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An Alternative Natural Deduction for the Intuitionistic Propositional Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)
A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via ...
Full Cut Elimination and Interpolation for Intuitionistic Logic with Existence Predicate
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)
In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that ...
Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)
We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering (or directed) unification, that is, the property that ...
Equivalential Algebras with Conjunction on Dense Elements
(Wydawnictwo Uniwersytetu Łódzkiego, 2022-10-25)
We study the variety generated by the three-element equivalential algebra with conjunction on the dense elements. We prove the representation theorem which let us construct the free algebras in this variety.
An Investigation into Intuitionistic Logic with Identity
(Wydawnictwo Uniwersytetu Łódzkiego, 2019-12-31)
We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s ...
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 ...