Questions tagged [modal-logic]
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115 questions
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What good naming alternatives are there for the schemas?
What to call schema $\forall xT\llcorner A\lrcorner\to T\llcorner\forall x A\lrcorner$ when one doesn't want "Barcan Formula"?
And what is a good name for the schema $T\llcorner\exists x A\...
- 4,178
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Pure buttons in the modal logic of forcing
I've been trying to understand what it means for a button to be pure in the context of the modal logic of forcing, and it would help to have an example of a button which is not a pure button. Based on ...
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Do independent collections of infinitely many buttons and infinitely many switches exist in models other than V=L?
The original paper by Hamkins and Löwe that the modal logic of forcing is exactly S4.2 uses the fact that there is consistently a model with an independent collection of infinitely many buttons and ...
- 345
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Correspondence for distribution?
Take the distribution axiom, DA, of a modal logic to be:
$\Box(A\to B)\to (\Box A \to \Box B).$
As there are distribution-free modal logics which do not have DA:
What does DA correspond to in frames ...
- 4,178
4
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Software for testing validity of propositional formulas in finite Kripke frames (modal SAT)
I have
a formula $\varphi$ of propositional modal logic or propositional intuitionistic logic,
a finite Kripke frame $W$,
and I would like to test whether $\varphi$ is valid in $W$.
This is an ...
- 40.2k
3
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1
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What corresponds to the necessitation rule in modal logics
In modal logics, the necessitation rule licences the inference from $\vdash p$ to $\vdash \Box p.$ Given a modal logic $\mathcal{L}$ with characteristic axioms in the set $\Sigma$, does the ...
- 4,178
3
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Proving a proposition about the provability logic GL without using its completeness theorem
Let $GL$ be the provability logic containing the axioms $K := \Box (\varphi\to \psi)\to (\Box \varphi\to \Box \psi)$ and $L := \Box(\Box \varphi \to \varphi)\to \Box \varphi$, along with the ...
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Christoph Benzmüller and Gödel's ontological proof?
Are there any notable mathematical or logical issues within Christoph Benzmüller and Bruno Woltzenlogel-Paleo formalized Gödel's ontological proof (pdf) that has been identified by the community?
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Is the class of strongly Kripke complete normal modal logics closed under sums?
Given an arbitrary set of normal modal logics $\mathcal{L}$, one can define their sum $\bigoplus \mathcal{L}$ (or $\bigoplus_{L \in \mathcal{L}} L$ if you prefer) to be the least normal modal logic ...
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Why is it not possible to define the necessity operator internally $\Box: \Omega \to \Omega$ in a topos?
I am looking for ways to internalize the modal operator of necessity $\Box$, ending up with a morphism $\Box: \Omega \to \Omega$ satisfying the necessitation rule (if $\phi$, then $\Box \phi$) and the ...
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Are there atoms in the lattice of intermediate logics?
A few days ago I stumbled upon this question on MS. The question is: Does the lattice of intermediate logics have an atom, i.e. an element that is strictly stronger than IPC but not strictly stronger ...
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2
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1
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203
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Kripke frame, lattice and some intermediate logics
For a given finite and rooted intuitionistic Kripke frame $\mathcal{F}$, let $\log(\mathcal{F})=\{\phi : \mathcal{F}\vDash \phi\}$ and assume $S=\{\log(\mathcal{F}): \mathcal{F} \text{ is finite and ...
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Do coproducts injections of Heyting algebras have left and right adjoints?
Given two Heyting algebras $A$ and $B$, let $A+B$ be their coproduct in the category of Heyting algebras. Is it true that the inclusion $A → A+B$ always has a left and a right adjoint ? (Actually, I ...
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two different intermediate logics whose intersection is Int
Call a partial order $\mathcal{F}=(F, \leq)$ rooted if there is an element $a \in F$ such that for any $b \in F$, $a\leq b$.
Let $\mathcal{F}_0$ and $\mathcal{F}_1$ be two different finite rooted ...
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Reference request for a modification of Bi-Intuitionistic Logic
I’ve asked this same question on math.stackexchange.com, but haven’t received any answers. I ask this question in good faith, so I hope it meets this site’s standards.
I have been spending the better ...
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