Question

Adding $\tfrac{}{\Gamma \varphi}$ (for a fixed non-correct $\Gamma \varphi$) to the rules of the sequent calculus, can one now derive every sequent?

score 99 · Answer 1 · 2023-03-15 12:56:01

99

Views

Adding $\tfrac{}{\Gamma \varphi}$ (for a fixed non-correct $\Gamma \varphi$) to the rules of the sequent calculus, can one now derive every sequent?

Published on 15 Mar 2023 - 12:56

score 63 · Answer 2 · 2026-02-23 06:42:05

63

Views

Proof in Natural Deduction, Sequent Calculus or Hilbert System

Published on 23 Feb 2026 - 6:42

score 92 · Answer 3 · 2023-03-17 07:08:40

92

Views

Is there a G4ip equivalent for first-order logic?

Published on 17 Mar 2023 - 7:08

score 59 · Answer 4 · 2023-03-25 20:07:37

59

Views

Reflection principle for finite subsystems of PA.

Published on 25 Mar 2023 - 20:07

score 66 · Answer 5 · 2023-03-26 20:21:57

66

Views

Establishing $\Gamma, A: Type \vdash (A)Type\ \textbf{kind}$ in LF

Published on 26 Mar 2023 - 20:21

score 33 · Answer 6 · 2023-04-20 21:11:10

33

Views

Equivalence of Martin-Löf sequent calculus and standard sequent calculus with material implications

Published on 20 Apr 2023 - 21:11

score 39 · Answer 7 · 2023-05-22 17:00:04

39

Views

Sequents in which succedents are restricted to one formula

Published on 22 May 2023 - 17:00

score 85 · Answer 8 · 2023-06-08 21:23:14

85

Views

Is there some variant of sequent calculus that allows for non-trivial axioms?

Published on 08 Jun 2023 - 21:23

score 95 · Answer 9 · 2023-07-13 10:11:47

95

Views

Exchange case in proving interpolation theorem by induction on the length of proof tree

Published on 13 Jul 2023 - 10:11

score 43 · Answer 10 · 2024-01-23 06:48:49

43

Views

What is the correct way to interpret the Intuitionistic rules of Kleene's sequent (Gentzen) system G1 (in sec. 77 of Kleene I.M. 1952)

Published on 23 Jan 2024 - 6:48

score 125 · Answer 11 · 2024-02-06 14:07:07

125

Views

What is the metatheory required for proving the cut-elimination theorem for classical logic? Is the proof circular?

Published on 06 Feb 2024 - 14:07

score 38 · Answer 12 · 2024-02-08 08:17:27

38

Views

Understanding quantifier rules in sequent calculus

Published on 08 Feb 2024 - 8:17

score 170 · Answer 13 · 2024-02-09 11:51:32

170

Views

Proving $\exists x[P(x)] \to \exists y[\exists x[P(x)]\to P(y)]$ in for intuitionistic $\varepsilon$-calculus.

Published on 09 Feb 2024 - 11:51

score 59 · Answer 14 · 2024-02-12 07:27:13

59

Views

Making sense of eigenvariable restriction in $\exists L$ rule in sequent calculus

Published on 12 Feb 2024 - 7:27

score 72 · Answer 15 · 2024-02-13 01:43:49

72

Views

Showing if $A[y/x]\models\Delta$ then $\exists x A(x)\models\Delta$

Published on 13 Feb 2024 - 1:43

List Question

Adding $\tfrac{}{\Gamma \varphi}$ (for a fixed non-correct $\Gamma \varphi$) to the rules of the sequent calculus, can one now derive every sequent?

Proof in Natural Deduction, Sequent Calculus or Hilbert System

Is there a G4ip equivalent for first-order logic?

Reflection principle for finite subsystems of PA.

Establishing $\Gamma, A: Type \vdash (A)Type\ \textbf{kind}$ in LF

Equivalence of Martin-Löf sequent calculus and standard sequent calculus with material implications

Sequents in which succedents are restricted to one formula

Is there some variant of sequent calculus that allows for non-trivial axioms?

Exchange case in proving interpolation theorem by induction on the length of proof tree

What is the correct way to interpret the Intuitionistic rules of Kleene's sequent (Gentzen) system G1 (in sec. 77 of Kleene I.M. 1952)

What is the metatheory required for proving the cut-elimination theorem for classical logic? Is the proof circular?

Understanding quantifier rules in sequent calculus

Proving $\exists x[P(x)] \to \exists y[\exists x[P(x)]\to P(y)]$ in for intuitionistic $\varepsilon$-calculus.

Making sense of eigenvariable restriction in $\exists L$ rule in sequent calculus

Showing if $A[y/x]\models\Delta$ then $\exists x A(x)\models\Delta$

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