{
  "compose": 1,
  "id": "ch13-worlds",
  "title": "World-Indexed Predicates (§13.4)",
  "domain": {
    "multiLetterNames": true,
    "constants": {
      "e": "f s g n a b l m o w"
    },
    "variables": {
      "e": "x y z",
      "s": "w0 w w' w''",
      "st": "p q",
      "et": "P Q",
      "set": "R S"
    }
  },
  "lexicon": [
    {
      "words": [
        "Frodo"
      ],
      "denotation": "f"
    },
    {
      "words": [
        "Sam"
      ],
      "denotation": "s"
    },
    {
      "words": [
        "Gandalf"
      ],
      "denotation": "g"
    },
    {
      "words": [
        "Sauron"
      ],
      "denotation": "n"
    },
    {
      "words": [
        "Aragorn"
      ],
      "denotation": "a"
    },
    {
      "words": [
        "Boromir"
      ],
      "denotation": "b"
    },
    {
      "words": [
        "Legolas"
      ],
      "denotation": "l"
    },
    {
      "words": [
        "Gimli"
      ],
      "denotation": "m"
    },
    {
      "words": [
        "Galadriel"
      ],
      "denotation": "w"
    },
    {
      "words": [
        "Bilbo"
      ],
      "denotation": "bi"
    },
    {
      "words": [
        "Strider"
      ],
      "denotation": "st"
    },
    {
      "words": [
        "Pippin"
      ],
      "denotation": "pi"
    },
    {
      "words": [
        "Tom"
      ],
      "denotation": "tm"
    },
    {
      "words": [
        "Elrond"
      ],
      "denotation": "el"
    },
    {
      "words": [
        "Saruman"
      ],
      "denotation": "sr"
    },
    {
      "words": [
        "Moria"
      ],
      "denotation": "mr"
    },
    {
      "words": [
        "rides",
        "ride"
      ],
      "denotation": "Lx.ride(w0,x)"
    },
    {
      "words": [
        "sings",
        "sing"
      ],
      "denotation": "Lx.sing(w0,x)"
    },
    {
      "words": [
        "rests",
        "rest"
      ],
      "denotation": "Lx.rest(w0,x)"
    },
    {
      "words": [
        "reads",
        "read"
      ],
      "denotation": "Ly.Lx.read(w0,x,y)"
    },
    {
      "words": [
        "finds",
        "find"
      ],
      "denotation": "Ly.Lx.find(w0,x,y)"
    },
    {
      "words": [
        "sees",
        "see"
      ],
      "denotation": "Ly.Lx.see(w0,x,y)"
    },
    {
      "words": [
        "guards",
        "guard"
      ],
      "denotation": "Ly.Lx.guard(w0,x,y)"
    },
    {
      "words": [
        "ring"
      ],
      "denotation": "Lx.ring(w0,x)"
    },
    {
      "words": [
        "map"
      ],
      "denotation": "Lx.map(w0,x)"
    },
    {
      "words": [
        "gate"
      ],
      "denotation": "Lx.gate(w0,x)"
    },
    {
      "words": [
        "dragon"
      ],
      "denotation": "Lx.dragon(w0,x)"
    },
    {
      "words": [
        "hobbit"
      ],
      "denotation": "Lx.hobbit(w0,x)"
    },
    {
      "words": [
        "elf"
      ],
      "denotation": "Lx.elf(w0,x)"
    },
    {
      "words": [
        "the"
      ],
      "denotation": "LX.Ix.X(x)"
    },
    {
      "words": [
        "every",
        "Every"
      ],
      "denotation": "LX.LY.Ax[X(x) -> Y(x)]"
    },
    {
      "words": [
        "some",
        "Some"
      ],
      "denotation": "LX.LY.Ex[X(x) & Y(x)]"
    },
    {
      "words": [
        "a"
      ],
      "denotation": "LX.LY.Ex[X(x) & Y(x)]"
    },
    {
      "words": [
        "necessarily"
      ],
      "denotation": "Lp.Aw'[acc(w0)(w') -> p(w')]"
    },
    {
      "words": [
        "possibly"
      ],
      "denotation": "Lp.Ew'[acc(w0)(w') & p(w')]"
    },
    {
      "words": [
        "necessarily_deon"
      ],
      "denotation": "Lp.Aw'[deon_acc(w0)(w') -> p(w')]"
    },
    {
      "words": [
        "possibly_deon"
      ],
      "denotation": "Lp.Ew'[deon_acc(w0)(w') & p(w')]"
    },
    {
      "words": [
        "necessarily_meta"
      ],
      "denotation": "Lp.Aw'[meta_acc(w0)(w') -> p(w')]"
    },
    {
      "words": [
        "possibly_epist"
      ],
      "denotation": "Lp.Ew'[epist_acc(w0)(w') & p(w')]"
    },
    {
      "words": [
        "possibly_meta"
      ],
      "denotation": "Lp.Ew'[meta_acc(w0)(w') & p(w')]"
    },
    {
      "words": [
        "necessarily_epist"
      ],
      "denotation": "Lp.Aw'[epist_acc(w0)(w') -> p(w')]"
    },
    {
      "words": [
        "seeks",
        "seek"
      ],
      "denotation": "LR.Lx.seek(w0,x,R)"
    },
    {
      "words": [
        "believes",
        "believe"
      ],
      "denotation": "Lp.Lx.Aw'[dox(w0)(x,w') -> p(w')]"
    },
    {
      "words": [
        "wants",
        "want"
      ],
      "denotation": "Lp.Lx.Aw'[boul(w0)(x,w') -> p(w')]"
    }
  ],
  "rules": {
    "composition": {
      "functionApplication": true,
      "nonBranchingNodes": true,
      "predicateModification": true,
      "predicateAbstraction": true
    }
  },
  "exercises": [
    {
      "title": "A. Intransitive predicates",
      "instructions": "All predicates now carry the evaluation world w0 as a free parameter. An intransitive sentence \"Frodo rides\" yields ride(w0,f): true in the current world just if Frodo rides in it. Compose by the familiar Function Application.",
      "items": [
        {
          "sentence": "Frodo rides.",
          "tree": "[.S [.DP Frodo ] [.VP rides ] ]",
          "targets": [
            "ride(w0,f)"
          ]
        },
        {
          "sentence": "Gandalf sings.",
          "tree": "[.S [.DP Gandalf ] [.VP sings ] ]",
          "targets": [
            "sing(w0,g)"
          ]
        },
        {
          "sentence": "Aragorn rests.",
          "tree": "[.S [.DP Aragorn ] [.VP rests ] ]",
          "targets": [
            "rest(w0,a)"
          ]
        }
      ]
    },
    {
      "title": "B. Transitive predicates",
      "instructions": "A two-place verb takes the world w0 as first argument. The object is a definite description \"the ring\" = ιz[ring(w0,z)] — its referent is computed relative to the evaluation world. Compose by FA.",
      "items": [
        {
          "sentence": "Frodo finds the ring.",
          "tree": "[.S [.DP Frodo ] [.VP [.V finds ] [.DP [.D the ] [.NP ring ] ] ] ]",
          "targets": [
            "find(w0,f,ιz[ring(w0,z)])"
          ]
        },
        {
          "sentence": "Gandalf reads the map.",
          "tree": "[.S [.DP Gandalf ] [.VP [.V reads ] [.DP [.D the ] [.NP map ] ] ] ]",
          "targets": [
            "read(w0,g,ιz[map(w0,z)])"
          ]
        },
        {
          "sentence": "Sam sees the gate.",
          "tree": "[.S [.DP Sam ] [.VP [.V sees ] [.DP [.D the ] [.NP gate ] ] ] ]",
          "targets": [
            "see(w0,s,ιz[gate(w0,z)])"
          ]
        }
      ]
    },
    {
      "title": "C. Quantified subjects",
      "instructions": "A quantified DP cannot fill the e-type subject slot directly. Raise it to S level (QR), leaving a type-e trace; apply Predicate Abstraction; then FA with the quantifier. The resulting truth conditions universally/existentially quantify over individuals in the evaluation world w0.",
      "items": [
        {
          "sentence": "Every hobbit rides.",
          "tree": "[.S [.DP [.D every ] [.NP hobbit ] ] [.VP rides ] ]",
          "targets": [
            "∀x[hobbit(w0,x) → ride(w0,x)]"
          ]
        },
        {
          "sentence": "Some elf sings.",
          "tree": "[.S [.DP [.D some ] [.NP elf ] ] [.VP sings ] ]",
          "targets": [
            "∃x[elf(w0,x) ∧ sing(w0,x)]"
          ]
        },
        {
          "sentence": "Gandalf finds some ring.",
          "tree": "[.S [.DP Gandalf ] [.VP [.V finds ] [.DP [.D some ] [.NP ring ] ] ] ]",
          "targets": [
            "∃x[ring(w0,x) ∧ find(w0,g,x)]"
          ]
        }
      ]
    }
  ]
}