Editing Logical disjunction (section)

=== Semantics ===

In the [[semantics of logic]], classical disjunction is a [[truth function]]al [[logical operation|operation]] which returns the [[truth value]] ''true'' unless both of its arguments are ''false''. Its semantic entry is standardly given as follows:{{efn|For the sake of generality across classical systems, this entry suppresses the parameters of evaluation. The [[double turnstile]] [[List of logic symbols|symbol]] <math> \models </math> here is intended to mean "semantically entails".<!--this is hardly readable without context, it means  "(X ⊨  phi ∨ psi) if [(X  ⊨  phi) or (X  ⊨  psi)], for any X", in other words, " '∨' means 'or' ".-->}}

:: <math> \models \phi \lor \psi</math> &nbsp; &nbsp; if &nbsp; &nbsp; <math> \models \phi</math> &nbsp; &nbsp; or &nbsp; &nbsp; <math>\models \psi</math> &nbsp; &nbsp; or &nbsp; &nbsp; both

This semantics corresponds to the following [[truth table]]:<ref name=":1" />

{{2-ary truth table|0|1|1|1|<math>A \lor B</math>}}