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7 votes
Accepted

Multimodal logic with quantification over modal operators

In topos theory there are modal operators known as the Lawvere-Tierney operators. Such an operator is a certain endomorphism $j : \Omega \to \Omega$ on the subobject classifier. The object $J$ of all ...
Andrej Bauer's user avatar
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5 votes
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Obtaining the Axiom of Choice through a modality in HTT

There is a trivial sense in which the answer is yes. For any proposition $P$, there's a modality $O_P$ called the open modality determined by $P$, defined by $O_P(X) \equiv (P\to X)$. If you take $P$...
Mike Shulman's user avatar
5 votes

Multimodal logic with quantification over modal operators

Perhaps relevant are term-modal logics. Term-modal logics are a family of qunatified modal logics in which the subscript of the modal operators are terms of a first-order language mkaing e.g. $\...
Rasmus's user avatar
  • 233
4 votes
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Complexity of modal logic IK5

The logic is EXP-complete. One way to prove the lower bound is to note that the logic KTB augmented with universal modality, or even just the global consequence relation of KTB, is EXP-complete (Chen ...
Emil Jeřábek's user avatar
4 votes
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Proof that the theory of rationals is convex

The key idea here is that for any conjunction of equations $F\equiv u_1=v_1\wedge\ldots\wedge u_k=v_k$, the set $S_F$ is convex in the geometric sense, i.e. for any two points $p,q\in S_F$, all points ...
Klaus Draeger's user avatar
3 votes
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What does the category of RDF models look like in Institution Theory?

There's a lot to unpack here and I don't know about Goguen's institutions. But perhaps I can give a partial answer to your question. Let's start with "simple interpretations" of RDF, as defined by ...
Evan Patterson's user avatar
3 votes

Is modal $\mu$-calculus "equivalent" to bisimulation?

For Q1, the answer is yes if we consider image-finite systems: for all node $t$ and label $a$, the number of $a$-successors of $t$ must be finite. In this case you don't even need fixpoints of the $\...
Denis's user avatar
  • 8,903
2 votes

Validity of a modal argument about "vagueness"

How about just a blanket statement with no assumptions: A and B may be the same part of C This would seem to be valid by the same reasoning! However it is only so if "may" ranges over all models ...
Bjørn Kjos-Hanssen's user avatar

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