Browsing Bulletin of the Section of Logic by Issue Date
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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 ... 
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 ... 
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 ... 
Commutative Energetic Subsets of BCKAlgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)The notions of a Cenergetic subset and (anti) permeable Cvalue in BCKalgebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable Cvalue are provided. ... 
Elementary Proof of Strong Normalization for Atomic F
(Wydawnictwo Uniwersytetu Łódzkiego, 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 Fₐₜ (a predicative restriction of Girard’s system F). 
Some Algebraic and Algorithmic Problems in Acoustocerebrography
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)Progress in the medical diagnostic is relentlessly pushing the measurement technology as well with its intertwined mathematical models and solutions. Mathematics has applications to many problems that are vital to human ... 
Simple Decision Procedure for S5 in Standard CutFree Sequent Calculus
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)In the paper a decision procedure for S5 is presented which uses a cutfree sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to ... 
A 2setup RoutleyMeyer Semantics for the 4valued Relevant Logic E4
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)The logic BN4 can be considered as the 4valued logic of the relevant conditional and the logic E4, as the 4valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2setup RoutleyMeyer semantics. ... 
Categorical Abstract Logic: Hidden MultiSorted Logics as MultiTerm Institutions
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)Babenyshev and Martins proved that two hidden multisorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with ...