# Questions tagged [modal-logic]

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

575 questions
Filter by
Sorted by
Tagged with
28 views

### How to prove this sequent system is sound and complete for S4 Modal Logic?

Take LK sequent calculus without cut, but change the $\to R$ rule to the following: $\cfrac{\Gamma’, A \vdash B}{\Gamma \vdash A \to B, \Delta}$ where $\Gamma’=\{C \in \Gamma|C=(D \to E)\}$ for well-...
• 1,413
104 views

### Why Does This Proof Hold?

I'm currently reading "Mathematics Without Numbers" by Hellman, G., and I'm on pages 26-27. It seems like Hellman is discussing opposition to viewing mathematical proofs solely through the ...
• 33
56 views

• 538
1 vote
67 views

### What do algebraic semantics look like for intuitionistic modal logic?

I know that a topological pseudo-Boolean algebra is an algebra ⟨L, I, ¬, ∧, ∨, →⟩ such that ⟨L, ¬, ∧, ∨, →⟩ is an algebra and I an interior unary monotone operator on L, where the operator is defined ...
• 11
42 views

### Distribution law in infinitary modal logic

This post is related to a question I originally asked on Philosophy Stack Exchange https://philosophy.stackexchange.com/questions/100055/infinitary-modal-logic In the modal logic (say, ${\bf K}$) the ...
• 584
110 views

### Constructing a Kripke model where $p \rightarrow \Box \Diamond q$ is false.

I have constructed the following Kripke model for this problem: My idea is the following: Implication is false iff we have $\top \implies \bot$. For world $0$, we have that $p$ is true. Now we need ...
• 623
1 vote
### Proving $\Box(p \land q) \rightarrow (\Box p \land \Box q)$ in modal system $K$
I need to prove $\Box(p \land q) \rightarrow (\Box p \land \Box q)$. Currently, I know of a proof that utilizes the tautology $(p \land q) \rightarrow p$ as a first premise, from which we use the ...