Notations

Revision as of 14:23, 29 December 2008

Logical systems

For a given logical system such as $M L L$ (for multiplicative linear logic), we consider the following variations:

Notation	Meaning	Connectives
$M L L$	propositional without units	$X,{\tens},{\parr}$
$M L L u$	propositional with units only	$\one,\bot,{\tens},{\parr}$
$M L L 0$	propositional with units and variables	$X,\one,\bot,{\tens},{\parr}$
$M L L 1$	first-order without units	$X\vec{t},{\tens},{\parr},\forall x A,\exists x A$
$M L L 01$	first-order with units	$X\vec{t},\one,\bot,{\tens},{\parr},\forall x A,\exists x A$
$M L L 2$	second-order propositional without units	$X,{\tens},{\parr},\forall X A,\exists X A$
$M L L 02$	second-order propositional with units	$X,\one,\bot,{\tens},{\parr},\forall X A,\exists X A$
$M L L 12$	first-order and second-order without units	$X\vec{t},{\tens},{\parr},\forall x A,\exists x A,\forall X A,\exists X A$
$M L L 012$	first-order and second-order with units	$X\vec{t},\one,\bot,{\tens},{\parr},\forall x A,\exists x A,\forall X A,\exists X A$

Formulas and proof trees

Formulas

First order quantification: $\forall x A$
Second order quantification: $\forall X A$
Quantification of arbitrary order (mainly first or second): $\forall\alpha A$

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. For example: $\wedge_1 \text{add} L$ .

Notations

Revision as of 14:23, 29 December 2008

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Logical systems

Formulas and proof trees

Formulas

Rule names

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