# Questions tagged [beth-tableau]

A refutation calculus for logic setting up an analytic tree structure on the subformulas to show that the negation of a formula cannot be satisfied. Also known as "semantic tableau" or "truth tree".

12 questions
Filter by
Sorted by
Tagged with
1 vote
74 views

### Does Dan Willard demonstrate that classical logics with the Law of the Excluded Middle versus those with Double Negation Elimination are distinct?

Context: Dan Willard's 2020 review paper of his work on Self-Verifying Theories/Self-Justifying Axiom Systems (SJAS) is titled "How the Law of Excluded Middle Pertains to the Second ...
• 61
1 vote
62 views

### Can we reduce the number of occurrences of the metavariable in Peano Arithmetic's axiom schema of induction?

Is there an axiomatization of Peano arithmetic where the axiom schema contains fewer than 4 distinct occurrences of the metavariable? Ideally, as few as possible. The immediate motivation is to come ...
• 12k
1 vote
88 views

### Is it correct to judiciously construct a quantifier tableau to yield a desired falsification of a formula, yet the rules to apply weren't exhausted?

I am a beginner in logic, which I am learning on my own. I am aware of the fact that a quantifier tableau with open branches doesn’t always show the formula under consideration is falsified- unless ...
• 4,442
148 views

### Non-tableau calculi for system K

What proof calculi are there besides the method of analytic tableaux for System K? The method of analytic tableaux is tricky to typeset and takes a lot of space, especially for modal logic. I'm ...
• 12k
1 vote
538 views

### Difference between Semantic Tableaux and Natural Deduction?

I recently started to learn about logic, so far I've learnt this two ways of logical proofs. As far as I know, they are two kinds of methods. One is a proof calculus in which logical reasoning is ...
46 views

### Cut theorem for tableau?

Cut theorem is Suppose Γ |- ϕ and Γ ∪{ϕ} |- ψ.Then Γ |- ψ. For natural deduction, it's simply a corollary of deduction theorem. PROOF.Suppose we have Γ |- ϕ and Γ ∪ {ϕ} |- ψ.Then by the deduc-tion ...
110 views

### Semantic tableau with variables [closed]

Is it possible to build a tableaux of a formula like this? $P(X,Y) \land P(Y,X)$, $X$ and $Y$ are variables. To close the tableaux $X$ and $Y$ must to be unified with something isn't it? But how ...
1 vote
661 views

### Issue proving a Formula to be Valid using Semantic Tableau

I'm having issues proving that ((p ∨ q) → r) → (p → (q ∨ r)) is valid by means of a semantic tableau. I know it is valid because I was able to prove it using the ...
516 views

### How to use a Semantic Tableau to show satisfiable and falsifiable

I'm working on using semantic tableau to prove properties of formulas. I've got the hang of building them, but there's some theory I'm unsure of. I'm aware that to a formula can be proven ...