nLab additive disjunction

Idea

In the context of linear logic or linear type theory, the additive disjunction “$\oplus$” is a form of disjunction whose categorical semantics is typically that of the direct sum (e.g. Mihályi & Novitzká (2013), p. 9).

Related concepts

• direct sum, quantum parallelism

Logical operations and notation in linear logic

$\phantom{-}$symbol$\phantom{-}$	$\phantom{-}$in linear logic$\phantom{-}$
$\phantom{A}$$\top$	$\phantom{A}$additive truth
$\phantom{A}$$\bot$	$\phantom{A}$additive falsehood
$\phantom{A}$$0$	$\phantom{A}$multiplicative falsehood
$\phantom{A}$$1$	$\phantom{A}$multiplicative truth
$\phantom{A}$$\multimap$$\phantom{A}$	$\phantom{A}$linear implication$\phantom{A}$
$\phantom{A}$$\otimes$$\phantom{A}$	$\phantom{A}$multiplicative conjunction$\phantom{A}$
$\phantom{A}$$\oplus$$\phantom{A}$	$\phantom{A}$additive disjunction$\phantom{A}$
$\phantom{A}$$\&$$\phantom{A}$	$\phantom{A}$additive conjunction$\phantom{A}$
$\phantom{A}$$\invamp$$\phantom{A}$	$\phantom{A}$multiplicative disjunction$\phantom{A}$
$\phantom{A}$$\;!$$\phantom{A}$	$\phantom{A}$exponential conjunction$\phantom{A}$
$\phantom{A}$$\;?$$\phantom{A}$	$\phantom{A}$exponential disjunction$\phantom{A}$
$\phantom{A}$$^\bot$$\phantom{A}$	$\phantom{A}$negation$\phantom{A}$

References

• Daniel Mihályi, Valerie Novitzká, What about Linear Logic in Computer Science?, Acta Polytechnica Hungarica 10 4 (2013) 147-160 [pdf, pdf]