# User:IssaRice/Computability and logic/List of possibilities for completeness and decidability

From Machinelearning

Decidable logic? | Complete logic? (semantic completeness) | Decidable theory? | Complete theory? (negation-completeness) | Example or proof of non-existence |
---|---|---|---|---|

Yes | Yes | Yes | Yes | Empty theory (theory with no non-logical axioms) inside propositional logic |

Yes | Yes | Yes | No | |

Yes | Yes | No | Yes | |

Yes | Yes | No | No | |

Yes | No | Yes | Yes | |

Yes | No | Yes | No | |

Yes | No | No | Yes | |

Yes | No | No | No | |

No | Yes | Yes | Yes | |

No | Yes | Yes | No | |

No | Yes | No | Yes | |

No | Yes | No | No | The theory of Robinson arithmetic inside first-order logic |

No | No | Yes | Yes | |

No | No | Yes | No | |

No | No | No | Yes | |

No | No | No | No |