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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Does adding the axiom schema $\varphi \rightarrow \lozenge \square \varphi$ to $K \rho$ imply $A \rightarrow \square A$?
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 ...
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Jónsson-Tarski duality in categorical terms
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 ...
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If a normal modal logic's theorems are not recursively enumerable, does it lack a finite axiomatization?
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 ...
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General frames for modal logic as topological spaces literature
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 ...
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Modal approach to autoepistemic logic?
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 $...
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Does the minimal filtration of a canonical preserves transitivity?
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 ...
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Does this Weird Correspondence of $\Box$ to $\top \to$ to the S4 Axioms Allow for a Companion to IS4 with No Modal Operators?
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,...
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Duality theory - proving that functor has an adjoint
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 ...
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Expressive power of boolean stack operations in Dynamic Logic
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 ...
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Definition of non-context-free language in MIC
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 ...
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Are the de Rham modalities the negations of the cohesion modalities?
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&...
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Where am I going wrong in this "proof" that S1 can prove the S2 axiom?
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 ...
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how to slove Russell paradox in modal set theory?
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 ...
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Is $\vdash_{GL} \square H \Rightarrow \vdash_{GL} H$ wrong in the modal provability logic GL?
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 ...
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Prove that K5 doesn't imply K4
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 ...