Algebraizing first-order logics

Project name in Czech
Algebraizing first-order logics
Annotation in Czech
The last 50 years saw the introduction of many logical systems going beyond clasical two-valued logic, with motivations coming from fields such as computer science, philosophy, game theory, and linguistics. In response to this multitude of logics, a general algebraic theory of non-classical propositional logics called abstract algebraic logic (AAL) was gradually developed. However, no satisfactory algebraic theory of comparable strength and generality exists at the first-order level. The main reason is that first-order quantifiers are cumbersome to handle using the standard methods of universal algebra. The aim of the project is to develop such a general theory by combining the methods of AAL with an analysis of quantification based on so-called nominal algebras, and to apply this theory to settle open questions about interpolation and Beth definability in non-classical first-order logics. Algebraizing first-order quantification in this way will also enable us to apply profinite methods from algebraic automata theory in the finite model theory of classical and non-classical logics.

R&D category
ZV - Basic research
OECD FORD - main branch
10101 - Pure mathematics
OECD FORD - secondary branch
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OECD FORD - another secondary branch
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CEP - equivalent branches <br>(according to the <a href="http://www.vyzkum.cz/storage/att/E6EF7938F0E854BAE520AC119FB22E8D/Prevodnik_oboru_Frascati.pdf">converter</a>)
BA - General mathematics

Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data delivery code
CEP26-GA0-GM-R
Data delivery date
Apr 27, 2026

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