All Questions
Tagged with symbolic-logic modal-logic
21
questions
3
votes
1
answer
155
views
Modal system K - prove ⊢ (□p ∨ □q) → □(p ∨ q)
I am trying to prove the following:
⊢ (□p ∨ □q) → □(p ∨ q)
However, I think that I am lacking the knowledge of a tautology in classical logic that would help me prove this.
I tried something, but it ...
- 133
0
votes
2
answers
112
views
Axiomatically prove □(A ∨ ¬B), ¬□A, ⊢ ◇¬B in modal system K
This time I have a more "complex" problem at first glance. I need to create a direct proof using the axioms of system K and rules of inference, but I have been unable to do so.
□(A ∨ ¬B), ¬□...
- 133
3
votes
2
answers
333
views
Proof of □P ⊢ □¬¬P in modal logic system K
I need to prove the aforementioned formula in modal logic system K, which I am having trouble to do.
Of course, this should be easy to prove if I had access to axiom T, but since it's system K, we can ...
- 133
1
vote
0
answers
40
views
Zero-one laws Model Logic, question regarding significance of domain size
Wikipedia informs me that:
Essentially (correct me if I'm wrong) the result states that as the domain of objects (domain of discourse) grows (n->inf), a static first order sentence (S) will be ...
- 79
1
vote
3
answers
205
views
How to prove, in modal logic, that □A→A is valid (T axiom) iff R is reflexive?
How to prove, in modal logic, that □A→A is valid (T axiom) iff R is reflexive? I'm not sure how to prove axiom in reverse?
0
votes
0
answers
308
views
Proving validity/invalidity of a modal argument
□(A v B) → (□A v □B) ...(1)
This symbolic argument is intuitively invalid. In (1), if we replace B with ~A, then we see that though the antecedent is necessary, the consequent is a contradiction since ...
0
votes
5
answers
184
views
Can you give me some concrete example, so that I could understand these modal logic sentences
So there is these simple modal logic sentences:
□(a → b) and a → □b
Can anyone help me with some real-life examples, because I have troubles grasping the difference?
edit
The simpler question is this: ...
- 285
2
votes
0
answers
86
views
What is 'expendable' in logic and how to explain 'tautology' given this image?
This image is from http://www.nfillion.com/index.php/teaching/9-logic-112. According to this, a proposition can have 4 basic properties: (1) necessarily, (2) not possibly, (3) missing, and (4) ...
1
vote
0
answers
55
views
Is there a non-transitive frame in which schema 4 is true? Or an irreflexive frame in which schema T is true?
So, I know that I can construct a frame {W, R, I} which is not transitive and in which schema 4 is not true (more specifically, Axiom Schema K and Axiom Schema 4 are not both true). I also know that I ...
4
votes
1
answer
195
views
Are there famous unsolved problems in logic akin to the Millenium Prize problems?
Are there major theorems that logicians have yet to tackle? And I don't mean any problems that pertain to the philosophy of logic (i.e. logical pluralism, the nature of logical consequence, etc), but ...
- 41
0
votes
0
answers
67
views
Alphabetic Substitution, Barcan, and Strict Implication
Context: I'm stuck on Axiom 8 from the introduction to Barcan 1946, "A Functional Calculus of First Order Based on Strict Implication." My instinct is that I'm missing a basic, perhaps obvious concept-...
- 27
1
vote
1
answer
71
views
In Quine's ontology, why does a 'recognition' of something lead to ontological commitment while a 'feeling' does not?
We are discussing Quine's On What There Is in a metaphysics class I am in. I felt like I understood what he meant, that if something has to be predicated for in a sentence, we are ontologically ...
- 49
-1
votes
3
answers
81
views
A question about possibility
If A, then B
~ A
So, possible that B
Valid or not?
My take: Not valid.
Reason:
Valid means if all the premises are true, the conclusion must be true
That means adding new information should not ...
2
votes
1
answer
58
views
Prove the rule that proves X(P) from X(a) preserves derivability in modal system K
I'm trying to solve a problem which asks me to show that the meta-rule defined by deriving X(P) from X(a) preserves derivability (i.e. if ⊢X(a) then ⊢X(P) in modal system K, where a is a sentence ...
- 21
3
votes
1
answer
587
views
S5 proof of ⊢◻(◻P→◻Q)∨◻(◻Q→◻P)
I'm trying to construct an S5 proof of ⊢◻(◻P→◻Q)∨◻(◻Q→◻P).
I know that ϕ∨ψ is equivalent to ~ϕ→ψ, and so what I'm really trying to derive is ~◻(◻P→◻Q)→◻(◻Q→◻P) (which is equivalent to ◊~(◻P→◻Q)→◻(◻Q→◻...
- 31