Sequent calculus for propositional logic
1
I think the propositional calculus must have a translation into the language of Gentzen's sequent calculus. I suppose, to obtain Gentzen's version of this we should just remove from LK the rules with the quantifiers, but, perhaps, we should also remove something more, maybe the cut rule... Can anybody clarify this to me and give a reference?
logic propositional-calculus sequent-calculus
edited Dec 3 '18 at 7:57
SnowOnion
52
asked Jun 17 '17 at 15:57
Sergei Akbarov
837516
|
show 12 more comments
1
I think the propositional calculus must have a translation into the language of Gentzen's sequent calculus. I suppose, to obtain Gentzen's version of this we should just remove from LK the rules with the quantifiers, but, perhaps, we should also remove something more, maybe the cut rule... Can anybody clarify this to me and give a reference?
logic propositional-calculus sequent-calculus
edited Dec 3 '18 at 7:57
SnowOnion
52
asked Jun 17 '17 at 15:57
Sergei Akbarov
837516
I mean, remove quantors and everything connected to them (in the language and everywhere).
– Sergei Akbarov
Jun 17 '17 at 16:15
@amWhy I don't know what will be the analogs of theories in this situation. There will be no quantifiers, but perhaps the construction will not be absolutely senseless... That is my question.
– Sergei Akbarov
Jun 17 '17 at 16:24
1
I asked because I am sure that this is well-known and elementary.
– Sergei Akbarov
Jun 17 '17 at 16:27
We are not a "do all the work necessary to test my conjecture for me" site. We will confirm, validate a particular (of reasonable length) proof, or point out flaws...etc.
– amWhy
Jun 17 '17 at 16:27
1
You can see Gentzen's original papers, but also some well-know textbooks: G.Takeuti, Proof Theory and Sara Negri &Jan von Plato, Structural Proof Theory.
– Mauro ALLEGRANZA
Jun 17 '17 at 16:51
|
show 12 more comments
1
1
1
I think the propositional calculus must have a translation into the language of Gentzen's sequent calculus. I suppose, to obtain Gentzen's version of this we should just remove from LK the rules with the quantifiers, but, perhaps, we should also remove something more, maybe the cut rule... Can anybody clarify this to me and give a reference?
logic propositional-calculus sequent-calculus
edited Dec 3 '18 at 7:57
SnowOnion
52
asked Jun 17 '17 at 15:57
Sergei Akbarov
837516
I think the propositional calculus must have a translation into the language of Gentzen's sequent calculus. I suppose, to obtain Gentzen's version of this we should just remove from LK the rules with the quantifiers, but, perhaps, we should also remove something more, maybe the cut rule... Can anybody clarify this to me and give a reference?
logic propositional-calculus sequent-calculus
logic propositional-calculus sequent-calculus
edited Dec 3 '18 at 7:57
SnowOnion
52
asked Jun 17 '17 at 15:57
Sergei Akbarov
837516
edited Dec 3 '18 at 7:57
SnowOnion
52
asked Jun 17 '17 at 15:57
Sergei Akbarov
837516
edited Dec 3 '18 at 7:57
SnowOnion
52
edited Dec 3 '18 at 7:57
SnowOnion
52
edited Dec 3 '18 at 7:57
SnowOnion
52
52
asked Jun 17 '17 at 15:57
Sergei Akbarov
837516
asked Jun 17 '17 at 15:57
Sergei Akbarov
837516
asked Jun 17 '17 at 15:57
Sergei Akbarov
837516
837516
I mean, remove quantors and everything connected to them (in the language and everywhere).
– Sergei Akbarov
Jun 17 '17 at 16:15
@amWhy I don't know what will be the analogs of theories in this situation. There will be no quantifiers, but perhaps the construction will not be absolutely senseless... That is my question.
– Sergei Akbarov
Jun 17 '17 at 16:24
1
I asked because I am sure that this is well-known and elementary.
– Sergei Akbarov
Jun 17 '17 at 16:27
We are not a "do all the work necessary to test my conjecture for me" site. We will confirm, validate a particular (of reasonable length) proof, or point out flaws...etc.
– amWhy
Jun 17 '17 at 16:27
1
You can see Gentzen's original papers, but also some well-know textbooks: G.Takeuti, Proof Theory and Sara Negri &Jan von Plato, Structural Proof Theory.
– Mauro ALLEGRANZA
Jun 17 '17 at 16:51
|
show 12 more comments
I mean, remove quantors and everything connected to them (in the language and everywhere).
– Sergei Akbarov
Jun 17 '17 at 16:15
@amWhy I don't know what will be the analogs of theories in this situation. There will be no quantifiers, but perhaps the construction will not be absolutely senseless... That is my question.
– Sergei Akbarov
Jun 17 '17 at 16:24
1
I asked because I am sure that this is well-known and elementary.
– Sergei Akbarov
Jun 17 '17 at 16:27
We are not a "do all the work necessary to test my conjecture for me" site. We will confirm, validate a particular (of reasonable length) proof, or point out flaws...etc.
– amWhy
Jun 17 '17 at 16:27
1
You can see Gentzen's original papers, but also some well-know textbooks: G.Takeuti, Proof Theory and Sara Negri &Jan von Plato, Structural Proof Theory.
– Mauro ALLEGRANZA
Jun 17 '17 at 16:51
I mean, remove quantors and everything connected to them (in the language and everywhere).
– Sergei Akbarov
Jun 17 '17 at 16:15
I mean, remove quantors and everything connected to them (in the language and everywhere).
– Sergei Akbarov
Jun 17 '17 at 16:15
@amWhy I don't know what will be the analogs of theories in this situation. There will be no quantifiers, but perhaps the construction will not be absolutely senseless... That is my question.
– Sergei Akbarov
Jun 17 '17 at 16:24
@amWhy I don't know what will be the analogs of theories in this situation. There will be no quantifiers, but perhaps the construction will not be absolutely senseless... That is my question.
– Sergei Akbarov
Jun 17 '17 at 16:24
1
1
I asked because I am sure that this is well-known and elementary.
– Sergei Akbarov
Jun 17 '17 at 16:27
I asked because I am sure that this is well-known and elementary.
– Sergei Akbarov
Jun 17 '17 at 16:27
We are not a "do all the work necessary to test my conjecture for me" site. We will confirm, validate a particular (of reasonable length) proof, or point out flaws...etc.
– amWhy
Jun 17 '17 at 16:27
We are not a "do all the work necessary to test my conjecture for me" site. We will confirm, validate a particular (of reasonable length) proof, or point out flaws...etc.
– amWhy
Jun 17 '17 at 16:27
1
1
You can see Gentzen's original papers, but also some well-know textbooks: G.Takeuti, Proof Theory and Sara Negri &Jan von Plato, Structural Proof Theory.
– Mauro ALLEGRANZA
Jun 17 '17 at 16:51
You can see Gentzen's original papers, but also some well-know textbooks: G.Takeuti, Proof Theory and Sara Negri &Jan von Plato, Structural Proof Theory.
– Mauro ALLEGRANZA
Jun 17 '17 at 16:51
|
show 12 more comments
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I mean, remove quantors and everything connected to them (in the language and everywhere).
– Sergei Akbarov
Jun 17 '17 at 16:15
@amWhy I don't know what will be the analogs of theories in this situation. There will be no quantifiers, but perhaps the construction will not be absolutely senseless... That is my question.
– Sergei Akbarov
Jun 17 '17 at 16:24
1
I asked because I am sure that this is well-known and elementary.
– Sergei Akbarov
Jun 17 '17 at 16:27
We are not a "do all the work necessary to test my conjecture for me" site. We will confirm, validate a particular (of reasonable length) proof, or point out flaws...etc.
– amWhy
Jun 17 '17 at 16:27
1
You can see Gentzen's original papers, but also some well-know textbooks: G.Takeuti, Proof Theory and Sara Negri &Jan von Plato, Structural Proof Theory.
– Mauro ALLEGRANZA
Jun 17 '17 at 16:51