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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeNov 5th 2012
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexThe recent changes to the various modal logic pages have changed the emphasis from the 'many agent' versions $S4(m)$.etc. to a type theoretic one. That would be okay but in so doing they have become a bit garbled so they refer to K(m) but then just describe $K$ itself. I am wondering what is planned for these. I originally wrote them with the aim of increasing the nPOV side of the Computer Science entries and to have some brief introduction to modal logs, what should they become?

   The recent changes to the various modal logic pages have changed the emphasis from the ’many agent’ versions $S4(m)$.etc. to a type theoretic one. That would be okay but in so doing they have become a bit garbled so they refer to K(m) but then just describe $K$ itself. I am wondering what is planned for these. I originally wrote them with the aim of increasing the nPOV side of the Computer Science entries and to have some brief introduction to modal logs, what should they become?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 5th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI found the entries as were pretty much lacking an explanation of what was going on. So I filled in some. It's straightforward to add more on the many-agent aspect. I can do that later.

   I found the entries as were pretty much lacking an explanation of what was going on. So I filled in some. It’s straightforward to add more on the many-agent aspect. I can do that later.

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeNov 5th 2012
   • (edited Nov 5th 2012)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexI had sort of hoped that someone would see some future development away from the Boolean/classical case, but I did not have the knowledge to push that through. Anyone know of sources.... ? I agree that the old entries were a bit 'stubby', and had hoped to see how to extend them in a sensible direction. The intriguing case is $S5(m)$ where the models are $m$-fold equivalence relations, so the natural way would seem to handle $m$-groupoids of higher and get a higher homotopy type theoretic version of that as a natural extension of the ideas. That made me also think that $S4(m)$ might go in the direction of $m$-simplicial sets and a form of directed homotopy that would have an interpretation for temporal logics, for instance, but I could not quite get the intuition right.

   I had sort of hoped that someone would see some future development away from the Boolean/classical case, but I did not have the knowledge to push that through. Anyone know of sources…. ?

   I agree that the old entries were a bit ’stubby’, and had hoped to see how to extend them in a sensible direction. The intriguing case is $S5(m)$ where the models are $m$-fold equivalence relations, so the natural way would seem to handle $m$-groupoids of higher and get a higher homotopy type theoretic version of that as a natural extension of the ideas. That made me also think that $S4(m)$ might go in the direction of $m$-simplicial sets and a form of directed homotopy that would have an interpretation for temporal logics, for instance, but I could not quite get the intuition right.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 5th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, I have added to [[S4 modal logic]] the following paragraph: > If instead of a single Box operator one considers $n \in \mathbb{N}$ box operators $\Box_i$ of this form the resulting modal logic is denote $S4(n)$. Here $\Box_i p$ is sometimes interpreted as "the $i$th agent knows $p$." This is based on me _guessing_ based on what you have about "agents" in related entries. Is that how it should read? Could you point out a reference where I can see this discussed? > I had sort of hoped that someone would see some future development away from the Boolean/classical case, but I did not have the knowledge to push that through. Anyone know of sources…. ? A long list of sources for intuitionistic modal logic is at _[[modal type theory]]_.

   Okay, I have added to S4 modal logic the following paragraph:

   If instead of a single Box operator one considers $n \in \mathbb{N}$ box operators $\Box_i$ of this form the resulting modal logic is denote $S4(n)$. Here $\Box_i p$ is sometimes interpreted as “the $i$th agent knows $p$.”

   This is based on me guessing based on what you have about “agents” in related entries. Is that how it should read? Could you point out a reference where I can see this discussed?

   I had sort of hoped that someone would see some future development away from the Boolean/classical case, but I did not have the knowledge to push that through. Anyone know of sources…. ?

   A long list of sources for intuitionistic modal logic is at modal type theory.

5. • CommentRowNumber5.
   • CommentAuthorTim_Porter
   • CommentTimeNov 5th 2012
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexI knew of the intuitionistic modal logic stuff from following up the paper by Eric Goubault and his brother. That did seem almost to indicate a useful interpretation but it did not quite do what I had hoped (my problem with it was a bit like you noted in another thread.) I will go and look at the S4(m) entry again. It may be best to split off the multiple agent case as a separate entry so as not to confuse things, and link from a renamed S4 entry, similarly for the others.

   I knew of the intuitionistic modal logic stuff from following up the paper by Eric Goubault and his brother. That did seem almost to indicate a useful interpretation but it did not quite do what I had hoped (my problem with it was a bit like you noted in another thread.)

   I will go and look at the S4(m) entry again. It may be best to split off the multiple agent case as a separate entry so as not to confuse things, and link from a renamed S4 entry, similarly for the others.