Timeline for Substitutional modality
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Jan 17, 2018 at 9:35 | comment | added | Emil Jeřábek | IIRC The argument for ML is given in Chagrov&Zakharyaschev; for $\sigma\ml$ it's essentially the same. The point is that $M_n$ and $M_m$ embed as disjoint generated subframes in $M_{n+m}$; unlike the usual "gluing" construction, the frame will contain various extra points besides the root and the two original frames, but this does not matter for the disjunction property. The gluing of $M_n$ and $M_m$ as such in general does not validate ML (or $\sigma\ml$): if it did, then Visser rules would be admissible in ML, hence derivable, hence the logic would have width at most $2$, quod non. | |
| Jan 17, 2018 at 1:34 | vote | accept | Andrew Bacon | ||
| Jan 17, 2018 at 1:34 | comment | added | Andrew Bacon | Wonderful! And thanks for the references, I will check those out later. Do you have a reference for the disjunction property for $\sigma ML$? (It wasn't jumping out to me as obvious: My strategy was to glue together an $M_i$ that falsified $\Box A$ and $M_j$ that falsified $\Box B$ to get something that falsified the disjunction, and show that it was bisimilar (or otherwise equivalent) to some $M_k$, but that's quite fiddly.) | |
| Jan 16, 2018 at 17:24 | history | answered | Emil Jeřábek | CC BY-SA 3.0 |