Results 1 
5 of
5
Modal Logic of Projective Geometries of Finite Dimension
, 1998
"... Introduction Extending an original idea of B. Jonsson, R. Lyndon showed in [Lyndon 1961] how to construct relation algebras  boolean algebras with the binary operator ; (composition), the unary operator (converse) and the constant 1' (identity) which satisfy the socalled Tarski axioms (see [ ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Introduction Extending an original idea of B. Jonsson, R. Lyndon showed in [Lyndon 1961] how to construct relation algebras  boolean algebras with the binary operator ; (composition), the unary operator (converse) and the constant 1' (identity) which satisfy the socalled Tarski axioms (see [Henkin et alii 1997], [J'onsson & Tarski 1952])  from projective geometries, thus providing "a method for deriving consequences in the algebraic theory of binary relations from certain familiar facts of projective geometry" [Lyndon 1961]. By a projective geometry he meant the following (the definition below is valid throughout the present paper): 1.1. Definition. A projective geometry (or projective space) is a structure G = (P; L; In), where P is a nonempty set of points, L is a family of subsets of P called lines, and In<F63.
Undecidable theories of Lyndon algebras
 J. Symbolic Logic
, 2001
"... With each projective geometry we can associate a Lyndon algebra. Such an algebra always satisfies Tarski’s axioms for relation algebras and Lyndon algebras thus form an interesting connection between the fields of projective geometry and algebraic logic. In this paper we prove that if G is a class o ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
With each projective geometry we can associate a Lyndon algebra. Such an algebra always satisfies Tarski’s axioms for relation algebras and Lyndon algebras thus form an interesting connection between the fields of projective geometry and algebraic logic. In this paper we prove that if G is a class of projective geometries which contains an infinite projective geometry of dimension at least three, then the class L(G) of Lyndon algebras associated with projective geometries in G has an undecidable equational theory. In our proof we develop and use a connection between projective geometries and diagonalfree cylindric algebras. 1
Coalgebras, Stone Duality, Modal Logic
, 2006
"... A brief outline of the topics of the course could be as follows. Coalgebras generalise transition systems. Modal logics are the natural logics for coalgebras. Stone duality provides the relationship between coalgebras and modal logic. Furthermore, some basic category theory is needed to understand c ..."
Abstract
 Add to MetaCart
A brief outline of the topics of the course could be as follows. Coalgebras generalise transition systems. Modal logics are the natural logics for coalgebras. Stone duality provides the relationship between coalgebras and modal logic. Furthermore, some basic category theory is needed to understand coalgebras as well as Stone duality. So we
Coalgebras and Their Logics 1
, 2006
"... Some comments about the last Logic Column, on nominal logic. Pierre Lescanne points out ..."
Abstract
 Add to MetaCart
Some comments about the last Logic Column, on nominal logic. Pierre Lescanne points out