Timeline for Can we avoid the modal collapse in a certain Intuitionistic modal logic by abandoning ¬◯⊥ but retaining the law of the excluded middle?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2018 at 17:58 | vote | accept | user65526 | ||
| Mar 30, 2018 at 7:03 | review | Close votes | |||
| Apr 5, 2018 at 3:03 | |||||
| Mar 29, 2018 at 19:41 | answer | added | Bjørn Kjos-Hanssen | timeline score: 3 | |
| Mar 29, 2018 at 17:46 | history | edited | user65526 | CC BY-SA 3.0 |
added 249 characters in body
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| Mar 29, 2018 at 17:08 | comment | added | user65526 | Ok, but what do you mean by saying "clearly not"? Clearly not what? And why clearly not? | |
| Mar 29, 2018 at 17:06 | comment | added | user65526 | How is it hardly any better? Because it makes $\bigcirc$ a rather weak modality? | |
| Mar 29, 2018 at 17:05 | comment | added | Emil Jeřábek | No, that's not what I wrote. "Contained in" means contained in, not equal. | |
| Mar 29, 2018 at 17:02 | comment | added | Emil Jeřábek | Anyway, the argument from the linked page shows that even without assuming $\neg{\bigcirc}\bot$, you get the schema $\bigcirc A\leftrightarrow A\lor{\bigcirc}\bot$, which is hardly any beter than full modal collapse. | |
| Mar 29, 2018 at 17:01 | comment | added | user65526 | Sorry, I didn't understand your response. You are saying that we clearly do not get the modal collapse with $PLL$ plus excluded middle without $\neg \bigcirc \bot$, since $\bigcirc A$ holds for all formuals $A$? | |
| Mar 29, 2018 at 16:54 | comment | added | Emil Jeřábek | (1) Clearly not, as the logic is contained in the logic axiomatized by classical logic and $\bigcirc A$ for all formulas $A$. | |
| Mar 29, 2018 at 16:40 | history | edited | user65526 | CC BY-SA 3.0 |
included more background on the logic discussed
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| Mar 29, 2018 at 15:38 | history | edited | user65526 | CC BY-SA 3.0 |
edited title
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| Mar 29, 2018 at 15:23 | history | edited | user65526 | CC BY-SA 3.0 |
Made the question shorter
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| Mar 29, 2018 at 12:55 | history | asked | user65526 | CC BY-SA 3.0 |