{
  "compose": 1,
  "id": "krifka-telicity",
  "title": "Krifka 1998 — The Origins of Telicity",
  "notation": "cc",
  "domain": {
    "multiLetterNames": true,
    "constants": {
      "e": "j m",
      "n": "two"
    },
    "variables": {
      "e": "x y z u",
      "v": "e e' e''",
      "et": "P Q",
      "t": "p q",
      "<<e,t>,t>": "K"
    }
  },
  "lexicon": [
    {
      "words": [
        "Mary"
      ],
      "denotation": "m"
    },
    {
      "words": [
        "John"
      ],
      "denotation": "j"
    },
    {
      "words": [
        "sleeps",
        "sleep"
      ],
      "denotation": "Lx.Le.sleep(x,e)"
    },
    {
      "words": [
        "eats",
        "eat"
      ],
      "denotation": "LP.Lx.Le.Ey[P(y) & eat(x,y,e)]"
    },
    {
      "words": [
        "drinks",
        "drink"
      ],
      "denotation": "LP.Lx.Le.Ey[P(y) & drink(x,y,e)]"
    },
    {
      "words": [
        "pushes",
        "push"
      ],
      "denotation": "LP.Lx.Le.Ey[P(y) & push(x,y,e)]"
    },
    {
      "words": [
        "apples"
      ],
      "denotation": "Lx.*apple(x)"
    },
    {
      "words": [
        "water"
      ],
      "denotation": "Lx.water(x)"
    },
    {
      "words": [
        "cart"
      ],
      "denotation": "Lx.cart(x)"
    },
    {
      "words": [
        "a",
        "an"
      ],
      "denotation": "LP.P"
    },
    {
      "words": [
        "two"
      ],
      "denotation": "LP.Lx.[P(x) & card(x) = two]"
    },
    {
      "words": [
        "two-liters-of"
      ],
      "denotation": "LP.Lx.[P(x) & liter(x) = two]"
    },
    {
      "words": [
        "is",
        "are"
      ],
      "denotation": "LK.K"
    },
    {
      "words": [
        "cumulative"
      ],
      "denotation": "LP.[Ex[Ey[P(x) & P(y) & ~(x = y)]] & Ax[Ay[P(x) & P(y) -> P(x ⊕ y)]]]"
    },
    {
      "words": [
        "quantized"
      ],
      "denotation": "LP.Ax[Ay[P(x) & P(y) -> ~((y ≤ x) & ~(y = x))]]"
    }
  ],
  "rules": {
    "composition": {
      "functionApplication": true,
      "predicateModification": false,
      "nonBranchingNodes": true,
      "predicateAbstraction": false
    },
    "typeShifts": [
      "ec-v"
    ]
  },
  "exercises": [
    {
      "id": "g1",
      "title": "A. Cumulative and quantized reference (defs. 3–4)",
      "instructions": "CUM and QUA are properties of predicates, not of things (Krifka: one entity can fall under apples and under two apples). Unfold the definitions by composing.",
      "derivations": [
        {
          "id": "d1",
          "tree": "[.t [.NP apples ] [.Pred [.Cop are ] [.A cumulative ] ] ]",
          "sentence": "Apples are cumulative.",
          "hints": [
            "are is vacuous here; cumulative denotes a property of predicates — apply it to ⟦apples⟧ = λx.∗apple(x).",
            "The result unfolds definition (3): non-triviality (two distinct instances) plus closure under sum ⊕."
          ],
          "targets": [
            "Ex[Ey[*apple(x) & *apple(y) & ~(x = y)]] & Ax[Ay[*apple(x) & *apple(y) -> *apple(x ⊕ y)]]"
          ],
          "reading": {
            "section": "1"
          }
        },
        {
          "id": "d2",
          "tree": "[.t [.NP [.Mea two-liters-of ] [.CN water ] ] [.Pred [.Cop is ] [.A quantized ] ] ]",
          "sentence": "Two liters of water is quantized.",
          "targets": [
            "Ax[Ay[(water(x) & liter(x) = two) & (water(y) & liter(y) = two) -> ~((y ≤ x) & ~(y = x))]]"
          ],
          "reading": {
            "section": "1"
          }
        }
      ]
    },
    {
      "id": "g2",
      "title": "B. Verbs have an event argument (def. 40)",
      "instructions": "Every n-place verbal predicate becomes an (n+1)-place relation with a final event argument. Close the event with Existential Closure (EC) at the top.",
      "derivations": [
        {
          "id": "d1",
          "tree": "[.t [.NP Mary ] [.VP sleeps ] ]",
          "sentence": "Mary sleeps.",
          "targets": [
            "Ee[sleep(m,e)]"
          ],
          "reading": {
            "section": "2"
          }
        },
        {
          "id": "d2",
          "tree": "[.t [.NP Mary ] [.VP [.V eats ] [.NP apples ] ] ]",
          "sentence": "Mary eats apples.",
          "targets": [
            "Ee[Ey[*apple(y) & eat(m,y,e)]]"
          ],
          "reading": {
            "section": "2"
          }
        }
      ]
    },
    {
      "id": "g3",
      "title": "C. Aspectual composition (§3): the object shapes the VP",
      "instructions": "Same verb, different objects, different telicity. The formulas differ only in the object conjuncts — the telicity difference is proved from them in the notes via TEL (37) and incrementality SINC (51).",
      "derivations": [
        {
          "id": "d1",
          "tree": "[.t [.NP Mary ] [.VP [.V eats ] [.NP [.Num two ] [.CN apples ] ] ] ]",
          "sentence": "Mary eats two apples.",
          "targets": [
            "Ee[Ey[*apple(y) & card(y) = two & eat(m,y,e)]]"
          ],
          "reading": {
            "section": "3"
          }
        },
        {
          "id": "d2",
          "tree": "[.t [.NP John ] [.VP [.V drinks ] [.NP [.Mea two-liters-of ] [.CN water ] ] ] ]",
          "sentence": "John drinks two liters of water.",
          "targets": [
            "Ee[Ey[water(y) & liter(y) = two & drink(j,y,e)]]"
          ],
          "reading": {
            "section": "3"
          }
        },
        {
          "id": "d3",
          "tree": "[.t [.NP John ] [.VP [.V pushes ] [.NP [.Det a ] [.CN cart ] ] ] ]",
          "sentence": "John pushes a cart.",
          "targets": [
            "Ee[Ey[cart(y) & push(j,y,e)]]"
          ],
          "reading": {
            "section": "3"
          }
        }
      ]
    }
  ],
  "reading": {
    "format": "latex",
    "markdown": "# Krifka 1998 · The Origins of Telicity\n\nWorksheet companion to Manfred Krifka, \"The Origins of Telicity\" (in\nS. Rothstein (ed.), *Events and Grammar*, Kluwer, 1998). The paper derives\nthe telic/atelic distinction from the algebra of parts — the same ⊕ and ≤\nyou know from the §10 worksheets — applied to objects *and* events, linked\nby thematic relations.\n\n## 1 Cumulative and quantized reference\n\nTelicity talk starts on the nominal side. With respect to a part structure,\nKrifka defines (his (3), (4)):\n\n\\begin{derivation}\nCUM(X) ↔ Ex,y[X(x) & X(y) & ~x=y] & Ax,y[X(x) & X(y) -> X(x ⊕ y)]\nQUA(X) ↔ Ax,y[X(x) & X(y) -> ~y < x]\n\\end{derivation}\n\nKrifka's own illustration (§2): \"Examples of cumulative predicates are\n*water* or *apples*: If x and y fall under *apples*, then the sum of x and y\nfalls under *apples* as well. Examples of quantized predicates are *three\nliters of water* or *three apples*: If x falls under *three apples*, then it\ncannot have a proper part y that also falls under *three apples*.\nCumulativity of a predicate X implies that X applies to at least two\ndistinct elements.\" For measured predicates he shows quantization follows\nfrom the properties of extensive measure functions (his (10) and the\nremainder principle). Rendering note: the worksheet writes proper part\n$y < x$ as $y \\leq x \\wedge \\neg y = x$.\n\n\\ex Apples are cumulative.\n\\xe\n\n\\ex Two liters of water is quantized.\n\\xe\n\n## 2 Verbs carry an event argument\n\nFollowing Davidson, every n-place verbal predicate translates as an\n(n+1)-place relation whose last argument is an event (Krifka's (40)):\n$sleep(x,e)$, $eat(x,y,e)$. Uniqueness of participants (41) keeps events\ntied to their participants. In these derivations you close the event\nargument at the top with Existential Closure (EC over events) — the same\nshift as in the ch11 worksheets.\n\n\\ex Mary sleeps.\n\\xe\n\n## 3 Aspectual composition\n\nThe telicity of a VP is computed, not listed: *eat apples* is atelic, *eat\ntwo apples* is telic, with one verb. Krifka defines telicity for event\npredicates (his (37), using initial/final parts (36)):\n\n\\begin{derivation}\nTEL(X) ↔ Ae,e'[X(e) & X(e') & e' ≤ e -> INI(e',e) & FIN(e',e)]\n\\end{derivation}\n\nand shows that quantized event predicates are telic, cumulative ones\n(non-contemporaneous) atelic. What transmits the object's reference type to\nthe event predicate is the **thematic relation** and its homomorphism\nproperties (his (43)–(51)): mapping to subevents MSE (46) — every proper\npart of the apples is eaten in a proper part of the event; mapping to\nsubobjects MSO (49) — every proper part of the event eats a proper part of\nthe apples; with uniqueness of events (47) and objects (50) these make θ a\none-to-one correspondence between object parts and event parts. The\nconjunction (plus non-atomicity) is **strict incrementality**, SINC (51).\n\nIf the patient relation of *eat* is strictly incremental and the object\npredicate is quantized, the VP's event predicate is quantized, hence telic;\nif the object is cumulative (*apples*), the VP is cumulative, hence atelic.\nCompare your three formulas below — they differ only in the object\nconjuncts:\n\n\\pex\n\\a Mary eats two apples. (telic: quantized object, incremental θ)\n\\a John drinks two liters of water. (telic, via the measure function)\n\\a John pushes a cart. (atelic: θ of push is NOT incremental — no part of\nthe cart is pushed in a part of the pushing; MSE/MSO fail)\n\\xe\n\nThe *push a cart* case is the paper's warning against reading telicity off\nthe object alone: the object description is quantized, but without an\nincremental thematic relation nothing transmits that to the event\npredicate. Krifka's counter-cases to weaker definitions — *see a picture*,\n*touch a cup* (satisfy mapping but not uniqueness), *make a dot* (atomic on\nboth sides) — are what force the full SINC package.\n\n## 4 What is simplified or omitted\n\nThe worksheet stops where the engine's comfortable expressivity stops:\nKrifka's extensive measure functions appear only as the $liter(x) = two$\nconjunct (his §2.3 develops the theory: additivity, commensurability, the\nremainder principle); the paths-and-movement half of the paper (*walk from\nthe university to the capitol*, adjacency structures, §§4–5) and the\nproperty-change cases (*bake the lobster*, §6) are not derived; and the\nhomomorphism properties (43)–(51) are stated and used in these notes rather\nthan composed in trees — they quantify over the thematic relation itself,\none level up from what tree composition manipulates. The definitions quoted\nare Krifka's own, cited by his numbering throughout.\n\n## Credits\n\nKrifka, M. (1998). The origins of telicity. In S. Rothstein (ed.), *Events\nand Grammar*, 197–235. Kluwer. — The mereological machinery follows the\n§10 (Coppock & Champollion ch. 10) worksheets; the event argument and EC\nfollow ch. 11. Notes text: quotes and definitions with the paper's own\nnumbering, plus flagged rendering notes; remaining prose is signposting."
  },
  "meta": {
    "author": "Thomas Stephen",
    "source": "after Krifka 1998, The Origins of Telicity",
    "license": "MIT",
    "difficulty": "challenge"
  }
}