Timeline for How are Modal Logic and Graph Theory related?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 7, 2016 at 20:45 | history | edited | Turbo |
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| Mar 14, 2013 at 1:35 | answer | added | rzach | timeline score: 6 | |
| Feb 26, 2013 at 19:55 | vote | accept | Samuel Reid | ||
| Feb 22, 2013 at 2:35 | comment | added | Noah Schweber | I believe the book "Toposes and local set theories" treats this to some extent, in chapter 6; I think Maclane/Moerdijk also goes into this, albeit at a much higher level of abstraction. | |
| Feb 6, 2013 at 17:16 | comment | added | Samuel Reid | @Peter LeFanu Lumsdaine: Your comment is very interesting to me and I can't find many references on the topic you alluded to. Have you thought of anything I could look up regarding this? Possibly a survey article, or at least a journal article which defines the words you are using in the context of modal logic? Thanks | |
| Feb 4, 2013 at 18:59 | comment | added | Rob Myers | The answers below have mentioned that not every first order definable class of graphs is definable by a formula of propositional modal logic. It might be worth mentioning that first order logic is the smallest extension of modal logic endowed with nominals (variables whose semantics is a singleton) and the universal modality (allowing one to assert truth at every state) that has interpolation. Also, modal logic with nominals and the universal modality is decidable. See Balder Ten Cate's thesis hylo.loria.fr/content/papers/files/phd-thesis.pdf. | |
| Feb 3, 2013 at 22:00 | answer | added | user30304 | timeline score: 5 | |
| Feb 3, 2013 at 21:10 | answer | added | Joel David Hamkins | timeline score: 11 | |
| Feb 3, 2013 at 20:19 | answer | added | Noah Schweber | timeline score: 16 | |
| Feb 3, 2013 at 19:28 | comment | added | Peter LeFanu Lumsdaine | One category-theoretic approach to this is that Kripke models of modal logic can be seen as sheaf/presheaf models, with the modalities often coming from sheafification for some Grothendieck coverage (equivalently, some Lawvere-Tierney closure operator). I can’t off the top of my head remember where is a good source for reading up on this, but hopefully those keywords should at least be useful for searching with. | |
| Feb 3, 2013 at 18:26 | history | asked | Samuel Reid | CC BY-SA 3.0 |