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Semantics: Difference between revisions
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In Toaq, we can use the complementizer {{Derani||ꝡä}} to create a reference to a proposition, which can then become the complement of another verb. So, our semantic theory needs to account for this construct, and it turns out that it's best to use two different "implementations" of propositions for this purpose. | In Toaq, we can use the complementizer {{Derani||ꝡä}} to create a reference to a proposition, which can then become the complement of another verb. So, our semantic theory needs to account for this construct, and it turns out that it's best to use two different "implementations" of propositions for this purpose. | ||
The first implementation is '''propositions as functions'''. The idea is to interpret a complementizer phrase as a function which takes a world as an input, and outputs the truth value of the proposition in that world (type <math>\left\langle \text{s}, \text{t} \right\rangle</math>). So for example, in {{Derani| |Chı jí, ꝡä za ruqshua}}, we would interpret the complementizer phrase as <math>\lambda w.\ \exists e.\ \tau(e) > \text{t} \land \text{ruqshua}_w(e)</math>, and pass this as an argument to the main verb, giving <math>\exists e.\ \tau(e) \subseteq t \land \text{chi}_{\text{w}}(\text{ji}, \lambda w.\ \exists e | The first implementation is '''propositions as functions'''. The idea is to interpret a complementizer phrase as a function which takes a world as an input, and outputs the truth value of the proposition in that world (type <math>\left\langle \text{s}, \text{t} \right\rangle</math>). So for example, in {{Derani| |Chı jí, ꝡä za ruqshua}}, we would interpret the complementizer phrase as <math>\lambda w.\ \exists e.\ \tau(e) > \text{t} \land \text{ruqshua}_w(e)</math>, and pass this as an argument to the main verb, giving <math>\exists e'.\ \tau(e') \subseteq \text{t'} \land \text{chi}_{\text{w}}(\text{ji}, \lambda w.\ \exists e.\ \tau(e) > \text{t} \land \text{ruqshua}_w(e))(e')</math>. Note that it would be wrong to interpret the complementizer phrase as <math>\exists e.\ \tau(e) > \text{t} \land \text{ruqshua}_{\text{w}}(e)</math>, because this evaluates to a simple truth value, which fails to capture the statement's semantic content. No one goes around saying "I believe [TRUE]" or "I believe [FALSE]". By using a function, we capture the statement's '''intension''' (its abstract connotation) rather than its '''extension''' (the concrete value held by the statement in the real world). | ||
TODO: finish | TODO: finish | ||