Description

• Title:
  Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term Institutions
• Creator:
  Voutsadakis, George
• Contributor:
  Lake Superior State University, School of Mathematics and Computer Science;
  gvoutsad@lssu.edu
• Description:
  Babenyshev and Martins proved that two hidden multi-sorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with substitutions. We show that the -institutions corresponding to the hidden multi-sorted deductive systems studied by Babenyshev and Martins satisfy the multi-term condition of Gil-Férez. This provides a proof of the result of Babenyshev and Martins by appealing to the general result of Gil-Férez pertaining to arbitrary multi-term -institutions. The approach places hidden multi-sorted deductive systems in a more general framework and bypasses the laborious reuse of well-known proof techniques from traditional abstract algebraic logic by using “off the shelf” tools.
• Object availability:
  free access
• Rights:
  © Copyright by Authors, Łódź 2016; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2016
• Date:
  2017.05.16;
  2016
• Type:
  Article
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;2;
  45
• Subject:
  Behavioral Equivalence;
  Hidden Logic;
  Multi-Sorted Logic;
  Multi-term -Institutions;
  Interpretability;
  Deductive Equivalence
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/21627 ;
  2449-836X;
  10.18778/0138-0680.45.2.04
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  seek permission
• Type:
  image