Talk:Kripke semantics

message: I've applied quite a major change, mostly a new section on History&Terminology, with a precis of the above work before Kripke, and a discussion of the rival terminology.  I could have pointed out that the Blackburn et al book, now the standard ref. on modal logic, talks about relational semantics, but I didn't, as does Goldblatt, but I didn't.  Possible world semantics is also widely used, perhaps as much as Kripke semantics, but it marks you as ignorant to use it: someone more diplomatic than me should put that in.  And I added four references. ---- Charles Stewart 16:47, 25 Aug 2004 (UTC)
replies: text: My understanding is that "possible world semantics" refers to the philosophical interpretation of intensional logics by possible worlds, rather than the formal relational semantics. -- EJ 14:56, 26 Aug 2004 (UTC)
thread_title: Major changes

message: Another issue: where does Kripke-Joyal semantics belong? I originally moved it to the section on intuitionistic logic, as I vaguely remembered that topoi have something to do with int. log., rather than modal logic. After reading the Goldblatt paper I'm not so sure about it. It might be better to leave it as a top-level section after all. Can someone who actually understands sheaves confirm this? -- EJ 14:56, 26 Aug 2004 (UTC)
replies: text: Perhaps it should be joined up with intuitionistic logic.  Note that the Tarski-Jonsson topological semantics ofr intuitionistic logic predates Kripke/frame semantics, and is really closer in spirit to what is going on in sheaf semantics anyhow.  (I'm not really on top of sheaves, but I have a rough idea about what is going on) ---- Charles Stewart 08:29, 16 Sep 2004 (UTC)
thread_title: Kripke-Joyal semantics

message: The phrase
:is a formal semantics for modal logic systems, created in late 1950's and early 1960's by Saul Kripke
should be changed to
:is a formal semantics created in late 1950's and early 1960's by Saul Kripke for modal logic systems
The reason is that it is a formal semantics for more than modal logics.  For example, it is used with intuitionistic logic. —the preceding comment is by 62.30.147.160 - 12:32, 24 July 2006 (UTC)
replies: text: Makes sense. And BTW, you can edit it yourself. -- EJ 18:11, 29 July 2006 (UTC)
thread_title:  First paragraph 

message: Can please someone explain the axiom 5 on the following frame?
:*1 -> 2
:*1 -> 3
:*2 -> 3
:*3 -> 2
This is an euclidean frame (1R2 and 1R3 -> 2R3 and 3R2), right? Then the axiom 5 must hold.
Now suppose that A holds only on 2. Then, on 1 holds \Diamond A, but \Box \Diamond A doesn't hold. Where is the mistake? I cannot figure it out. I suppose the point is that this frame is not euclidean, but this means that there is something in the definition that I'm not able to catch... Thanks! -- Stefano 11:53, 7 June 2010  —Preceding unsigned comment added by 95.244.18.126 (talk)  
:This is not a Euclidean frame, as 1 → 2 and 1 → 2 would force 2 → 2. By the same token, 3 → 3 (and in general, the target of every arrow has to be reflexive). When you fix the frame like this, \Box \Diamond A does indeed hold in 1.—Emil J. 11:26, 7 June 2010 (UTC)
replies: text: Woa, thank you soooo much! -- Stefano  —Preceding unsigned comment added by 95.244.18.126 (talk) 12:29, 7 June 2010 (UTC)
thread_title:  5 

message: Is it really different than this? I know that Kripke semantics do not involve an ontological commitment to possible worlds: . So, please explain what's the difference claimed in the lead here. Tijfo098 (talk) 17:19, 20 April 2011 (UTC)
replies: text: Agreed.  I was a bit taken aback to read that relational semantics was not possible-world semantics as I've been using the two interchangeably for decades.  --Vaughan Pratt (talk) 20:36, 23 November 2012 (UTC)
thread_title:  [[Possible world semantics]] 

message: OK the only thing I can follow is \Box p \leftrightarrow \lnot \Diamond \lnot p
Can an analog of truth tables be made?
In combinational logic you list the possible states of variables (for each variable either true or false) and the result of logic gates, but also => etc can be written this way...
what are the modal values of the completely parsed statements? true/false? 
necesary,possible?
or true and necessary, true and possible, false and necessary false and possible (4)
or 8: 
true, necessary, possible
true, necessary, not possible,
true, not necessary, possible,
...
?
Can these symbols be seen as logic gates with value tables?
Is there software that lets you compute on relatively short expressions? perhaps the easiest way to learn these things is by many examples...  — Preceding unsigned comment added by 83.134.181.100 (talk) 02:10, 23 January 2012 (UTC)
thread_title:  hard to grasp 

message: Text for the second table mentions "the logics are complete with respect to the frame classes given in the table, but they may correspond to a larger class of frames".
Is it possible to add a column to show which logics actually correspond to the listed classes of frames?
I would also be interested in a few more examples, maybe here or a reference if available.  — Preceding unsigned comment added by 173.74.57.70 (talk) 15:38, 12 April 2014 (UTC)
thread_title:  Frame conditions 

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thread_title:  External links modified 

message: Is the use of \Vdash (\Vdash) rather than \models (\models) for the satisfaction relation merely a glyph variation (like \phi versus \varphi), or is there some technical nuance that this choice seeks to express? I'm not suggesting changing the article, just seeking clarification of whether this means anything. One reason this puzzles me is that
: 
is using \models throughout, except in the chapter about modal logic, where instead the definition of Kripke model uses \Vdash for the satisfaction relation; this becomes doubly odd considering that the definitions op. cit. of satisfaction are essentially the same in temporal logic as in modal logic, but the authors are using different symbols. (Of course, it could be that one author wrote one chapter whereas the second wrote the other, and no editor enforced notational consistency.) Here in Wikipedia, articles Kripke semantics and Modal logic use different commands for the satisfaction relation. 95.195.195.123 (talk) 12:42, 10 November 2019 (UTC)
thread_title:  Satisfaction relation symbol 

message: According to the article at sign, "a 'designated' world in a Kripke model may be labelled '@'", but I see nothing in this article to support that claim. Is it true? If so, does anyone have a citation? --John Maynard Friedman (talk) 00:01, 25 March 2021 (UTC)
thread_title:  @ sign