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Questions tagged [modal-logic]

Questions relating to deductions relating to the expressions "it is necessary that" and "it is possible that"

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5 votes
1 answer
112 views

This is a homework problem from a modal logic course I took several years ago. I've spent hours over the years trying to solve it and I have never been able to figure it out. The professor did give us ...
4 votes
0 answers
73 views

I've seen that on nLab, Stone duality is written in categorical terms (https://ncatlab.org/nlab/show/Stone+duality#StoneSpacesAndBooleanAlgebras) by regarding a two element Boolean algebra as a ...
0 votes
0 answers
75 views

I have defined some normal modal logic $L$. By $L$ being normal I mean that axiom (K) $\Box(\varphi \rightarrow \psi) \rightarrow (\Box \varphi \rightarrow \Box \psi)$ is derivable and the ...
Dert's user avatar
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1 vote
0 answers
29 views

I'm doing research on a modal-like logics. A lot of properties of these logics are very similar to those of modal logics. They are modeled by Kripke-like frames, they can be bisimilar, I can define ...
0 votes
0 answers
45 views

I've recenty taken an interest in non-monotonic logics, and I've stumbled upon autoepistemic logic. On Wikipedia page, it mentions that In terms In terms of possible world semantics, an expansion of $...
2 votes
1 answer
53 views

It is known, that in general the minimal filtration of a transitive frame does not preserve transitivity. It seems plausible though, that if we make the minimal filtration of a canonical model of some ...
2 votes
1 answer
94 views

This just struck me as weird while I was reading a bunch of papers on modal decision procedures for intuitionistic propositional logic: N : If $A$ is a theorem, derive $\Box A$. ~ If $A$ is a theorem,...
1 vote
0 answers
68 views

What are some ways to prove that a functor has an adjoint? I have defined algebras for my logic which extends modal logic by adding an additional operation and would like to check if this logic has an ...
1 vote
0 answers
53 views

I’m currently slowly working my way through Harel et. al’s textbook Dynamic Logic (https://www.weizmann.ac.il/math/harel/dynamic-logic) and find myself stuck on the following exercise: Exercise 11.1 ...
1 vote
0 answers
53 views

Hey y'all, I’ve been reading a chapter from the article Inflationary Fixed Points in Modal Logic. MIC is a modal logic extension that includes an operator for inflationary fixed points, similar to the ...
1 vote
0 answers
58 views

Given an idempotent monad $\bigcirc$ and comonad $\Box$ on some category $\mathbf{C},ドル with the unit and counit \begin{eqnarray} \eta^\bigcirc &:& &&\mathrm{Id}_{\mathbf{C}} &\to&...
2 votes
2 answers
225 views

I can see what feels exactly like a proof of what Lewis calls "the consistency postulate" (added to S1 to obtain S2): $$\Diamond (p \land q) \Rightarrow \Diamond p$$ from the following (see ...
PW_246's user avatar
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0 votes
0 answers
66 views

I am currently reading Nil Barton's "Iterative Set Theory." at pp.42-45. It explains that modal set theory resolves Russell's paradox, but I don't fully understand it. If a set x satisfies ...
3 votes
1 answer
247 views

I am currently reading about Gödel's second incompleteness theorem in Rautenberg's Einführung in die Mathematische Logik (see A Concise Introduction to Mathematical Logic p. 289 for an English version ...
0 votes
1 answer
93 views

I wanted to convince myself that modal logic K5 doesn't imply K4 So $\mathbf{K} + \Diamond A \rightarrow \Box\Diamond A \not\vdash\Box A \rightarrow\Box\Box A $ I tried this by constructing a model ...

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