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Simple Logics for Basic Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)
An MV-algebra is an algebra (A, ⊕, ¬, 0), where (A, ⊕, 0) is a commutative monoid and ¬ is an idempotent operation on A satisfying also some additional axioms.
Basic algebras are similar algebras that can roughly be ...
Tense Polyadic N × M-Valued Łukasiewicz–Moisil Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)
In 2015, A.V. Figallo and G. Pelaitay introduced tense n×m-valued Łukasiewicz–Moisil algebras, as a common generalization of tense Boolean algebras and tense n-valued Łukasiewicz–Moisil algebras. Here we initiate an ...
On Halldén Completeness of Modal Logics Determined by Homogeneous Kripke Frames
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)
Halldén complete modal logics are defined semantically. They have a nice characterization as they are determined by homogeneous Kripke frames.
A Short and Readable Proof of Cut Elimination for Two First-Order Modal Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)
A well established technique toward developing the proof theory of a Hilbert-style modal logic is to introduce a Gentzen-style equivalent (a Gentzenisation), then develop the proof theory of the latter, and finally transfer ...
Minimal Sequent Calculi for Łukasiewicz’s Finitely-Valued Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)
The primary objective of this paper, which is an addendum to the author’s [8], is to apply the general study of the latter to Łukasiewicz’s n-valued logics [4]. The paper provides an analytical expression of a 2(n−1)-place ...