Del Pinal (2015): Dual Content Semantics, privative adjectives, and dynamic compositionality #
Del Pinal's dual content semantics gives a common noun two parts, an E-structure that determines its extension and a C-structure that assigns a property to each of the four qualia of Pustejovsky. A privative adjective such as fake is a semantic restructuring operator, a function from noun meanings to noun meanings that reads the noun's C-structure, so that a fake gun is not a gun, was not made as a gun, and was made to look like one. The C-structure of the result does further compositional work, in typical fake gun and in the two bracketings of fake plastic gun and fake Chanel handbag. Against Partee's shifting heads, on which fake is subsective once the head noun is coerced, the literal fake N needs no coercion, and a first-order fake would make shifting heads read every fake gun as a gun.
Main statements #
disjoint_privativeE: no fake, counterfeit or artificial N is an N.typical_fake_formal_not_telic: a typical fake N looks like an N and cannot serve as one, which a fake N need not do (fake_not_formal_not_telic).typicalE_eq_cStructure: where an N's C-structure is narrower than its extension, the typical Ns are those with the whole C-structure.fake_bracketing,fake_brand_made_by_brand_reading: fake B N denotes real Ns on [[fake B] N] and things that are not B Ns on [fake [B N]], so only the latter covers a fake handbag made by Chanel.fake_isNonVacuous,fake_vacuous_in_head: the literal fake N has a positive and a negative extension, and is vacuous only within its head, where Partee's shift applies.shifting_heads_evil_park_owner: with a first-order fake, one fake paintball gun that is a real gun keeps shifting heads from shifting gun, so every fake gun is a gun.
Implementation notes #
A dual content pairs the E-structure N.extension with the C-structure N.quale, whose values
are the paper's qualia functions; dual contents are ordered componentwise. The paper composes each
of a modifier's five components with the noun's full meaning; transposed, the five are one
Modifier of dual contents, and that composition rule is its application. A quale without a
value is the trivial property (footnote 10), so the intersective shift (20) is
Modifier.intersective on dual contents; brand names such as Chanel are taken to shift the
same way, the paper saying only that they add a condition to the agentive. The making events
∃e[making(e) ∧ goal(e, P(x))] are a primitive made P, which does not distinguish the
two-place making of (15).
TODO #
Section 3 also attributes to the bracketing [fake [plastic gun]] a reading on which a fake plastic gun is a real gun made of plastic. The entry (16) applied to (21) does not derive it, since the E-structure of fake plastic gun denies the compound plastic gun.
References #
Dual contents #
A dual content pairs an E-structure, which determines the extension, with a C-structure, which assigns a property to each quale.
- extension : Semantics.Property W E
The E-structure.
- quale : Pustejovsky1995.QualeRole → Semantics.Property W E
The C-structure, the property of each quale.
Instances For
A dual content as the ordered pair of its E-structure and its C-structure.
Instances For
Equations
- DelPinal2015.DualContent.instPartialOrder = PartialOrder.lift DelPinal2015.DualContent.toProd ⋯
Equations
- DelPinal2015.DualContent.instMin = { min := fun (M N : DelPinal2015.DualContent W E) => { extension := M.extension ⊓ N.extension, quale := M.quale ⊓ N.quale } }
Equations
- DelPinal2015.DualContent.instMax = { max := fun (M N : DelPinal2015.DualContent W E) => { extension := M.extension ⊔ N.extension, quale := M.quale ⊔ N.quale } }
Dual contents form a lattice componentwise.
Equations
- DelPinal2015.DualContent.instLattice = Function.Injective.lattice DelPinal2015.DualContent.toProd ⋯ ⋯ ⋯ ⋯ ⋯
The C-structure read as one predicate, the conjunction of the qualia (§7.4).
Equations
- N.cStructure = ⨅ (r : Pustejovsky1995.QualeRole), N.quale r
Instances For
The restructuring operators C, F, T and A of §3 restrict the extension to one quale,
as A(lion) holds of the lions born as lions.
Equations
- DelPinal2015.DualContent.withQuale r N = N.extension ⊓ N.quale r
Instances For
The entries #
made P is made with the goal that P hold, ∃e[making(e) ∧ goal(e, P(x))].
The E-structure of a privative holds of what is not an N, lacks the N's r quale, and was
made with the goal g.
Equations
- DelPinal2015.privativeE made r g N = N.extensionᶜ ⊓ (N.quale r)ᶜ ⊓ made g
Instances For
fake (16) maps an N to what is not an N, lacks an N's origin, and was made to look like an N. It keeps the N's constitutive and formal qualia, negates its telic, and records the making as its agentive.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The E-structure of counterfeit (11) is that of fake with the goal of looking and functioning like an N.
Equations
Instances For
The E-structure of artificial (12) is that of fake with the goal of functioning like an N.
Equations
Instances For
The E-structure of fake modulated for substance terms (15) holds of what is not an N, lacks an N's constitution, and was made to look like an N.
Equations
Instances For
A privative N is not an N.
A privative N lacks the quale its E-structure negates, a fake N an N's origin and a fake_m N an N's constitution.
For an artifact, whose agentive is being made for its function as in (8), a fake was not made to serve the function (10).
The E-structure of typical (13) holds of an N with every quale of an N.
Equations
- DelPinal2015.typicalE N = N.extension ⊓ N.cStructure
Instances For
typical is subsective.
A typical N has each quale of an N.
typical is the meet of the restructuring operators C, F, T and A.
Where an N's C-structure picks out only Ns, as §7.4 says that of gun does, the typical Ns are exactly those with the whole C-structure.
What the C-structure adds #
A typical fake N looks like an N and cannot serve an N's function (18), as the C-structure that (16) gives fake N says.
A fake N need do neither (10), since a badly made fake need not look like an N and may still serve an N's function.
A fake N need not be made to function like an N, which a counterfeit N is (footnote 14).
An artificial N need not be made to look like an N, which fakes and counterfeits are (12).
A fake N may have an N's constitution, as a fake gun may be made of a gun's parts, which a
fake_m N may not (privativeE_le_compl, footnote 17).
Bracketing #
On the bracketing [[fake B] N] a fake B N is a real N that is not a B, a real gun made of fake plastic, and on [fake [B N]] it is not a B N (§3).
What is not from the brand and was made to look like a B N is a fake B N on [fake [B N]], even a real N, so a handbag not from Chanel made to pass for a Chanel handbag is a fake Chanel handbag (p. 7:15).
Something that is not an N, lacks an N's origin, and was made to look like a B N is a fake B N on [fake [B N]] whatever its relation to B's origin, so a fake handbag made by Chanel is a fake Chanel handbag; on [[fake B] N] it is not (p. 7:15 and footnote 12).
Against shifting heads #
On E-structures fake is privative in the sense of [Kam75], over any lexicon whose E-structures are the properties themselves.
Hence the literal fake N is vacuous within its head, the local domain of head primacy, which is what triggers the head shift of [Par10].
No shift is needed (§5), since in any domain with a fake N and an N the literal fake N has a positive extension, the fake Ns, and a negative extension, which contains every N.
If attributive fake is the first-order predicate (33), a world with a gun that is fake, as in the evil park owner scenario, and a gun that is not makes the literal fake gun non-vacuous among the guns, so shifting heads does not shift gun and every fake gun is a gun, a reading fake gun never has (§6).