Timeline for How can implications in Gödel logic be understood as assumptions?
Current License: CC BY-SA 4.0
6 events
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| Aug 14, 2023 at 14:41 | comment | added | Alex Kruckman | @blk I think what you're expressing in your last comment is that proving $\varphi\to \psi$ is the same as proving $\psi$, but considering those cases where $\varphi$ holds. This is just a restatement of the adjointness: $\chi$ entails $\varphi\to \psi$ if and only if $\chi\land \varphi$ entails $\psi$. | |
| Aug 14, 2023 at 0:15 | comment | added | blk | This may be a bit naive, but say I want to prove $\psi$. Then I have to consider only those cases where $\varphi$ holds. For cases where $\varphi$ does not hold, I don't have to prove anything (because I assume that $\varphi$ is definitely true). | |
| Aug 14, 2023 at 0:12 | comment | added | Alex Kruckman | @blk Well, can you explain how precisely you think of $\varphi\to \bullet$ as "making the assumption $\varphi$ in classical logic? Then maybe I would have some sense of the kind of explanation you're looking for. | |
| Aug 13, 2023 at 23:53 | comment | added | blk | Thanks Alex, this is a nice account of the semantics of Gödel implication and its adjoint $\wedge$. But I don't understand how this answers my question. I am aware of all of the above and still have the question: In which way can I think of $\varphi \rightarrow {\cdot}$ as "making the assumption $\varphi$"? It might be obvious, but I don't see it. | |
| Aug 13, 2023 at 0:58 | history | edited | Alex Kruckman | CC BY-SA 4.0 |
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| Aug 13, 2023 at 0:41 | history | answered | Alex Kruckman | CC BY-SA 4.0 |