# Boolean-valued function

A Boolean-valued function is a function of type $f:X\to \mathbb{B}$, where $X$ is an arbitrary set and where $\mathbb{B}$ is a Boolean domain.

A Boolean function (of finite arity $k$) is a Boolean-valued function of type $f:{\mathbb{B}}^{k}\to \mathbb{B}$.

In some contexts a Boolean-valued function may be referred to as a predicate or a proposition^{}. In other contexts these terms may be used to describe the syntactic entities that denote or express Boolean-valued functions, or that have Boolean-valued functions among their canonical or intended models (http://planetmath.org/Model). When necessary to avoid confusion, terms like propositional expression or predicate formula^{} may be used to distinguish signs (http://planetmath.org/SignRelation) from their objects.

Title | Boolean-valued function |

Canonical name | BooleanvaluedFunction |

Date of creation | 2013-03-22 17:58:12 |

Last modified on | 2013-03-22 17:58:12 |

Owner | Jon Awbrey (15246) |

Last modified by | Jon Awbrey (15246) |

Numerical id | 10 |

Author | Jon Awbrey (15246) |

Entry type | Definition |

Classification | msc 68Q01 |

Classification | msc 68P01 |

Classification | msc 06E30 |

Classification | msc 03G05 |

Classification | msc 03C55 |

Classification | msc 03B05 |

Classification | msc 68R01 |

Synonym | characteristic function^{} |

Synonym | indicator function |

Synonym | predicate |

Synonym | proposition |

Related topic | BooleanDomain |

Defines | Boolean function |