Reference: the rules
Here are links to all the rules of inference for the deductive systems presented in these notes. The quantifier rules for restricted quantifiers and free logic are bundled with those for the "standard" unrestricted ones, but the sequent calculus rules are presented separately, as they are all different from the coresponding natural deduction rules.
The non-classical logics requiring a distinction between two modes of premise combination, symbolised by the comma and semicolon, are presented together, since the difference between them is just a matter of varying the structural rules governing the semicolon. Intuitionist logic is not detailed separately from classical logic; instead, the adjustments necessary to secure it are noted along with the standard rules.
- Standard calculus Classical natural deduction and variants
- Sequent calculus Left and right rules for general sequents
- Substructural logics Rules of the non-classical deductive systems