. [[ he ]]Barack = Barack b. [[ he ]]Joe = JoeSeth Cable Semantics and Generative Grammar Fall 2011 Ling610 4 The introduction of variable assignments to our interpretation function “[[ . ]]” requires that we make a few minor adjustments to our semantic interpretation rules… (13) General Convention for Non-Pronominals If X is not a pronoun, then [[X]]g = [[X]] Illustration [[ smokes ]]Obama = [[ smokes ]] = [ λxe : x smokes ] (14) General Convention for Semantic Rules Our existing rules of semantic composition are not yet sensitive to variable assignments. a. (New) Function Application Let g be any variable assignment. If X is a branching node that has two daughters – Y and Z – and if [[Y]]g is a function whose domain contains [[Z]]g, then [[X]]g = [[Y]]g ( [[Z]]g ) b. (New) Non-Terminal Nodes Let g by any variable assignment. If X is a non-branching node, and Y is its sole daughter, then [[X]]g = [[Y]]g c. (New) Terminal Nodes Let g be any variable assignment. If X is a terminal node and is not a pronoun, then [[X]]g (= [[X]]) is specified in the lexicon d. (New) Predicate Modification Let g be any variable assignment. If X is a branching node that has two daughters – Y and Z – and if both [[Y]]g and [[Z]]g are in D<et>, then [[X]]g = [ λx : x ∈ De . [[Y]]g (x) = T and [[Z]]g (x) = T ] These notational additions allow our system to: (i) calculate T-conditions for sentences containing pronouns (relative to a given context) (ii) capture the fact that the T-conditions of such sentences can vary with the context.Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 5 (15) Sample Derivation 1