Assertional logics, truth-equational logics, and the hierarchies of abstract algebraic logic
Result description
We establish some relations between the class of truth-equational logics, the class of assertional logics, other classes in the Leibniz hierarchy, and the classes in the Frege hierarchy. We argue that the class of assertional logics belongs properly in the Leibniz hierarchy. We give two new characterizations of truth-equational logics in terms of their full generalized models, and use them to obtain further results on the internal structure of the Frege hierarchy and on the relations between the two hierarchies. Some of these results and several counter examples contribute to answer a few open problems in abstract algebraic logic, and open a new one.
Keywords
Abstract algebraic logicLeibniz hierarchyFrege hierarchytruth-equational logicsassertional logicsFregean logicsfull generalized modelsunital matrices
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Assertional logics, truth-equational logics, and the hierarchies of abstract algebraic logic
Original language description
We establish some relations between the class of truth-equational logics, the class of assertional logics, other classes in the Leibniz hierarchy, and the classes in the Frege hierarchy. We argue that the class of assertional logics belongs properly in the Leibniz hierarchy. We give two new characterizations of truth-equational logics in terms of their full generalized models, and use them to obtain further results on the internal structure of the Frege hierarchy and on the relations between the two hierarchies. Some of these results and several counter examples contribute to answer a few open problems in abstract algebraic logic, and open a new one.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science
ISBN
978-3-319-74771-2
Number of pages of the result
27
Pages from-to
53-79
Number of pages of the book
454
Publisher name
Springer
Place of publication
Cham
UT code for WoS chapter
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Basic information
Result type
C - Chapter in a specialist book
OECD FORD
Pure mathematics
Year of implementation
2018