Course by T. L. Yavorskaya "Justification logic" February 14–May 2, 2023, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
In this course we describe the area of justification logics and the main
results obtained for them. Justification logics were introduced by S
Artemov in 1995. Propositional justification logics are formulated in
the extension of standard propositional language by special terms that
denote evidence for the truth of formulas. Replacing these terms by the
modality expressing existence of such evidence converts justification
logic to some propositional modal logic. So, justification logics can be
considered as an explicit analog of modal logics. We will describe
justification logics corresponding to some well-known modal logics and
the appropriate semantics for them. We will prove completeness with
respect to this semantics and realization of the corresponding modal
logics, that is, the fact that for a number of modal logics $L$ for
any formula $F$ derivable in $L$ there exists the way to ascribe
justification terms to occurrences of modalities in $F$ which converts
$F$ into a theorem of the justification logic $J(L)$.
Then we pay more attention to the logic of proofs $LP$ (S.N. Artemov,
1995), which started an investigation in this area. We will prove that
the modal analog of $LP$ is the modal logic $S4$ and describe
translation of propositional intuitionistic logic in $LP$. Then we
supply $LP$ with the arithmetical semantics in which propositional
variables stand for arithmetical sentences and justification terms
denote codes of arithmetical derivations. We will prove that $LP$ is
sound and complete with respect to this semantics. Arithmetical
completeness of $LP$ together with the realization results for $S4$ and
intuitionistic logic enables us to describe arithmetical semantics for
them.
Another point of our interest is first order justification logic, for
which we describe language and semantics and prove realization theorems
for the appropriate first order modal logics. Also we will discuss
possible ways of arithmetical reading for first order justification
logic.
Lecturer
Yavorskaya Tatiana Leonidovna
Financial support
The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2022-265).
Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Steklov International Mathematical Center |
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Course by T. L. Yavorskaya "Justification logic", February 14–May 2, 2023 |
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May 2, 2023 (Tue) |
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Lecture 10. Justification logic T. L. Yavorskaya May 2, 2023 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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April 25, 2023 (Tue) |
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Lecture 9. Justification logic T. L. Yavorskaya April 25, 2023 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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April 11, 2023 (Tue) |
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Lecture 8. Justification logic T. L. Yavorskaya April 11, 2023 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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April 4, 2023 (Tue) |
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Lecture 7. Justification logic T. L. Yavorskaya April 4, 2023 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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March 28, 2023 (Tue) |
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Lecture 6. Justification logic T. L. Yavorskaya March 28, 2023 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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March 14, 2023 (Tue) |
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Lecture 5. Justification logic T. L. Yavorskaya March 14, 2023 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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March 7, 2023 (Tue) |
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Lecture 4. Justification logic T. L. Yavorskaya March 7, 2023 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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February 28, 2023 (Tue) |
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Lecture 3. Justification logic T. L. Yavorskaya February 28, 2023 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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February 21, 2023 (Tue) |
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Lecture 2. Justification logic T. L. Yavorskaya February 21, 2023 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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February 14, 2023 (Tue) |
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Lecture 1. Justification logic T. L. Yavorskaya February 14, 2023 18:00, Steklov Mathematical Institute, Room 303 (8 Gubkina) + online
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