# interpolation property

A logic is said to have the *interpolation property* if whenever $\varphi (R,S)\to \psi (R,T)$ holds, then there is a sentence^{} $\theta (R)$, so that both $\varphi (R,S)\to \theta (R)$ and $\theta (R)\to \psi (R,T)$ hold, where $R,S$ and $T$ are some sets of symbols that occur in the formulas^{}, $R$ being the set of symbols common to both $\varphi $ and $\psi $.

The interpolation property holds for first order logic. The interpolation property is related to Beth definability property and Robinson’s consistency property. Also, a natural generalisation is the concept $\mathrm{\Delta}$-closed logic.

Title | interpolation property |
---|---|

Canonical name | InterpolationProperty |

Date of creation | 2013-03-22 13:49:36 |

Last modified on | 2013-03-22 13:49:36 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 7 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 03B99 |

Defines | interpolation property |