
Authors:
Maria MANZANO, Manuel Crescenio MORENO
Title:Identity, Equality, Nameability and
Completeness. Part II
Pages:141158
File:bibtex
Abstract ( + )
This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge.
We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a
notion which has to be defined and, in the other case, identity is a notion used to define other logical concepts.
In our previous paper, [16], we investigated whether identity can be introduced by definition arriving to the conclusion that only in full higherorder logic
with standards emantics a reliable definition of identity is possible.
In the present study we have moved to modal logic and realized that here we can distinguish in the formal language between two different equality symbols, the first one shall be interpreted as extensional genuine identity and only applies for objects, the second one applies for non rigid terms and has the characteristic of synonymy. We have also analyzed the hybrid modal logic where we can introduce rigid terms by definition and can express that two worlds are identical by using
the nominals and the @ operator.
We finish our paper in the kingdom of identity where the only primitives are
lambda and equality. Here we show how other logical concepts can be defined in terms of the identity relation.
We have found at the end of our walk a possible point of convergence in the
logic Equational Hybrid Propositional Type Theory (EHPTT), [14] and [15].

Authors:
Zofia KOSTRZYCKA
Title:On Interpolation in NEXT(KB.Alt(2))
Pages:159170
File:bibtex
Abstract ( + )
We prove that there is infinitely many tabular modal logics extending KB.Alt(2)
which have interpolation.

Authors:
Berhanu ASSAYE, Mihret ALEMNEH and Gerima TEFERA
Title:BAlmost Distributive Fuzzy Lattice
Pages:171185
File:bibtex
Abstract ( + )
The concept of BAlmost distributive fuzzy lattice (B — ADFL) interms of its
principal ideal fuzzy lattice is introduced.Necessary and suficient conditions for
an ADFL to become a B — ADFL are investigated. We also proved the equivalency of Balgebra and Bfuzzy algebra. In addition we extend PSADL to
PSADFL and proved B — ADFL implies PSADFL and many Lemmas, theorems and Corollaries are elaborated.
Keywords: Almost Distributive Lattice,Heyting Almost Distributive Lattice(HADL), BAlmost Distributive Lattice, Principal ideals of an Almost
Distributive Lattice.

Authors:
Rafal GRUSZCZYNSKI and Andrzej PIETRUSZCZAK
Title:A Comparison of Two Systems
of Pointfree Topology
Pages:187200
File:bibtex
Abstract ( + )
This is a spinoff paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk's pointfree topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the
Grzegorczyk's system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to
dissimilarities, we also demonstrate that the theories coincide (in the sense that their axioms are satisfied in the same class of structures) in presence of axiom
stipulating nonexistence of atoms.
Keywords: pointfree topology; regionbased topology; foundations of topology;
mereology; mereological structures; separation structures; connection
structures; Grzegorczyk structures; BiacinoGerla structures.

Authors:
Mateusz KLONOWSKI
Title:A Poststyle Proof of Completeness Theorem
for Symmetric Relatedness Logic S
Pages:201215
File:bibtex
Abstract ( + )
One of the logic defined by Richard Epstein in a context of an analysis of subject matter relationship is Symmetric Relatedness Logic S. In the monograph [2]
we can find some open problems concerning relatedness logic, proof of Post's
completeness theorem for logic S is one of them. Our paper introduces a solution of this metalogical issue.
Keywords: Normal forms, Poststyle proof of completeness, Relatedness
logic, Relating logic