Notations
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=== Coherent spaces === |
=== Coherent spaces === |
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* Web of the space <math>X</math>: <math>\web X</math> |
* Web of the space <math>X</math>: <math>\web X</math> |
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| − | * Coherence relation of the space <math>X</math>: <math>\coh_X</math> |
+ | * Coherence relation of the space <math>X</math>: large <math>\coh_X</math> and strict <math>\scoh_X</math> |
Revision as of 16:44, 7 February 2009
Contents |
Logical systems
For a given logical system such as MLL (for multiplicative linear logic), we consider the following variations:
| Notation | Meaning | Connectives |
|---|---|---|
| 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
Formulas
- 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]
Rule names
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: 
.
Semantics
Coherent spaces
- Web of the space X:
- Coherence relation of the space X: large
and strict 
