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Proving the non-derivability of formula using the of the kripke model

I try proving the non-derivability of $(p\to q) \to \lnot p \lor q$, using the of the kripke model. I tried using different combinations of $Wi$, but I get fail.
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The definition of interpretation in a Kripke model collides with my intuition of what it should do

In Lindröm and Segerberg (2007) exposition of a Kripke model, with frame $F= \langle W,D,R,E,w_0\rangle$, they define an interpretation $I$ as a family of functions $I_w$, where $w$ ranges over ...
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1answer
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Propositional S5: is there a consistent set requiring continuously many worlds?

A recent question asked whether in systems of modal propositional logic having the "finite model property" there are consistent sets of sentences that were not satisfied by a finite model. @Carl ...
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84 views

Propositional modal logic: infinite models required in systems with finite model property?

A system of propositional modal logic has the "finite model property" if any consistent sentence is satisfiable at a model with finitely many possible worlds. Some systems have this property and ...
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Proving Gabbay rule for Modal Logic

I'm currently working on exercises of the book "Modal Logic" by A.Chagrov and M.Zakharyaschev (for pleasure, not homework). One exercise asks to prove this version of Gabbay rule (exercise $3.10$): A ...
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33 views

Explanation of states, worlds and models?

Can someone explain to me how the concepts of states, models and worlds work together in Kripke semantics? I've been trying to piece together how the parts work are linked together but cannot figure ...
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84 views

Question concerning satisfiability in a certain Kripke model

My question concerns the exercise on p.77 of Boolos, Logic of Provability: True or false: if $A$ is satisfiable in some finite transitive and irreflexive [FIT] model and contains at most one ...
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What is the difference between First-Order Structures and Kripke Structures?

In the SEP article on Model Theory by Wilfrid Hodges (here), he writes: Particular kinds of model theory use particular kinds of structure; for example mathematical model theory tends to use ...
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A question on intuitionistc propositional logic

Prove that: Two finite rooted frames are isomorphic iff they validate the same formulas. (This is an exercise in the book "Modal Logic" by A.Chagrov and M.Zakharyaschev)