Browsing Bulletin of the Section of Logic by Issue Date
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Tense Polyadic N × MValued Łukasiewicz–Moisil Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)In 2015, A.V. Figallo and G. Pelaitay introduced tense n×mvalued Łukasiewicz–Moisil algebras, as a common generalization of tense Boolean algebras and tense nvalued Łukasiewicz–Moisil algebras. Here we initiate an ... 
On Some Applied FirstOrder 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 LatticesIII
(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 meetirreducible element ... 
NonFregean 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. 
A Short and Readable Proof of Cut Elimination for Two FirstOrder Modal Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)A well established technique toward developing the proof theory of a Hilbertstyle modal logic is to introduce a Gentzenstyle equivalent (a Gentzenisation), then develop the proof theory of the latter, and finally transfer ... 
A Note on some Characterization of Distributive Lattices of Finite Length
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)Using known facts we give a simple characterization of the distributivity of lattices of finite length. 
Minimal Sequent Calculi for Łukasiewicz’s FinitelyValued Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)The primary objective of this paper, which is an addendum to the author’s [8], is to apply the general study of the latter to Łukasiewicz’s nvalued logics [4]. The paper provides an analytical expression of a 2(n−1)place ... 
Categorical Abstract Algebraic Logic: Referential πInstitutions
(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 ... 
NonFregean Logics of Analytic Equivalence (I)
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)The identity connective is usually interpreted in nonFregean 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 MValgebra 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 ... 
An Elementary Proof of Strong Normalization for Atomic F
(Uniwersytet Łódzki. Katedra Logiki i Metodologii Nauk, 2016)We give an elementary proof (in the sense that it is formalizable in Peano arithmetic) of the strong normalization of the atomic polymorphic calculus F_{at} (a predicative restriction of Girard’s system F). 
Irredundant Decomposition of Algebras into OneDimensional Factors
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)We introduce a notion of dimension of an algebraic lattice and, treating such a lattice as the congruence lattice of an algebra, we introduce the dimension of an algebra, too. We define a starproduct as a special kind of ... 
Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering (or directed) unification, that is, the property that ... 
Interpolation in Normal Extensions of the Brouwer Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)The Craig interpolation property and interpolation property for deducibility are considered for special kind of normal extensions of the Brouwer logic. 
On Direct Limit Closed Classes of Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)Axiomatic classes of algebras of a given type which are closed with respect to direct limits are studied in this paper. 
Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and AntiUniform Parts
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)We describe here a special subdirect decomposition of algebras with modular congruence lattice. Such a decomposition (called a stardecomposition) is based on the properties of the congruence lattices of algebras. We ... 
Characterization of Birkhoff’s Conditions by Means of CoverPreserving and Partially CoverPreserving Sublattices
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)In the paper we investigate Birkhoff’s conditions (Bi) and (Bi*). We prove that a discrete lattice L satisfies the condition (Bi) (the condition (Bi*)) if and only if L is a 4cell lattice not containing a coverpreserving ...