This thesis studies the extensions of the four-valued Belnap-Dunn logic, called super-Belnap logics, from the point of view of abstract algebraic logic. We describe the global structure of the lattice of super-Belnap logics and show that this lattice can be fully described in terms of classes of finite graphs satisfying some closure conditions. We also introduce a theory of so- called explosive extensions and use it to prove new completeness theorems for super-Belnap logics. A Gentzen-style proof theory for these logics is then developed and used to establish interpolation for many of them. Finally, we also study the expansion of the Belnap-Dunn logic by the truth operator ∆. Keywords: abstract algebraic logic, Belnap-Dunn logic, paraconsistent logic, super-Belnap logics
Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:384186 |
Date | January 2018 |
Creators | Přenosil, Adam |
Contributors | Bílková, Marta, Noguera, Carles, Jansana, Ramon |
Source Sets | Czech ETDs |
Language | English |
Detected Language | English |
Type | info:eu-repo/semantics/doctoralThesis |
Rights | info:eu-repo/semantics/restrictedAccess |
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