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#### Erratum to: Congruences and Ideals in a Distributive Lattice with Respect to a Derivation

(Wydawnictwo Uniwersytetu Łódzkiego, 2019)

The present note is an Erratum for the two theorems of the paper "Congruences and ideals in a distributive lattice with respect to a derivation" by M. Sambasiva Rao.

#### Positive Implicative Soju Ideals in BCK-Algebras

(Wydawnictwo Uniwersytetu Łódzkiego, 2019)

The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations ...

#### Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E

(Wydawnictwo Uniwersytetu Łódzkiego, 2019)

The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite ...

#### A Modified Subformula Property for the Modal Logic S4.2

(Wydawnictwo Uniwersytetu Łódzkiego, 2019)

The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is ...

#### 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 ...

#### Functional Completeness in CPL via Correspondence Analysis

(Wydawnictwo Uniwersytetu Łódzkiego, 2019)

Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only ...

#### 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 ...

#### Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic

(Wydawnictwo Uniwersytetu Łódzkiego, 2019-12-31)

Sentences containing definite descriptions, expressions of the form `The F', can be formalised using a binary quantier that forms a formula out of two predicates, where ℩x[F;G] is read as `The F is G'. This is an innovation ...

#### 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 ...