# logic

Generally, by logic, people mean first order logic, a formal set of rules for building mathematical statements out of symbols like $\mathrm{\neg}$ (negation^{}) and $\to $ (implication^{}) along with quantifiers^{} like $\forall $ (for every) and $\exists $ (there exists).

More generally, a *logic* is any set of rules for forming sentences^{} (the logic’s *syntax*) together with rules for assigning truth values to them (the logic’s *semantics*). Normally it includes a (possibly empty) set of *types* $T$ (also called *sorts*), which represent the different kinds of objects that the theory discusses (typical examples might be sets, numbers, or sets of numbers). In addition^{} it specifies particular quantifiers, connectives^{}, and variables. Particular theories in the logic can then add relations^{} and functions to fully specify a logical language.

Title | logic |

Canonical name | Logic |

Date of creation | 2013-03-22 13:00:09 |

Last modified on | 2013-03-22 13:00:09 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 9 |

Author | Henry (455) |

Entry type | Definition |

Classification | msc 03B15 |

Classification | msc 03B10 |

Related topic | FuzzySubset |

Defines | syntax |

Defines | semantics |

Defines | type |

Defines | sort |