Talk:Sequent calculus
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| − | == Two-sided sequent calculus == |
+ | == Equivalences == |
| − | I think the terminology "two-sided sequent calculus" should be used for the system where all the connectives are involved and all the rules are duplicated (with respect to the one-sided version) and negation is a connective. |
+ | Equivalences might deserve a specific page (maybe merged with [[isomorphism]]s and [[equiprovability]]?). |
| − | In this way, we obtain the one-sided version from the two-sided one by: |
+ | We might imagine a page or some pages giving a collection of [[Provable formulas|valid principles]] of linear logic (with appropriate proofs) and specifying which ones correspond to implications, equivalences or isomorphisms. |
| − | * quotient the formulas by de Morgan laws and get negation only on atoms, negation is defined for compound formulas (not a connective) |
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| − | * fold all the rules by <math>\Gamma\vdash\Delta \mapsto {}\vdash\Gamma\orth,\Delta</math> |
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| − | * remove useless rules (negation rules become identities, almost all the rules appear twice) |
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| − | A possible name for the two-sided system presented here could be "two-sided positive sequent calculus". |
+ | -- [[User:Olivier Laurent|Olivier Laurent]] 10:39, 15 March 2009 (UTC) |
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| − | -- [[User:Olivier Laurent|Olivier Laurent]] 21:34, 15 January 2009 (UTC) |
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Latest revision as of 21:01, 25 April 2013
[edit] Equivalences
Equivalences might deserve a specific page (maybe merged with isomorphisms and equiprovability?).
We might imagine a page or some pages giving a collection of valid principles of linear logic (with appropriate proofs) and specifying which ones correspond to implications, equivalences or isomorphisms.
-- Olivier Laurent 10:39, 15 March 2009 (UTC)
