### Abstract

It can be very advantageous to borrow key components of a logic for use in another logic. The advantages may be not only conceptual; due to the existence of software systems supporting mechanized reasoning in a given logic, it may be possible to reuse a system developed for one logic—for example, a theorem-prover—to obtain a new system for another. Translations between logics by appropriate mappings provide a first way of reusing tools of one logic in another. This paper generalizes this idea to the case where entire components—for example, the proof theory—of one of the logics involved may be completely missing, so that the appropriate mapping could not even be defined. The idea then is to borrow the missing components (as well as their associated tools if they exist) from a logic that has them in order to create the full-fledged logic and tools that we desire. The relevant structure is transported using maps that only involve a limited aspect of the two logics in question—for example, their model theory. The constructions accomplishing this kind of borrowing of logical structure are very general and simple. They only depend upon a few abstract properties that hold under very general conditions given a pair of categories linked by adjoint functors.

Original language | English (US) |
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Title of host publication | Mathematical Foundations of Computer Science 1993 - 18th International Symposium, MFCS 1993, Proceedings |

Editors | Andrzej M. Borzyszkowski, Stefan Sokolowski |

Publisher | Springer-Verlag Berlin Heidelberg |

Pages | 342-351 |

Number of pages | 10 |

ISBN (Print) | 9783540571827 |

State | Published - Jan 1 1993 |

Event | 18th International Symposium on Mathematical Foundations of Computer Science, MFCS 1993 - Gdansk, Poland Duration: Aug 30 1993 → Sep 3 1993 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 711 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 18th International Symposium on Mathematical Foundations of Computer Science, MFCS 1993 |
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Country | Poland |

City | Gdansk |

Period | 8/30/93 → 9/3/93 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Mathematical Foundations of Computer Science 1993 - 18th International Symposium, MFCS 1993, Proceedings*(pp. 342-351). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 711 LNCS). Springer-Verlag Berlin Heidelberg.