Added explicit definition in terms of coalgebras for the powerset functor (and thus, the definition of morphisms of Kripke frames) and a brief of discussion of duality results.
Evan Washington
]]>and this one:
added also this reference:
Have re-written and expanded this entry.
Also added the original references:
Saul A. Kripke, A Completeness Theorem in Modal Logic, The Journal of Symbolic Logic 24 1 (1959) 1-14 [doi:10.2307/2964568, jstor:2964568, pdf]
Saul A. Kripke, Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi, Mathematical Logic Quaterly 9 5-6 (1963) 67-96 [doi:10.1002/malq.19630090502]
Well I think I’ve made it a lot clearer that it’s a subsidiary concept. It only makes proper sense when taken up in the larger notion of a Kripke model. It’s like we’re dwelling on the contents of a page for the carrier set of a group, and you’re saying there must be more to it than the carrier set being a non-empty set.
]]>Hm, I didn’t think that removing information was the way to go in the face of too little information. :-)
If it helps, imagine a student asking you for what a Kripke frame is, how would they ever understand it from this entry?
But never mind, evidently I should go and edit myself instead of trying to make somebody else do it. I’ll try to find the time later, at some point.
]]>It really doesn’t deserve any length this entry, so I’ve pruned it.
]]>So that needs changing. A Kripke frame isn’t defined relative to a given modal operator. It just is a non-empty set with a binary relation. A Kripke model then adds to a frame a valuation, a map from propositional variables to subsets of worlds. Then we can speak of what it means to say of a model that at some given world some modal proposition is true.
It really is a concept with an attitude, the attitude being how it will be taken up by the concept of a model, and the satisfaction relation relative to a model.
I’ll see what I can do to make this clear.
]]>The definition in the entry says essentially:
“Given a modal operator, then a Kripke frame is a binary relation . Period.”
This is not contentful. For it to be contentful, there needs to be a statement that refers back to the modal operator in the assumption.
Otherwise the content of the entry is logically equivalent to: “Given a pink elephant, a Kripke frame is a binary relation .”
So at the very least it needs to say something like this:
“Given a modal operator , then a Kripke frame is a set equipped with a binary relation , where is interpreted as asserting that holds in world if holds in world .”
]]>Better now?
]]>But the entry still just declares the bare concept and not its actual attitude.
Why not add a line connecting the modal operator to the relation. Without that discussed, it seems all pointless.
]]>Have added something to the introduction, along the lines of #3.
]]>Adding reference
The entry geometric model for modal logics is only marginally better: Who spots the connection between the modal operator and those relations (hidden in the fifth item of “Satisfaction”, using undeclared notation) without which there is no meaning to the definitions.
]]>Right, something of a concept with an attitude. Perhaps the entry could make clearer that Kripke frames are a component part of Kripke models, as described at geometric model for modal logics (contrasted with algebraic model for modal logics).
]]>I have touched wording, hyperlinking and formatting throughout the entry.
But this entry is still lacking content. E.g. it defines a Kripke frame to be exactly a binary relation and then leaves it at that.
In particular the comments in the References-section seem out of place until there is some content here that could possibly be erroneous.
]]>Clarify by replacing nonsensical “n-unary” and “n-binary”.
Mark John Hopkins
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