| 1. Janusz CZELAKOWSKI, Fixed-Points for Relations and the Back and Forth Method | 63 [Abstract] [PDF] |
| 2. Wojciech DZIK, Transparent Unifiers in Modal Logics with Self-Conjugate Operators | 73 [Abstract] [PDF] |
| 3. Anetta GORNICKA, Axiomatization of the Sentential Logic Dual with Respect to Lukasiewicz's Three-Valued Logic | 85 [Abstract] [PDF] |
| 4. Joanna GRYGIEL, Some Properties of Double Skeletons | 95 [Abstract] [PDF] |
| 5. Adam KOLANY, Lattices of non-Locally Finite Hypergraphs are not Heyting | 105 [Abstract] [PDF] |
| 6. Miroslawa KOLOWSKA-GAWIEJNOWICZ, A Note on Bilinear Algebras | 111 [Abstract] [PDF] |
| 7. Zofia KOSTRZYCKA, On Formulas of one Variable in NEXT(KTB) | 119 [Abstract] [PDF] |
| 8. Jean-Yves BEZIAU, 13 Questions about Universal Logic | 133 [Abstract] [PDF] |
1. Janusz CZELAKOWSKI, Fixed-Points for Relations and the Back and Forth Method
In this paper we discuss some model-theoretic constructions with the purpose of providing a general, abstract framework
for them based on the order-oriented fixed-point 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.
2. Wojciech DZIK, Transparent Unifiers in Modal Logics with Self-Conjugate Operators
It is shown that weakly transitive normal modal logics containing D, with (definable) self-conjugate 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.
3. Anetta GORNICKA, Axiomatization of the Sentential Logic Dual with Respect to
Lukasiewicz's Three-Valued 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
three-valued matrix is strongly adequate.
4. Joanna GRYGIEL, Some Properties of Double Skeletons
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.
5. Adam KOLANY, Lattices of non-Locally Finite Hypergraphs are not Heyting
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.
6. Miroslawa KOLOWSKA-GAWIEJNOWICZ, A Note on Bilinear Algebras
We present the basic facts concerning bilinear algebras. We focus our attention on connections between bilinear
algebras, Grishin algebras and pregroups.
7. Zofia KOSTRZYCKA, On Formulas of one Variable in NEXT(KTB)
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 non-equivalent formulas written in one variable and some family of models to construct
continuum of logics over T2.
8. Jean-Yves BEZIAU, 13 Questions about Universal Logic