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Two Modes of Nonmonotonic Consequence
Alexei Muravitsky
This is the text of my speech at the Logica Universalis webinar, which took place on May 11, 2022. I discuss two ways to implement a semantic approach to nonmonotonic consequence r…
On Matrix Consequence (Extended Abstract)
Alexei Muravitsky
These results are a contribution to the model theory of matrix consequence. We give a semantic characterization of uniform and couniform consequence relations. These properties hav…
Lindenbaum Method
Alex Citkin, Alexei Muravitsky
During his brief life, the Polish mathematician and logician Adolf Lindenbaum (1904--1941) contributed to mathematical logic, among other things, by several significant achievement…
On one embedding of Heyting algebras
Alexei Muravitsky
The paper is devoted to an algebraic interpretation of Kuznetsov's theorem which establishes the assertoric equipollence of intuitionistic and proof-intuitionistic propositional ca…
On the Equipollence of the Calculi Int and KM
Alexei Muravitsky
Following A. Kuznetsov's outline, we restore Kuznetsov's syntactic proof of the assertoric equipollence of the intuitionistic propositional calculus and the proof-intuitionistic ca…
On Some Syntactic Properties of the Modalized Heyting Calculus
Alexei Muravitsky
We show that the modalized Heyting calculus~\cite{esa06} admits a normal axiomatization. Then we prove that in this calculus the inference rule is admissible (Proposit…
Lindenbaum method (propositional language)
Alex Citkin, Alexei Muravitsky
Lindenbaum method is named after the Polish logician Adolf Lindenbaum who prematurely and without a clear trace disappeared in the turmoil of the Second World War at the age of abo…