The modal-logic tag has no wiki summary.
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How should I prove $\Box (\Box p \rightarrow q) \vee \Box (\Box q \rightarrow \Box p)$ using KT45.
How am I supposed to prove the same using natural deduction? I started my proof with a LEM
$$\Box (\Box p \rightarrow \Box q) \vee \neg \Box (\Box p \rightarrow \Box q)$$
I split the LEM via $\vee$ ...
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1answer
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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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The Logic of Satisfiability?
I am aware of some study into the logic of provability. It is generally taken to be intermediate in strength between S4 and S5 modal logics. Is there corresponding study into something like the logic ...
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Prove that $\Diamond\Box p \rightarrow \Diamond (\Box (p\land q) \lor \Box(p\land\neg q))$ does not define a first-order condition on frames
First of all, the modal logic we are working with in this case is the basic one: that is, all propositional formulas, plus formulas of the form $\Diamond\phi$, where $\phi$ is any modal formula (we ...
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Modal theorems valid in a set theory model
This is the question i would like to discuss, properly stated.
Given a model $M$ for a collection of set theory axioms (ZFC, for example), list all basic modal formulas $\phi$ such that $M\Vdash ...
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1answer
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Modal Logic Questions Validity
These are some examples in modal logic, I am not too sure why the first two are valid and why the last one specifically is not valid. Hope someone can explain!
$\square(P \rightarrow P)$ (VALID)
...
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1answer
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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)
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5answers
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Why modal logic needs modalities
Why does modal logic need modalities like provability or others like necessity and possibility? Could they be replaced with equivalent predicates?
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Why isn't GL system of provability logic reflexive?
Formula $\square p \rightarrow p$ (axiom T; corresponding to reflexive modal frames) is interpreted as "if p is provable, then p", or more precisely: for all realizations (all substitutions for $p$), ...
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1answer
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Is it possible to prove that the Grz axiom is valid in a modal frame iff the frame is reflexive and transitive?
We need to prove (or disprove?) that $ \square (\square (A \rightarrow \square A) \rightarrow A) \rightarrow A $ is valid in the Kripke modal frame $ F = <S, R> $ iff R is transitive and ...
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1answer
194 views
Need help understanding a proof in Boolos's “The Logic of Provability”
I'm currently reading The Logic of Provability by George Boolos and there's a step in a proof that I don't understand.
The author has defined a system of modal logic called GL; its language has a ...
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2answers
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In modal logic, is $\lnot\square P\equiv\lozenge\lnot P$?
"Possibly" and "necessarily" seem very much like "exists" and "for-all", but does the following hold true: $\neg \square P \equiv \lozenge \neg P$ in the same way as $\neg\forall P \equiv \exists\neg ...
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1answer
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Modal logic as a quotient Boolean-valued logic
I never really studied modal logic, but to my better understanding this is similar to classical logic adding two modal operations:
$\square P\ $ meaning necessarily $P$,
$\lozenge P\ $ meaning ...
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1answer
110 views
Translation of nabla modality with box and diamond modalities
I got an exercise from my teacher to translate formulas of modal logic with modal operator $\nabla$ into formulas with operators $\Box$ and $\Diamond$.
If the set of possible worlds is $X$, the ...
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Can you express a logic system like S5 using only a Gödel number?
Since logic systems are just statements and/or axioms, can we formulate a logic system gödel numbering the system itself so that the system becomes nothing but a gödel number? For instance the modal ...
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1answer
171 views
Nash equilibrium and common knowledge
If NE is a CK? It seems that yes since given all information about payoffs/strategies players can derive NE based on the procedures similar to that of in the common knowledge, but I'm not sure.
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Common knowledge as a fixed point
I read on a wikipedia page that from the modal logic formalization CK can be formulated as a fixed point. If it also holds for the set theory formalization? If it does, where I can find about it?
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