Editing Linear logic (section)

===Multiplicatives===

The rules for multiplicative conjunction (⊗) and disjunction (⅋):

{| style="margin:auto"
|-
| style="text-align: center;" |
{| border="0"
|-
| {{math|{{tee}} Γ, <VAR>A</VAR>}} || &nbsp;&nbsp; || &nbsp;&nbsp; || {{math|{{tee}} Δ, <VAR>B</VAR>}}
|-
| colspan=4 style="border-top:2px solid black;" |
|-
| colspan=4 align="center" | {{math|{{tee}} Γ, Δ, <VAR>A</VAR> ⊗ <VAR>B</VAR>}}
|}
| width="50" |
| style="text-align: center;" |
{| border="0"
|-
| {{math|{{tee}} Γ, <VAR>A</VAR>, <VAR>B</VAR>}}
|-
| style="border-top:2px solid black;" |
|-
| {{math|{{tee}} Γ, <VAR>A</VAR> ⅋ <VAR>B</VAR>}}
|}
|}

and for their units:

{| style="margin:auto"
|-
| style="text-align: center;" |
{| border="0"
|-
| &nbsp;
|-
| colspan=4 style="border-top:2px solid black;" |
|-
| colspan=4 align="center" | {{math|{{tee}} 1}}
|}
| width="50" |
| style="text-align: center;" |
{| border="0"
|-
| {{math|{{tee}} Γ}}
|-
| style="border-top:2px solid black;" |
|-
| {{math|{{tee}} Γ, ⊥}}
|}
|}

Observe that the rules for multiplicative conjunction and disjunction are [[Admissible rule|admissible]] for plain ''conjunction'' and ''disjunction'' under a classical interpretation
(i.e., they are admissible rules in [[Sequent calculus#The system LK|LK]]).