# Questions tagged [modal-logic]

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

549 questions
Filter by
Sorted by
Tagged with
20 views

### show that every S5-satisfiable formula is satisfiable in a universal Kripke frame, i.e. in a frame of the form (X, R) where R = X × X.

Inductive Proof of S5 Model ChatGPT 4 User ueb3.pdf PDF Can you please solve exercise 4 using structural induction? ChatGPT Exercise 4 from your document asks to show that every S5-satisfiable formula ...
16 views

34 views

65 views

If $\Gamma$ is a maximal K-consistent set of formulas, where K is the minimal modal logic, is $\Gamma$ closed under the necessitation rule? That is, if $\phi\in\Gamma$, do I necessarily have $\Box\phi\... 0 votes 0 answers 43 views ### Do all modal formulae classify digraphs? I know that some modal formulae do classify digraphs. For example,$\Box \phi \rightarrow \Diamond \phi$classifies all serial digraphs, i.e. digraphs such that for all vertices$v_i,$there exists ... 2 votes 2 answers 117 views ### How do I solve exercise 2.2.4 Blackburn/de Rijke/Venema’s “Modal Logic” Here’s a transcript of the original exercise. (There‘s even a hint given by the authors in the textbook as you can see. But precisely this hint confuses me). 2.2.4 Consider the binary until operator$... 1 vote
66 views

### Proof in KTB (modal logic) using KTB and propositional logic [closed]

I am trying to prove that $\neg \lozenge p$ from $\square (p \rightarrow q)$ and $\lozenge \square \neg q$ using only the axioms in KTB and propositional logic. I can prove using tableux, but not ...
1 vote
### In Modal Logic, if something is true, is it necessarily true? $P\implies\square P$ [duplicate]
I'm new to modal logic and I am trying to understand it more intuitively. If something is true, is it necessarilly true? I.e. $$P\implies\square P$$ This seems intuitive but it is not an axiom. This ...
$□p$, $□q$ therefore, $□(p→q)$ according to the K system of modal logic, the argument is invalid. I tried proving it using a truth tree, but all the branches unfortunately close, I don't know how to ...