Basic Propositional Logic

Student: Kirill Aleksandrov

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2024

Basic propositional logic $\mathbf{BPL}$ was introduced by Albert Viser in 1981. It is the logic of the class of Kripke frames with transitive and antisymmetric accessibility relation. We consider link between algorithmic properties of $\mathbf{BPL}$ and size of the smallest Kripke counterframes for non-theorems of $\mathbf{BPL}$. We prove existence, for every degree of unsolvability, of a linear approximable extension of $\mathbf{BPL}$ with variable-free fragment belongs to the degree.

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