Timeline for Modal collapse upon addition of the law of the excluded middle to an Intuitionistic modal logic
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2022 at 11:09 | comment | added | user65526 | ...in that same context, then I am able to perform an action consisting of both the actions. Incidentally, we know from natural language theory that ability modals don't necessarily distributive over disjunction (see the paper by Rick Nouwen in Semantics and Pragmatics). | |
| Apr 22, 2022 at 11:07 | comment | added | user65526 | Perhaps an ability modal where propositional letters are restricted the actions performed by some fixed agent, so that the injection reads "If I perform an action then I am able to perform that action", and the other axioms read "If I am able to make it the case that I am able to make it the case that I perform an action, then I am able to perform the action. The third axiom is more tricky on this reading perhaps, for their may be mutually exclusive actions. But it seems reasonable for many actions that if I am able to perform an action in a fixed context and am able to perform another action | |
| Apr 21, 2022 at 10:20 | comment | added | Peter LeFanu Lumsdaine | @user65526: Yes, I agree it’s not a terribly good reading. Unfortunately I’ve never found a satisfactory intuitive reading for modalities satisfying this combination of axioms (even though they’re very important in several topics I’m interested in, e.g. topos theory). Alternative suggestions are very welcome indeed… | |
| Apr 20, 2022 at 20:27 | comment | added | user65526 | Great but I don't think "usually" is a good reading of $\bigcirc$, for the would mean that "If I win the lottery then it is is usual that I win the lottery" by the injection axiom. | |
| Apr 19, 2022 at 15:03 | history | answered | Peter LeFanu Lumsdaine | CC BY-SA 4.0 |