Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term π-Institutions

• Autorzy: George Voutsadakis
• Języki publikacji: EN

Abstrakty

EN

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 π-institutions corresponding to the hidden multi-sorted deductive systems studied by Babenyshev and Martins satisfy the multi-term condition of Gil-F´erez. This provides a proof of the result of Babenyshev and Martins by appealing to the general result of Gil-F´erez pertaining to arbitrary multi-term π-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.

Słowa kluczowe

EN

Behavioral Equivalence; Hidden Logic; Multi-Sorted Logic; Multi-term π-Institutions; Interpretability; Deductive Equivalence

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2016
• Tom: 45
• Numer: 2

Daty

wydano

2016-06-30

Twórcy

autor

George Voutsadakis

Identyfikatory

DOI

10.18778/0138-0680.45.2.04