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Now showing items 1-10 of 13

#### 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 ...

#### 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 ...

#### Tense Polyadic N × M-Valued Łukasiewicz–Moisil Algebras

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

In 2015, A.V. Figallo and G. Pelaitay introduced tense n×m-valued Łukasiewicz–Moisil algebras, as a common generalization of tense Boolean algebras and tense n-valued Łukasiewicz–Moisil algebras. Here we initiate an ...

#### On Some Applied First-Order Theories which Can Be Represented by Definitions

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

In the paper we formulate a sufficient criterion in order for the first order theory with finite set of axioms to be represented by definitions in predicate calculus. We prove the corresponding theorem. According to this ...

#### Closure Operators on Complete Almost Distributive Lattices-III

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meet-irreducible element ...

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

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

This paper presents the main assumptions of Andrzej Grzegorczyk’s last research project concerning the logic of synonymity. It shows that the basis of logic of analytic equivalence, presented in the ﬁrst part of the work, ...

#### On Halldén Completeness of Modal Logics Determined by Homogeneous Kripke Frames

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

Halldén complete modal logics are defined semantically. They have a nice characterization as they are determined by homogeneous Kripke frames.