May I borrow your logic?

Maura Cerioli, José Meseguer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationMathematical Foundations of Computer Science 1993 - 18th International Symposium, MFCS 1993, Proceedings
EditorsAndrzej M. Borzyszkowski, Stefan Sokolowski
PublisherSpringer-Verlag Berlin Heidelberg
Pages342-351
Number of pages10
ISBN (Print)9783540571827
StatePublished - Jan 1 1993
Event18th International Symposium on Mathematical Foundations of Computer Science, MFCS 1993 - Gdansk, Poland
Duration: Aug 30 1993Sep 3 1993

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume711 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other18th International Symposium on Mathematical Foundations of Computer Science, MFCS 1993
CountryPoland
CityGdansk
Period8/30/939/3/93

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Cerioli, M., & Meseguer, J. (1993). May I borrow your logic? In A. M. Borzyszkowski, & S. Sokolowski (Eds.), 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.