Metcalfe, George; Tuyt, Olim
(2020).
*
A monadic logic of ordered abelian groups.
*
In:
Olivetti, Nicola; Verbrugge, Rineke; Negri, Sara; Sandu, Gabriel
(eds.)
Proceedings of AiML 2020. Advances in Modal Logic: Vol. 13 (pp. 441-457).
College Publications

Text
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A many-valued modal logic with connectives interpreted in the ordered additive group of real numbers is introduced as a modal counterpart of the one-variable fragment of a (monadic) first-order real-valued logic. It is shown that the logic is decidable and admits an interpretation of the one-variable fragment of first-order Lukasiewicz logic. Completeness of an axiom system for the modal-multiplicative fragment is established via a Herbrand theorem for its first-order counterpart. A functional representation theorem is then proved for a class of monadic lattice-ordered abelian groups and used to establish completeness of an axiom system for the full logic.

## Item Type: |
Book Section (Book Chapter) |
---|---|

## Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |

## UniBE Contributor: |
Metcalfe, George and Tuyt, Olim Frits |

## Subjects: |
500 Science > 510 Mathematics |

## ISBN: |
978-1-84890-341-8 |

## Series: |
Advances in Modal Logic |

## Publisher: |
College Publications |

## Language: |
English |

## Submitter: |
George Metcalfe |

## Date Deposited: |
02 Sep 2020 08:45 |

## Last Modified: |
02 Sep 2020 08:45 |

## BORIS DOI: |
10.7892/boris.146150 |

## URI: |
https://boris.unibe.ch/id/eprint/146150 |