Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term π-Institutions
| Autor: | George Voutsadakis |
|---|---|
| Přispěvatelé: | Lake Superior State University, School of Mathematics and Computer Science |
| Rok vydání: | 2016 |
| Předmět: |
Behavioral Equivalence
Discrete mathematics Theoretical computer science Deductive Equivalence Logic Existential quantification Multi-Sorted Logic Term (logic) Philosophy TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES If and only if Hidden Logic Interpretability Isomorphism Abstract algebraic logic Multi-term -Institutions Categorical variable Abstract logic Mathematics |
| Zdroj: | Bulletin of the Section of Logic. 45 |
| ISSN: | 2449-836X 0138-0680 |
| DOI: | 10.18778/0138-0680.45.2.04 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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