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Semantics: Difference between revisions
Use a consistent syntax for restricted quantification
(brismu is being worked on again?? update the link) |
(Use a consistent syntax for restricted quantification) |
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** <math>\forall</math> for "every" | ** <math>\forall</math> for "every" | ||
For example, we might write the interpretation of "indeed, every person is living or dead" as <math>\dagger \forall a | For example, we might write the interpretation of "indeed, every person is living or dead" as <math>\dagger \forall a : \text{poq}(a).\ \text{mie}(a) \lor \text{muaq}(a)</math>. | ||
== Events == | == Events == | ||
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We use the function representation whenever a property in Toaq is spelled out explicitly with the complementizer {{Derani||lä}}. For example, the property in {{Derani| |Leo jí, lä nuo já}} would be interpreted as <math>\lambda a.\ \lambda w.\ \exists e.\ \tau(e) \subseteq \text{t} \land \text{nuo}_w(a)(e)</math>, a function of type <math>\left\langle \text{e}, \left\langle \text{s}, \text{t} \right\rangle \right\rangle</math>. And for a property with two blanks, you would use a function of type <math>\left\langle \text{e}, \left\langle \text{e}, \left\langle \text{s}, \text{t} \right\rangle \right\rangle \right\rangle</math>. | We use the function representation whenever a property in Toaq is spelled out explicitly with the complementizer {{Derani||lä}}. For example, the property in {{Derani| |Leo jí, lä nuo já}} would be interpreted as <math>\lambda a.\ \lambda w.\ \exists e.\ \tau(e) \subseteq \text{t} \land \text{nuo}_w(a)(e)</math>, a function of type <math>\left\langle \text{e}, \left\langle \text{s}, \text{t} \right\rangle \right\rangle</math>. And for a property with two blanks, you would use a function of type <math>\left\langle \text{e}, \left\langle \text{e}, \left\langle \text{s}, \text{t} \right\rangle \right\rangle \right\rangle</math>. | ||
But whenever a Toaq variable is used as a property, we need to fall back to the properties as individuals approach, using <math>\text{iq}</math> (type <math>\left\langle \text{e}, \left\langle \text{e}, \left\langle \text{s}, \text{t} \right\rangle \right\rangle \right\rangle</math>) or <math>\text{cuoi}</math> (type <math>\left\langle \text{e}, \left\langle \text{e}, \left\langle \text{e}, \left\langle \text{s}, \text{t} \right\rangle \right\rangle \right\rangle \right\rangle</math>) to access its semantic content. So, the correct interpretation of {{Derani| |Che nháo sá jua}} would be <math>\exists a | But whenever a Toaq variable is used as a property, we need to fall back to the properties as individuals approach, using <math>\text{iq}</math> (type <math>\left\langle \text{e}, \left\langle \text{e}, \left\langle \text{s}, \text{t} \right\rangle \right\rangle \right\rangle</math>) or <math>\text{cuoi}</math> (type <math>\left\langle \text{e}, \left\langle \text{e}, \left\langle \text{e}, \left\langle \text{s}, \text{t} \right\rangle \right\rangle \right\rangle \right\rangle</math>) to access its semantic content. So, the correct interpretation of {{Derani| |Che nháo sá jua}} would be <math>\exists a : \text{jua}(a).\ \exists e.\ \tau(e) \subseteq \text{t} \land \text{che}(\text{nh}\mathrm{\acute{a}}\text{o}, \lambda b.\ \text{iq}(b, a))(e) </math>. | ||
TODO: point out that questions are isomorphic to properties | TODO: point out that questions are isomorphic to properties | ||