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Provability multilattice logic

Provability multilattice logic In this paper, we introduce provability multilattice logic and multilattice arithmetic which extends first-order multilattice logic with equality by multilattice versions of Peano axioms. We show that has the provability interpretation with respect to and prove the arithmetic completeness theorem for it. We formulate in the form of a nested sequent calculus and show that cut is admissible in it. We introduce the notion of a provability multilattice and develop algebraic semantics for on its basis, by the method of Lindenbaum-Tarski algebras we prove the algebraic completeness theorem. We present Kripke semantics for and establish the Kripke completeness theorem via syntactical and semantic embeddings from into and vice versa. Last but not least, the decidability of is shown. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

Provability multilattice logic

Petrukhin, Yaroslav
Journal of Applied Non-Classical Logics , Volume 32 (4): 34 – Oct 2, 2022
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Publisher
Taylor & Francis
Copyright
© 2023 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.2023.2178780
Publisher site
See Article on Publisher Site

Abstract

In this paper, we introduce provability multilattice logic and multilattice arithmetic which extends first-order multilattice logic with equality by multilattice versions of Peano axioms. We show that has the provability interpretation with respect to and prove the arithmetic completeness theorem for it. We formulate in the form of a nested sequent calculus and show that cut is admissible in it. We introduce the notion of a provability multilattice and develop algebraic semantics for on its basis, by the method of Lindenbaum-Tarski algebras we prove the algebraic completeness theorem. We present Kripke semantics for and establish the Kripke completeness theorem via syntactical and semantic embeddings from into and vice versa. Last but not least, the decidability of is shown.

Journal

Journal of Applied Non-Classical Logics – Taylor & Francis

Published: Oct 2, 2022

Keywords: Multilattice logic; provability logic; nested sequent calculus; Peano arithmetic; embedding theorem

References

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