
Authors:
Anna GLENSZCZYK
Title:Monadic Fragments of Intuitionistic Control Logic
Pages:143154
File:bibtex
Abstract ( + )
We investigate monadic fragments of Intuitionistic Control Logic (ICL), which is obtained from Intuitionistic Propositional Logic (IPL) by extending language of IPL by a constant distinct from intuitionistic constants. In particular we present the complete description of purely negational fragment and show that most of monadic fragments are finite.

Authors:
Emilia HALUSKOVA
Title:On Direct Limit Closed Classes of Algebras
Pages:155170
File:bibtex
Abstract ( + )
Axiomatic classes of algebras of a given type which are closed with respect to direct limits are studied in this paper.

Authors:
Zofia Kostrzycka
Title:Interpolation in Normal Extensions of the Brouwer Logic
Pages:171186
File:bibtex
Abstract ( + )
The Craig interpolation property and interpolation property for deducibility are considered for special kind of normal extensions of the Brouwer logic.

Authors:
Marcin LAZARZ
Title:Characterization of Birkhoff's Conditions by Means of CoverPreserving and Partially CoverPreserving Sublattices
Pages:187200
File:bibtex
Abstract ( + )
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 sublattice isomorphic to the lattice S_{7}^{*} (the lattice S_{7} ). As a corollary we obtain a well known result of J. Jakubik from [6]. Furthermore, lattices S_{7} and S_{7}^{*} are considered as socalled partially coverpreserving sublattices of a given lattice L, S_{7}«L and S_{7}^{*} « L, in symbols. It is shown that an upper continuous lattice L satisfies (Bi^{*} ) if and only if L is a 4cell lattice such that S_{7} « L. The final corollary is a generalization of Jakubik´s theorem for upper continuous and strongly atomic lattices.

Authors:
Bogdan STARUCH and Bozena STARUCH
Title:Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and AntiUniform Parts
Pages:201214
File:bibtex
Abstract ( + )
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 consider four proper ties of lattices: atomic, atomless, locally uniform and antiuniform. In effect, we describe a stardecomposition of a given algebra with modular congruence lattice into two or three parts associated to these properties.

Authors:
Bogdan STARUCH
Title:Irredundant Decomposition of Algebras into OneDimensional Factors
Pages:215240
File:bibtex
Abstract ( + )
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 subdirect product. We obtain the stardecomposition of algebras into onedimensional factors, which generalizes the known decomposition theorems e.g. for Abelian groups, linear spaces, Boolean algebras.

Authors:
Adam KOLANY and Miroslaw WROBEL
Title:Some Algebraic and Algorithmic Problems in Acoustocerebrography
Pages:241258
File:bibtex
Abstract ( + )
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 health but not for all. In this article we describe how the mathematics of acoustocerebrography has become one of the most important applications of mathematics to the problems of brain monitoring as well we will show some algebraic problems which still have to be solved. Acoustocerebrography ([4, 1]) is a set of techniques of visualizing the state of (human) brain tissue and its changes with use of ultrasounds, which mainly rely on a relation between the tissue density and speed of propagation for ultrasound waves in this medium. Propagation speed or, equivalently, times of arriving for an ultrasound pulse, can be inferred from phase relations for various frequencies. Since, due to KramersKronig relations, the propagation speeds depend significantly on the frequency of inves tigated waves, we consider multispectral wave packages of the form W (n) =
with appropriately chosen frequencies
f_{h}, h = 1,...,H, amplifications
A_{h}, h = 1, . . . , H, start phases ψ_{h}, h = 1, . . . , H, and sampling frequency F . In this paper we show some problems of algebraic and, to some extend, algorithmic nature which raise up in this topic. Like, for instance, the influence of relations between the signal length and frequency values on the error on estimated phases or on neutralizing alien frequencies. Another problem is finding appropriate initial phases for avoiding improper distributions of peaks in the resulting signal or fin

Authors:
Wojciech DZIK and Sandor RADELECZKI
Title:Preserving Filtering Unification By Adding Compatible Operations To Some Heyting Algebras
Pages:259269
File:bibtex
Abstract ( + )
We show that adding compatible operations to Heyting algebras and to commu tative residuated lattices, both satisfying the Stone law ¬x⋁¬¬x = 1, preserves filtering (or directed) unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To prove the results we apply the theorems of [9] on direct products of lalgebras and filter ing unification. We consider examples of frontal Heyting algebras, in particular Heyting algebras with the successor, γ and G operations as well as expansions of some commutative integral residuated lattices with successor operations.