Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Sequent calculus
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
===Minor structural alternatives=== There is some freedom of choice regarding the technical details of how sequents and structural rules are formalized without changing what sequents the system derives. First of all, as mentioned above, the sequents can be viewed to consist of sets or [[multiset]]s. In this case, the rules for permuting and (when using sets) contracting formulas are unnecessary. The rule of weakening becomes [[admissible rule|admissible]] if the axiom (I) is changed to derive any sequent of the form <math>\Gamma , A \vdash A , \Delta</math>. Any weakening that appears in a derivation can then be moved to the beginning of the proof. This may be a convenient change when constructing proofs bottom-up. One may also change whether rules with more than one premise share the same context for each of those premises or split their contexts between them: For example, <math>({\lor}L)</math> may be instead formulated as :<math> \cfrac{\Gamma, A \vdash \Delta \qquad \Sigma, B \vdash \Pi}{\Gamma, \Sigma, A \lor B \vdash \Delta, \Pi}. </math> Contraction and weakening make this version of the rule interderivable with the version above, although in their absence, as in [[linear logic]], these rules define different connectives.
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)