{
  "compose": 1,
  "id": "partee-rooth-conj",
  "title": "Partee & Rooth 1983 — Generalized Conjunction",
  "notation": "cc",
  "domain": {
    "multiLetterNames": true,
    "constants": {
      "e": "j m"
    },
    "variables": {
      "e": "x y z",
      "et": "P Q X Y",
      "<<e,t>,t>": "T U",
      "<e,<e,t>>": "R1 R2"
    }
  },
  "lexicon": [
    {
      "words": [
        "John"
      ],
      "denotation": "j"
    },
    {
      "words": [
        "Mary"
      ],
      "denotation": "m"
    },
    {
      "words": [
        "woman"
      ],
      "denotation": "Lx.woman(x)"
    },
    {
      "words": [
        "student"
      ],
      "denotation": "Lx.student(x)"
    },
    {
      "words": [
        "teacher"
      ],
      "denotation": "Lx.teacher(x)"
    },
    {
      "words": [
        "car"
      ],
      "denotation": "Lx.car(x)"
    },
    {
      "words": [
        "walks",
        "walk"
      ],
      "denotation": "Lx.walk(x)"
    },
    {
      "words": [
        "talks",
        "talk"
      ],
      "denotation": "Lx.talk(x)"
    },
    {
      "words": [
        "arrived",
        "arrive"
      ],
      "denotation": "Lx.arrive(x)"
    },
    {
      "words": [
        "needed",
        "need"
      ],
      "denotation": "Ly.Lx.need(x,y)"
    },
    {
      "words": [
        "bought",
        "buy"
      ],
      "denotation": "Ly.Lx.buy(x,y)"
    },
    {
      "words": [
        "every"
      ],
      "denotation": "LX.LY.Ax[X(x) -> Y(x)]"
    },
    {
      "words": [
        "a",
        "an"
      ],
      "denotation": "LX.LY.Ex[X(x) & Y(x)]"
    },
    {
      "words": [
        "the"
      ],
      "denotation": "LX.Ix.X(x)"
    },
    {
      "words": [
        "andP"
      ],
      "displayAs": "and",
      "denotation": "LQ.LP.Lx.[P(x) & Q(x)]"
    },
    {
      "words": [
        "andT"
      ],
      "displayAs": "and",
      "denotation": "LU.LT.LP.[T(P) & U(P)]"
    },
    {
      "words": [
        "andTV"
      ],
      "displayAs": "and",
      "denotation": "LR2.LR1.Ly.Lx.[R1(y)(x) & R2(y)(x)]"
    }
  ],
  "rules": {
    "composition": {
      "functionApplication": true,
      "predicateModification": false,
      "nonBranchingNodes": true,
      "predicateAbstraction": true
    },
    "typeShifts": [
      "lift",
      "iota"
    ],
    "quantifierRaising": true
  },
  "exercises": [
    {
      "id": "g1",
      "title": "A. ⊓ at ⟨e,t⟩ — the base of the recursion",
      "instructions": "Generalized conjunction: at conjoinable types ⟨a,b⟩, f ⊓ g = λx[f(x) ⊓ g(x)], bottoming out in ∧ at t.",
      "derivations": [
        {
          "id": "d1",
          "tree": "[.t [.DP John ] [.IV [.IV walks ] [.ConjP [.Conj andP ] [.IV talks ] ] ] ]",
          "sentence": "John walks and talks.",
          "targets": [
            "walk(j) & talk(j)"
          ],
          "reading": {
            "section": "1"
          }
        }
      ]
    },
    {
      "id": "g2",
      "title": "B. Conjoining unlike NPs — lift as coercion",
      "instructions": "P&R's processing strategy: use the simplest types, shift only under coercion. To conjoin an e-type NP with a quantifier, LIFT it.",
      "derivations": [
        {
          "id": "d1",
          "tree": "[.t [.DP [.DP John ] [.ConjP [.Conj andT ] [.DP [.Det every ] [.CN woman ] ] ] ] [.IV arrived ] ]",
          "sentence": "John and every woman arrived.",
          "targets": [
            "arrive(j) & Ax[woman(x) -> arrive(x)]"
          ],
          "reading": {
            "section": "2"
          }
        },
        {
          "id": "d2",
          "tree": "[.t [.DP [.DP [.Det the ] [.CN teacher ] ] [.ConjP [.Conj andT ] [.DP [.Det every ] [.CN student ] ] ] ] [.IV arrived ] ]",
          "sentence": "The teacher and every student arrived.",
          "targets": [
            "arrive(Ix[teacher(x)]) & Ax[student(x) -> arrive(x)]"
          ],
          "reading": {
            "section": "2"
          }
        }
      ]
    },
    {
      "id": "g3",
      "title": "C. Conjoined transitive verbs share their object",
      "instructions": "Conjoin the TVs pointwise first, then let the object take scope (QR): one car, needed and bought.",
      "derivations": [
        {
          "id": "d1",
          "tree": "[.t [.DP John ] [.IV [.TV [.TV needed ] [.ConjP [.Conj andTV ] [.TV bought ] ] ] [.DP [.Det a ] [.CN car ] ] ] ]",
          "sentence": "John needed and bought a car.",
          "targets": [
            "Ez[car(z) & need(j,z) & buy(j,z)]"
          ],
          "reading": {
            "section": "3"
          }
        }
      ]
    }
  ],
  "reading": {
    "format": "latex",
    "markdown": "# Partee & Rooth 1983 · Generalized Conjunction\n\nCompanion to Barbara Partee & Mats Rooth, \"Generalized Conjunction and Type\nAmbiguity\" (in Bäuerle, Schwarze & von Stechow (eds.), *Meaning, Use, and\nInterpretation of Language*, de Gruyter, 1983). Cases and the processing\nstrategy are as summarized by Partee herself (Partee 2006, Lecture 14, which\nthis reading consulted directly).\n\n## 1 Generalized meet\n\nPartee & Rooth generalize ∧ to every \"conjoinable type\" — the types ending\nin t. As Partee (2006, Lecture 14) states their definition:\n\n\\begin{derivation}\nat t:        p ⊓ q = p ∧ q\nat <a,b>:    f ⊓ g = λx[f(x) ⊓ g(x)]   (b conjoinable)\n\\end{derivation}\n\nAt ⟨e,t⟩ this gives λP.λQ.λx[P(x) ∧ Q(x)] — your *walks and talks*. COMPOSE\nis simply typed, so the worksheet provides ⊓ at each type as its own lexical\nentry (all displayed as *and*); the recursion above is the single definition\nthey instantiate.\n\n\\ex John walks and talks.\n\\xe\n\n## 2 Type multiplicity and coercion\n\nTheir processing strategy: \"Use the simplest types consistent with coherent\ntyping of the entire sentence\" — higher types only under coercion. To\nconjoin an e-type NP with a quantifier, LIFT the name; an e-type definite\nlifts the same way (via iota, then lift).\n\n\\pex\n\\a John and every woman arrived.\n\\a The teacher and every student arrived.\n\\xe\n\n## 3 Conjoined transitive verbs\n\nConjoining TVs pointwise and then letting one object take scope derives the\nshared-object reading: one car, both needed and bought. On the type\nquestion, Partee's summary (2008, Lecture 4, §1) of the paper's claim,\nverbatim: \"It is argued in Partee and Rooth (1983) that this is the correct\ntype for intensional verbs like seek and need, but not for extensional\nverbs, which form the great majority, like love, eat, hit, buy\" — \"this\"\nbeing the quantifier-taking TV type ⟨⟨⟨e,t⟩,t⟩,⟨e,t⟩⟩. Their higher-type\nanalysis of intensional verbs with lowering as the default is omitted here;\nsee the PTQ Part B worksheet for the machinery it presupposes.\n\n\\ex John needed and bought a car.\n\\xe\n\n## Credits\n\nPartee, B. & M. Rooth (1983). Generalized conjunction and type ambiguity.\nIn R. Bäuerle et al. (eds.), *Meaning, Use, and Interpretation of Language*,\n361–383. de Gruyter. — Partee, B. (2006). *The Structure of Meaning*,\nLecture 14 (people.umass.edu/partee) and Partee, B. (2008), RGGU Lecture 4 —\nquoted as marked. Notes text: quotes as marked, plus flagged rendering notes\n(the per-type ⊓ entries); remaining prose is signposting."
  },
  "meta": {
    "author": "Thomas Stephen",
    "license": "MIT",
    "difficulty": "challenge"
  }
}