
Authors:
M. Sambasiva RAO
Title:Congruences and Ideals in a Distributive Lattice with Respect to a Derivation
Pages:110
File:bibtex
Abstract ( + )
Two types of congruences are introduced in a distributive lattice, one in terms of ideals generated by derivations and the other in terms of images of derivations. An equivalent condition is derived for the corresponding quotient algebra to become a Boolean algebra. An equivalent condition is obtained for the existence of a derivation.

Authors:
Morteza Moniri and S. Hosein Sajjadi
Title:Regular Cuts in Models of Bounded Arithmetic
Pages:1120
File:bibtex
Abstract ( + )
We study some model theoretic properties of cuts in models of bounded arithmetic theories like S_{2}^{i} and T_{2}^{i}. We consider suitable versions of the notion of regular cut in models of these theories. We study the relation between this notion and some versions of the collection axiom. As a consequence, we construct certain extensions of models of theories of bounded arithmetic. Each of these extensions contains a nonstandard initial segment which is a model of S_{2}.

Authors:
Josep Maria Font
Title:Atoms in a Lattice of Theories
Pages:2132
File:bibtex
Abstract ( + )
The logic I is defined, in a language with just the implication connective →, by the axiom of reflexivity or identity "φ→φ'' and the rule of Modus Ponens "from φ and φ→ψ to infer ψ" its theorems are formulas of the form: "φ→φ''. This paper continues the study of this logic as begun in the previous paper "The simplest protoalgebraic logic''. Here, I study some points of the lattice structure of its set of theories, which shows some unusual features. I prove it is atomic, determine its (denumerable) atoms, prove that there is a single atom below any principal theory, and prove that principal theories form a subsemilattice of the lattice of theories which is orderisomorphic to the tree of finite sequences of natural numbers. I also prove that this logic has a nontermdefinable weak disjunction operation.

Authors:
Grzegorz DYMEK and Anna KOZANECKADYMEK
Title:PseudoBCILogic
Pages:3342
File:bibtex
Abstract ( + )
A noncommutative version of the BCIlogic, pseudoBCIlogic, is introduced. Although it is not algebraizable, it is extended to logic which is so. The main result of the paper says that a pseudoBCIalgebra is an algebraic counterpart of this extended logic (Theorem 3.2).

Authors:
MRUCZEKNASIENIEWSKA and Marek NASIENIEWSKI
Title:A SegerbergLike Connection Between Certain Classes of Propositional Logics
Pages:4352
File:bibtex
Abstract ( + )

Authors:
Marek NOWAK
Title:On Some Application of the Concept of Residuated Pair of Mappings
Pages:5368
File:bibtex
Abstract ( + )
We present a new simple criterion establishing under which conditions a subset of a complete lattice forms its complete sublattice. The existence of interiorclosure pair of operations asssociated on the subset, is the criterion. It is shown that such a pair of operations is simply a residuated pair of mappings that is identical with its pair of interiorclosure operations. In the sequel we consider all interiorclosure pairs of operations associated on a subset B of the family P(A) of all the subsets of given set A. Next, we provide a natural generalization of the concept of rough sets. The generalization is similar to that of [10] and based on interiorclosure pair of operations associated on a set of discourse.

Authors:
LeiBo WANG
Title:Closure Extended Double Stone Algebras
Pages:6982
File:bibtex
Abstract ( + )
The variety CDS of closure extended double Stone algebras consists of the algebras (L;∧,∨,^{*},^{+},°,0,1) of type (2,2,1,1,1,0,0) where (L;∧,∨,^{*},^{+},0,1) is a double Stone algebra, ° is a lattice endomorphism on L with x⩽ x°=x°° and the operations x↦ x^{*}, x↦ x^{+} and x↦ x° are linked by the identities x^{*}°=x°^{*} and x^{+}°= x°^{+}. In this paper, we characterize congruences on a CDSalgebra, and show that there are precisely seven nonisomorphic subdirectly irreducible members in the class of these algebras and give a complete description of them.

Authors:
Marcin Lazarz
Title:Characterization of Medvedev's Logic by Means of Kubinski's Frames
Pages:8390
File:bibtex
Abstract ( + )
In the paper we deal with the frames introduced by T. Kubinski, and show that the intersection of their content coincides with the well known Medvedev's logic of finite problems.