
Authors:
Marcelo F. FRIAS and Ewa ORLOWSKA
Title:Equational reasoning in nonclassical logics
Pages:211
File:bibtex
Abstract ( + )
The purpose of this paper is to develop an equational formalism that is capable of modeling a great variety of applied nonclassical logics and of simulating nonclassical means of reasoning. The formalism is based on relation algebras augmented with a fork operator and known as fork algebras.

Authors:
Adam KOLANY
Title:Representation theorems for hypergraph satisfiability
Pages:1219
File:bibtex
Abstract ( + )
Given a set of propositions, one can consider its inconsistency hypergraph. Then the satisfiability of sets of clauses with respect to that hypergraph turns out to be the usual satisfiability. The problem is which hypergraphs can be obtained from sets of formulas as inconsistency hypergraphs. In the present paper it is shown that this can be done for all hypergraphs with countably many vertices and pairwise incomparable edges. Then, a general method of transforming the combinatorial problems into the satisfiability problem is shown.

Authors:
Paulo A.S. VELOSO
Title:Is fork settheoretical?
Pages:2030
File:bibtex
Abstract ( + )
We examine the settheoretical nature of fork algebras, namely to what extent fork algebras of relations are really setbased. We show that every fork algebra of relations (FAR, for short) can be represented by a cartesian FAR by making use of the room provided by the neutral element I for relational composition. If one insists in taking I as the concrete identity (diagonal) relation, then such representation is not always possible: we show that there are many interesting FARs that cannot be represented by proper cartesian FARs.

Authors:
Mauricio Pablo MARLANGEON
Title:Catalizer of binary relations and the fork operator as image of a general disjoint unionfunction of a cartesian product functions
Pages:3138
File:bibtex
Abstract ( + )
In the present paper the composition fog of two binary relations f and g is taken as if they were functions. In general f and g are incoherent and heterogeneous, in a sense specified below. The concept of catalyzer of that composition is introduced and the compatibility relation of catalyzing the same ordered pair of fog is defined over the catalyzer. In passing a theoretical way of getting a partition from the covering of the catalyzer of fog is indicated. Next a bijection between that covering and fog itself is established. Through this bijection a family is formed assigning to each (c,b) from fog the set of all possible ordered pairs with second component being (c,b) and first component being a catalyzer of (c,b). Finally the preceding procedure is applied to the composition gof^{c}, where ^{c} denotes the converse or transpose, and f and g are coherent heterogeneous binary relations of predomain A and codomain B, this last having an arbitrary binary operation, thus arriving at the expression of the fork operator addressed in the title.

Authors:
Stephane DEMRI and Ewa ORLOWSKA
Title:A class of modal logics with a finite model property with respect to the set of Mformulae
Pages:3949
File:bibtex
Abstract ( + )
We propose a formalism for presentation and classification of modal logics that admit a possible world semantics. We introduce a broad family of operators acting on binary relations and we show how various classes of accessibility relations from modal frames can be uniformly represented using these operators. Within this framework we define a class of modal logics that possess the finite model property with respect to the set of Mformulae.

Authors:
R. ZUBER
Title:On negatively restricting Boolean algebras
Pages:5054
File:bibtex
Abstract ( + )
[Abstract]