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Now showing items 21-30 of 76

#### A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. ...

#### Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term Institutions

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

Babenyshev and Martins proved that two hidden multi-sorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with ...

#### Quasiorders, Tolerance Relations and Corresponding “Partitions”

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based ...

#### Axiomatization of a Basic Logic of Logical Bilattices

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing (J Philos Logic 34:121–153, 2005) as a candidate for the basic logic of logical bilattices.

#### A New Arithmetically Incomplete First- Order Extension of Gl All Theorems of Which Have Cut Free Proofs

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

Reference [12] introduced a novel formula to formula translation tool (“formulators”) that enables syntactic metatheoretical investigations of first-order modal logics, bypassing a need to convert them first into Gentzen ...

#### 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 ...