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User:Magnap/Inquisitive Semantics Proposal: Difference between revisions
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Revision as of 13:52, 26 September 2024
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Finally, the {{t|hí}} problem: if we want to remain backwards compatible with existing Toaq Delta wh-questions, we must assign it a meaning. Unfortunately, whether or not wh-questions generate presuppositions (in our notation, whether {{t|hí}} means <math>;\exists</math> or <math>?\exists</math>) is a highly contested issue that we would be forced to pick a side on... | Finally, the {{t|hí}} problem: if we want to remain backwards compatible with existing Toaq Delta wh-questions, we must assign it a meaning. Unfortunately, whether or not wh-questions generate presuppositions (in our notation, whether {{t|hí}} means <math>;\exists</math> or <math>?\exists</math>) is a highly contested issue that we would be forced to pick a side on... | ||
We might also want new or different connectives, or at least to give specific denotations for them. For example, we probably want {{t|ró}} to create two alternatives, which means we'd want it to be <math>\left(P \land \neg\text{Q}\right) \lor \left(\neg\text{P} \land{} \text{Q}\right)</math>. Other potentially quite useful connectives are (sometimes writing them out in a more verbose way than necessary to make their alternatives clearer): | We might also want new or different connectives, or at least to give specific denotations for them. For example, we probably want {{t|ró}} to create two alternatives, which means we'd want it to be <math>\left(P \land \neg\text{Q}\right) \lor \left(\neg\text{P} \land{} \text{Q}\right)</math>. | ||
Other potentially quite useful connectives are (sometimes writing them out in a more verbose way than necessary to make their alternatives clearer): | |||
* <math>?\text{P} \land{} ?\text{Q}</math> (one or the other or both or neither) | * <math>?\text{P} \land{} ?\text{Q}</math> (one or the other or both or neither) | ||
* <math>\left(P \land \text{Q}\right) \lor \left(P \land \neg\text{Q}\right) \lor \left(\neg\text{P} \land \text{Q}\right)</math> (one or the other or both) | * <math>\left(P \land \text{Q}\right) \lor \left(P \land \neg\text{Q}\right) \lor \left(\neg\text{P} \land \text{Q}\right)</math> (one or the other or both) | ||
* <math>\left(P \land \neg\text{Q}\right) \lor \left(\neg\text{P} \land \text{Q}\right) \lor \left(\neg\text{P} \land \neg\text{Q}\right)</math> (one or the other or neither) | * <math>\left(P \land \neg\text{Q}\right) \lor \left(\neg\text{P} \land \text{Q}\right) \lor \left(\neg\text{P} \land \neg\text{Q}\right)</math> (one or the other or neither) | ||
And so many more, this is rich bikeshedding territory and luckily more can easily be added later. | And so many more, this is rich bikeshedding territory and luckily more can easily be added later. | ||
Another concern is {{t|rí}} which is weird in the refgram, allowing you to answer with a connective!? I think we should fix that one up somehow. We almost certainly need a denotation that generates a non-informative proposition and doesn't presuppose anything, but there are many of those. Two reasonably intuitive options would be <math>?\left(\text{P} \lor \text{Q}\right)</math> and <math>?\text{P} \land{} ?\text{Q}</math>. | |||