A *modal algebra* is a structure ** A** = (

(

◊ is

◊ is

**Remark**:
Modal algebras provide algebraic models for modal logic. The operator ◊ is the
*possibility operator*, and the *necessity operator* □ is defined as □*x* = ¬◊¬*x*.

Let ** A** and

Classtype | variety |

Equational theory | decidable |

Quasiequational theory | decidable |

First-order theory | undecidable |

Locally finite | no |

Residual size | unbounded |

Congruence distributive | yes |

Congruence modular | yes |

Congruence n-permutable | yes, n = 2 |

Congruence regular | yes |

Congruence uniform | yes |

Congruence extension property | yes |

Definable principal congruences | no |

Equationally definable principal congruences | no |

[Discriminator variety]? | no |

Amalgamation property | yes |

Strong amalgamation property | yes |

Epimorphisms are surjective | yes |

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