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Four-valued expansions of Dunn-Belnap's logic (I): Basic characterizations
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)
Basic results of the paper are that any four-valued expansion L4 of Dunn-Belnap's logic DB4 is de_ned by a unique (up to isomorphism) conjunctive matrix ℳ4 with exactly two distinguished values over an expansion 4 of a De ...
Length Neutrosophic Subalgebras of BCK=BCI-Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)
Given i, j, k ∈ {1,2,3,4}, the notion of (i, j, k)-length neutrosophic subalgebras in BCK=BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed ...
The Phenomenology of Second-Level Inference: Perfumes in The Deductive Garden
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)
We comment on certain features that second-level inference rules commonly used in mathematical proof sometimes have, sometimes lack: suppositions, indirectness, goal-simplification, goal-preservation and premise-preservation. ...
Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)
We continue the investigation of the first paper where we studied logics with various negations including empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CCω as ...
From Intuitionism to Brouwer's Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)
We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication ...