{
  "compose": 1,
  "id": "hk9-pronouns",
  "title": "Bound & Referential Pronouns (§9.1–9.2)",
  "subtitle": "Heim & Kratzer — pronouns as variables, and the co-reference vs. binding contrast",
  "notation": "hk",
  "domain": {
    "multiLetterNames": true,
    "constants": {
      "e": "j b x1 x2"
    },
    "variables": {
      "e": "x y z",
      "et": "f g P Q X Y",
      "t": "p q"
    }
  },
  "lexicon": [
    {
      "words": [
        "John"
      ],
      "denotation": "j"
    },
    {
      "words": [
        "Bill"
      ],
      "denotation": "b"
    },
    {
      "words": [
        "woman"
      ],
      "denotation": "Lx.woman(x)"
    },
    {
      "words": [
        "man"
      ],
      "denotation": "Lx.man(x)"
    },
    {
      "words": [
        "smokes",
        "smoke"
      ],
      "denotation": "Lx.smoke(x)"
    },
    {
      "words": [
        "left",
        "leave"
      ],
      "denotation": "Lx.leave(x)"
    },
    {
      "words": [
        "blamed",
        "blame"
      ],
      "denotation": "Ly.Lx.blame(x,y)"
    },
    {
      "words": [
        "likes",
        "like"
      ],
      "denotation": "Ly.Lx.like(x,y)"
    },
    {
      "words": [
        "is"
      ],
      "denotation": "LX.X"
    },
    {
      "words": [
        "she1",
        "he1",
        "him1",
        "his1",
        "himself1",
        "herself1",
        "her1"
      ],
      "denotation": "x1"
    },
    {
      "words": [
        "she2",
        "he2",
        "him2",
        "his2",
        "himself2",
        "herself2",
        "her2"
      ],
      "denotation": "x2"
    },
    {
      "words": [
        "every",
        "Every"
      ],
      "denotation": "Lf.Lg.Ax[f(x) -> g(x)]"
    },
    {
      "words": [
        "no",
        "No"
      ],
      "denotation": "Lf.Lg.~Ex[f(x) ∧ g(x)]"
    }
  ],
  "rules": {
    "composition": {
      "functionApplication": true,
      "nonBranchingNodes": true,
      "predicateAbstraction": true
    },
    "quantifierRaising": true
  },
  "exercises": [
    {
      "title": "A. Referential pronouns as free variables (§9.1)",
      "instructions": "A pronoun she₁ denotes g(1) — the individual the assignment maps its index to. With a FREE index, the denotation is an OPEN term (a free variable x₁ = g(1)), made definite only by the utterance context.",
      "items": [
        {
          "sentence": "She smokes.",
          "tree": "[.S [.DP she1 ] [.VP smokes ] ]",
          "targets": [
            "smoke(x1)"
          ],
          "reading": {
            "section": "9.1"
          }
        },
        {
          "sentence": "He left.",
          "tree": "[.S [.DP he1 ] [.VP left ] ]",
          "targets": [
            "leave(x1)"
          ],
          "reading": {
            "section": "9.1"
          }
        },
        {
          "sentence": "John likes her.",
          "tree": "[.S [.DP John ] [.VP [.V likes ] [.DP her2 ] ] ]",
          "targets": [
            "like(j,x2)"
          ],
          "reading": {
            "section": "9.1"
          }
        }
      ]
    },
    {
      "title": "B. Co-reference: a free pronoun with a name (§9.2)",
      "instructions": "On the CO-REFERENCE LF, the reflexive is composed as a free pronoun himself₁; with no movement, the denotation is the open term blame(j,x₁), true iff John blamed g(1). The context maps 1 to John. (H&K run §9.2 on “John hates his father” — both LFs are fine there; our reflexive is a fragment-friendly stand-in, and ch. 10's Condition A, which we bracket here, demands the bound LF.)",
      "items": [
        {
          "sentence": "John blamed himself. (co-reference LF)",
          "tree": "[.S [.DP John ] [.VP [.V blamed ] [.DP himself1 ] ] ]",
          "targets": [
            "blame(j,x1)"
          ],
          "reading": {
            "section": "9.2"
          }
        }
      ]
    },
    {
      "title": "C. Binding: movement + Predicate Abstraction (§9.2)",
      "instructions": "On the BINDING LF, the antecedent raises, leaving a trace co-indexed with the pronoun; PA binds both. The denotation is the CLOSED term blame(j,j) — no dependence on the assignment. A quantifier antecedent allows ONLY this LF.",
      "items": [
        {
          "sentence": "John blamed himself. (binding LF)",
          "tree": "[.S [.DP John ] [.LP 1 [.S [.DP t1 ] [.VP [.V blamed ] [.DP himself1 ] ] ] ] ]",
          "targets": [
            "blame(j,j)"
          ],
          "reading": {
            "section": "9.2"
          }
        },
        {
          "sentence": "Every woman blamed herself.",
          "tree": "[.S [.DP [.D every ] [.NP woman ] ] [.LP 1 [.S [.DP t1 ] [.VP [.V blamed ] [.DP herself1 ] ] ] ] ]",
          "targets": [
            "∀x[woman(x) → blame(x,x)]"
          ],
          "reading": {
            "section": "9.2"
          }
        },
        {
          "sentence": "No man likes himself.",
          "tree": "[.S [.DP [.D no ] [.NP man ] ] [.LP 1 [.S [.DP t1 ] [.VP [.V likes ] [.DP himself1 ] ] ] ] ]",
          "targets": [
            "¬∃x[man(x) ∧ like(x,x)]"
          ],
          "reading": {
            "section": "9.2"
          }
        }
      ]
    }
  ],
  "reading": {
    "format": "latex",
    "markdown": "# Chapter 9 · Bound and Referential Pronouns\n\nReferential pronouns pick up an individual from context; bound pronouns are\nvariables bound by a quantifier. One mechanism covers both: pronouns are variables,\ninterpreted relative to an assignment `g`. Officially every bracket here is\n`⟦·⟧^g` (p. 243); the superscript is suppressed where no confusion arises.\n\n## 9.1 Referential pronouns as free variables\n\nPronouns and Traces Rule: relative to `g`, an indexed pronoun `α_i` denotes `g(i)`\n(p. 241). A free index leaves the denotation open — the utterance context supplies\n`g` (§9.1.2, appropriateness condition, p. 243):\n\n\\begin{derivation}\n[[she1]]        = g(1)            : e\n[[She smokes]]  = smoke(g(1))=1   : t\n\\end{derivation}\n\nWriting `x` for `g(1)`: the open term `smoke(x)=1`, definite once context fixes `g`.\n\n\\ex<ref> She smokes.\n\\xe\n\n\\ex He left.\n\\xe\n\n## 9.2 Co-reference or binding?\n\nH&K run §9.2 on *John hates his father* (pp. 246–248): the possessive pronoun can\nbe bound by *John*, or free and co-referential with him (context c₃,\n`g = [1→John]`, p. 248) — both LFs fine English. Our fragment has no possessives;\nthe exercises substitute *John blamed himself* (\\ref{cb}) to run the same two\nderivations. Seam: ch. 10's Condition A (p. 261) requires reflexives to be bound —\nbracketed here; the reflexive is a compositional stand-in.\n\nCo-reference — no movement; the pronoun is free; open term, true given `g(1)=j`:\n\n\\begin{derivation}\n[[John blamed himself1]]   = blame(j,g(1))=1    : t      (co-reference: g(1)=j)\n\\end{derivation}\n\nBinding — *John* raises, PA binds trace and pronoun; closed term, no dependence\non `g`:\n\n\\begin{derivation}\n[[1 [t1 blamed himself1]]]   = λx . blame(x,x)=1    : <e,t>   (PA)\n[[John 1 [t1 blamed himself1]]] = blame(j,j)=1      : t       (binding)\n\\end{derivation}\n\nWith a name antecedent the LFs are truth-conditionally equivalent. A quantifier\ndenotes no individual, so it cannot co-refer: (\\ref{ewb}) has only the binding LF —\nthe diagnostic for binding.\n\n\\begin{derivation}\n[[Every woman blamed herself]]  = ∀x[woman(x)=1 → blame(x,x)=1]    : t\n\\end{derivation}\n\n\\ex<cb> John blamed himself.\n\\xe\n\n\\ex<ewb> Every woman blamed herself.\n\\xe\n\n> **Beyond this chapter (§9.3, \"Pronouns in the theory of ellipsis\").** Under\n> VP-ellipsis the co-reference/binding distinction resurfaces as the\n> strict/sloppy ambiguity (*John blamed himself, and Bill did too* — our example;\n> the book's runs on Philipp and Marcel, pp. 252–255). Ellipsis resolution needs\n> an LF-identity condition (p. 250) we do not model; see the book."
  }
}