For a given logical system such as MLL (for multiplicative linear logic), we consider the following variations:
|MLL||propositional without units|
|MLLu||propositional with units only|
|MLL0||propositional with units and variables|
|MLL1||first-order without units|
|MLL01||first-order with units|
|MLL2||second-order propositional without units|
|MLL02||second-order propositional with units|
|MLL12||first-order and second-order without units|
|MLL012||first-order and second-order with units|
Formulas and proof trees
- First order quantification: with substitution A[t / x]
- Second order quantification: with substitution A[B / X]
- Quantification of arbitrary order (mainly first or second): with substitution A[τ / ξ]
Name of the connective, followed by some additional information if required, followed by "L" for a left rule or "R" for a right rule. This is for a two-sided system, "R" is implicit for one-sided systems. For example: .
- Web of the space X:
- Coherence relation of the space X: large and strict
- Web of the finiteness space :
- Finiteness structure of the space : (we use \mathfrak, which is consistent with the fact that ).
- The free ports of a net R: fp(R).
- The result of the connection of two nets R and R', given the partial bijection : .
- The number of loops in the resulting net: (includes the loops already present in R and R').
- partial injection: