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Semi-Heyting Algebras and Identities of Associative Type
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)
An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. SH denotes ...
The Method of Socratic Proofs Meets Correspondence Analysis
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)
The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej ...
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 ...
A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)
This paper presents a way of formalising definite descriptions with a binary quantifier ℩, where ℩x[F, G] is read as `The F is G'. Introduction and elimination rules for ℩ in a system of intuitionist negative free logic ...