Question

Does $\Gamma \vDash \alpha \iff \Gamma \vDash \beta$ implies $\alpha \iff \beta$?

score 88 · Answer 1 · 2023-05-27 03:04:28

88

Views

Does $\Gamma \vDash \alpha \iff \Gamma \vDash \beta$ implies $\alpha \iff \beta$?

Published on 27 May 2023 - 3:04

score 75 · Answer 2 · 2023-05-28 01:43:42

75

Views

Can a contradiction prove a contradiction like this?

Published on 28 May 2023 - 1:43

score 116 · Answer 3 · 2026-03-26 02:44:45

116

Views

Satisfiability in an Heyting algebra implies satisfiability in a Boolean algebra for propositional logic?

Published on 26 Mar 2026 - 2:44

score 85 · Answer 4 · 2026-04-11 21:07:48

85

Views

How is the logical connective $\bot$ used in formulae

Published on 11 Apr 2026 - 21:07

score 191 · Answer 5 · 2026-04-11 12:51:00

191

Views

Is "$(\exists z)$ the sky is blue" a proposition?

Published on 11 Apr 2026 - 12:51

score 24 · Answer 6 · 2026-04-12 01:53:38

24

Views

How does functional completeness relate to expressiveness in higher-order logics?

Published on 12 Apr 2026 - 1:53

score 75 · Answer 7 · 2023-06-02 12:13:52

75

Views

If you can prove $\bot$, why are you allowed to conclude anything?

Published on 02 Jun 2023 - 12:13

score 61 · Answer 8 · 2026-04-09 10:17:15

61

Views

How to formalize "if and only" in propositional logic

Published on 09 Apr 2026 - 10:17

score 115 · Answer 9 · 2023-06-04 22:32:53

115

Views

In propositional logic, is F ⊨ ¬G the same as F ⊭ G?

Published on 04 Jun 2023 - 22:32

score 370 · Answer 10 · 2023-06-05 01:05:03

370

Views

In a direct proof, do your chain of deductions have to involve the antecedent in any way in order for this to be considered a "direct proof"?

Published on 05 Jun 2023 - 1:05

score 51 · Answer 11 · 2026-04-09 03:57:28

51

Views

Does this proof of the compactness theorem assumes countable atomic formulas?

Published on 09 Apr 2026 - 3:57

score 154 · Answer 12 · 2026-04-09 10:13:30

154

Views

What is the relationship between ultrafilters and propositional theories?

Published on 09 Apr 2026 - 10:13

score 30 · Answer 13 · 2023-06-06 15:05:49

30

Views

Need help with using fitch system for this proof: Given ¬q, (¬p⇒(¬q⇒¬r)), (s∨r), (s⇒t), and (p⇒t), prove t.

Published on 06 Jun 2023 - 15:05

score 86 · Answer 14 · 2023-06-13 16:45:13

86

Views

Completeness theorem in case of nonlogical axioms

Published on 13 Jun 2023 - 16:45

score 90 · Answer 15 · 2026-04-09 14:04:40

90

Views

How to understand Tarski's definition of negation

Published on 09 Apr 2026 - 14:04

List Question

Does $\Gamma \vDash \alpha \iff \Gamma \vDash \beta$ implies $\alpha \iff \beta$?

Can a contradiction prove a contradiction like this?

Satisfiability in an Heyting algebra implies satisfiability in a Boolean algebra for propositional logic?

How is the logical connective $\bot$ used in formulae

Is "$(\exists z)$ the sky is blue" a proposition?

How does functional completeness relate to expressiveness in higher-order logics?

If you can prove $\bot$, why are you allowed to conclude anything?

How to formalize "if and only" in propositional logic

In propositional logic, is F ⊨ ¬G the same as F ⊭ G?

In a direct proof, do your chain of deductions have to involve the antecedent in any way in order for this to be considered a "direct proof"?

Does this proof of the compactness theorem assumes countable atomic formulas?

What is the relationship between ultrafilters and propositional theories?

Need help with using fitch system for this proof: Given ¬q, (¬p⇒(¬q⇒¬r)), (s∨r), (s⇒t), and (p⇒t), prove t.

Completeness theorem in case of nonlogical axioms

How to understand Tarski's definition of negation

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