Logical disjunction

In <a href="/facts/Logic/8JnpJLtt">logic</a>, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a <a href="/facts/Logical_connective/VkPhUs6M">logical connective</a> typically notated as 
 
 
 
 ∨
 
 
 {\displaystyle \lor }
 
 and read aloud as "or". For instance, the <a href="/facts/English_language/tpkxGt7b">English</a> language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula 
 
 
 
 S
 ∨
 W
 
 
 {\displaystyle S\lor W}
 
, assuming that 
 
 
 
 S
 
 
 {\displaystyle S}
 
 abbreviates "it is sunny" and 
 
 
 
 W
 
 
 {\displaystyle W}
 
 abbreviates "it is warm".
In <a href="/facts/Classical_logic/ls62MAms">classical logic</a>, disjunction is given a <a href="/facts/Truth_function/aH5kBhQ7">truth functional</a> semantics according to which a formula 
 
 
 
 ϕ
 ∨
 ψ
 
 
 {\displaystyle \phi \lor \psi }
 
 is true unless both 
 
 
 
 ϕ
 
 
 {\displaystyle \phi }
 
 and 
 
 
 
 ψ
 
 
 {\displaystyle \psi }
 
 are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an inclusive interpretation of disjunction, in contrast with <a href="/facts/Exclusive_disjunction/FHyr7hGQ">exclusive disjunction</a>. Classical <a href="/facts/Proof_theory/kopBdQn9">proof theoretical</a> treatments are often given in terms of rules such as <a href="/facts/Disjunction_introduction/dI7RYkQR">disjunction introduction</a> and <a href="/facts/Disjunction_elimination/vode1DSs">disjunction elimination</a>. Disjunction has also been given numerous <a href="/facts/Nonclassical_logic/caR36T5n">non-classical</a> treatments, motivated by problems including <a href="/facts/Aristotle%2527s_sea_battle_argument/NV07N2wh">Aristotle's sea battle argument</a>, <a href="/facts/Heisenberg/n4qzYvj4">Heisenberg</a>'s <a href="/facts/Uncertainty_principle/UUSoSp4T">uncertainty principle</a>, as well as the numerous mismatches between classical disjunction and its nearest equivalents in <a href="/facts/Natural_language/B4gLS7Kd">natural languages</a>.
An <a href="/facts/Operand/HSuUzrKz">operand</a> of a disjunction is a disjunct.

Logical disjunction open-in-new

Logical disjunction