Timeline for A question on intuitionistic propositional logic
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 18, 2012 at 11:50 | comment | added | Emil Jeřábek | As for pretabular logics, there is no short answer. You apply the same method as in Thm. 12.13 or 12.16: a nontabular logic extending K4BD_n has finite frames of unbounded cluster size or unbounded width, and you try to sort of minimize the set of frames with this property. (This is not a terribly difficult exercise after reading section 12.3, but it’s rather tedious.) I’d guess the result should include logics of frames consisting of an infinite cluster sitting below a generated subframe of the universal frame $F_{K4}^{< n}(0)$, and something similar with infinite width. | |
| Oct 18, 2012 at 11:36 | comment | added | Emil Jeřábek | Well, the exercises in C&Z are sometimes quite tough. I’m not aware of any essentially different method of proving the isomorphism, and there are no techniques introduced in Chapter 2 that would be sufficient. Maybe they do intend for the reader to invent frame formulas themselves (the needed property is fairly basic, one does not need the full machinery of Ch. 9 for that). | |
| Oct 18, 2012 at 1:30 | comment | added | Set | I want to ask another question on modal logic: Show that the set of pretabular logics in NEx$tK4BD_n$ is finite for every $n<\omega$ and that all of them are finitely axiomatizable. | |
| Oct 18, 2012 at 1:24 | comment | added | Set | Thank you very much. In Chagrov's excellent book, this exercise is in Chapter 2 but the notation "the frame formula of $F$" is in chapter 9. What is the author's intention? | |
| Oct 18, 2012 at 0:47 | vote | accept | Set | ||
| Oct 17, 2012 at 19:00 | history | answered | Emil Jeřábek | CC BY-SA 3.0 |