
Authors:
Janusz CZELAKOWSKI
Title:FixedPoints for Relations and the Back and Forth Method
Pages:6371
File:bibtex
Abstract ( + )
In this paper we discuss some modeltheoretic constructions with the purpose of providing a general, abstract framework for them based on the orderoriented fixedpoint theory. The so called back and forth method is particularly useful in many branches of algebra and model theory. It originates with the proof of the famous Cantor's theorem that any two countable linear dense orders without endpoints are isomorphic. In a systematic way the back and forth method was studied by Fraisse, Ehrenfeucht and others. The aim of this note is to present a plausible and general abstract formulation of this method in the context of the theory of reflexive points for ordered Kripke frames.

Authors:
Wojciech DZIK
Title:Transparent Unifiers in Modal Logics with SelfConjugate Operators
Pages:7383
File:bibtex
Abstract ( + )
It is shown that weakly transitive normal modal logics containing D, with (definable) selfconjugate operators in the sense of Jonsson and Tarski have transparent unifiers, hence, unitary unification. There are continuum many such logics. Transparent unifiers are given in a simple explicit form. In logics with transparent unifiers every admissible rule with unifiable premises is derivable, which is a kind of structural completeness.

Authors:
Anetta GORNICKA
Title:Axiomatization of the Sentential Logic Dual with Respect to Lukasiewicz's ThreeValued Logic
Pages:8594
File:bibtex
Abstract ( + )
Lukasiewicz's ThreeValued Logic Dual logics with respect to Lukasiewicz's logics were investigated by G.Malinowski, M.Spasowski and R.Wojcicki. On the basis of their work no axiomatics for these logics were given. They were only referred according to the set of tautologies. Our aim is to build such an axiomatic system, for which the matrix dual to Lukasiewicz's threevalued matrix is strongly adequate.

Authors:
Joanna GRYGIEL
Title:Some Properties of Double Skeletons
Pages:95103
File:bibtex
Abstract ( + )
For a finite lattice L we consider the ordered set of all zeroes and units of blocks of the skeleton tolerance of L, called the double skeleton of L, and examine its properties.

Authors:
Adam KOLANY
Title:Lattices of nonLocally Finite Hypergraphs are not Heyting
Pages:105109
File:bibtex
Abstract ( + )
We have already proved, that given a hypergraph with finite edges one can define a free distributive lattice which is a Heyting algebra for locally finite hypergraphs. In the present paper we show that this assumption is necessary. That is, if a hypergraph is not locally finite then the underlying lattice is not a Heyting algebra.

Authors:
Miroslawa KOLOWSKAGAWIEJNOWICZ
Title:A Note on Bilinear Algebras
Pages:111117
File:bibtex
Abstract ( + )
We present the basic facts concerning bilinear algebras. We focus our attention on connections between bilinear algebras, Grishin algebras and pregroups.

Authors:
Zofia KOSTRZYCKA
Title:On Formulas of one Variable in NEXT(KTB)
Pages:119131
File:bibtex
Abstract ( + )
In this paper we consider formulas written in one variable in the normal logic T2. We present some special model for T2 to construct infinitely many nonequivalent formulas written in one variable and some family of models to construct continuum of logics over T2.

Authors:
JeanYves BEZIAU
Title:13 Questions about Universal Logic
Pages:133150
File:bibtex
Abstract ( + )
[Abstract]