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#### On Injective MV-Modules

(Wydawnictwo Uniwersytetu Łódzkiego, 2018)

In this paper, by considering the notion of MV-module, which is the structure that naturally correspond to lu-modules over lu-rings, we study injective MV-modules and we investigate some conditions for constructing injective ...

#### On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories

(Wydawnictwo Uniwersytetu Łódzkiego, 2018)

We formulate a certain subtheory of Ishimoto’s [1] quantifier-free fragment of Leśniewski’s ontology, and show that Ishimoto’s theory can be reconstructed in it. Using an epimorphism theorem we prove that our theory is ...

#### Rule-Generation Theorem and its Applications

(Wydawnictwo Uniwersytetu Łódzkiego, 2018)

In several applications of sequent calculi going beyond pure logic, an introduction of suitably defined rules seems to be more profitable than addition of extra axiomatic sequents. A program of formalization of mathematical ...

#### Labeled Sequent Calculus for Orthologic

(Wydawnictwo Uniwersytetu Łódzkiego, 2018)

Orthologic (OL) is non-classical logic and has been studied as a part of quantumlogic. OL is based on an ortholattice and is also called minimal quantum logic.Sequent calculus is used as a tool for proof in logic and has ...

#### Categorical Abstract Algebraic Logic: Referential π-Institutions

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of ...

#### Non-Fregean Logics of Analytic Equivalence (I)

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

The identity connective is usually interpreted in non-Fregean logic as an operator representing the identity of situations. This interpretation is related to the modal criterion of the identity of sentence correlates, ...

#### An Observation Concerning Porte’s Rule in Modal Logic

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

It is well known that no consistent normal modal logic contains (as theorems) both ◊A and ◊¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent ...

#### 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 ...

#### Unifiability and Structural Completeness in Relation Algebras and in Products of Modal Logic S5

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties ...

#### Simple Logics for Basic Algebras

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

An MV-algebra is an algebra (A, ⊕, ¬, 0), where (A, ⊕, 0) is a commutative monoid and ¬ is an idempotent operation on A satisfying also some additional axioms.
Basic algebras are similar algebras that can roughly be ...