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Matroid Decomposition

Matroids, firscapturematroiddecompositiont defined in 1935, are an abstract generalization of graphs and matrices. By now, there is a large body of matroid theory. The book covers the part of the theory dealing with composition and decomposition of matroids.

The book is a revised version of the original publication of 1992. It does not assume any prior knowledge of matroid theory. Indeed, for the reader unfamiliar with matroid theory, the book may serve as an easy and intuitive introduction to that beautiful part of combinatorics.  For the expert, the book is intended to provide a pleasant tour over familiar terrain.

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Effective Logic Computation

The engineering advances started in the second half of the 20th century have created an avalanche of new technology. Control and use of that technology require, among many things, effective computational methods for logic.

This book proposes one such method. It makes use of a theory of logic computation based on matroid theory, in particular matroid decomposition. Main features of the theory are an extension of propositional logic, an analysis of logic formulas via combinatorial structures, and a construction of logic solution algorithms based on that analysis. The results have been implemented in a software system for logic programming called the Leibniz System.

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Introduction to Wittgenstein’s Tractatus Logico-Philosophicus

capturephilosophybookIn 1921, Ludwig Wittgenstein (1889-1951) published a landmark book in philosophy: the Tractatus Logico-Philosophicus, usually called just the Tractatus. It puts forth a profound theory — now called the picture theory — about the meaning of language. Simply put, the Tractatus aims to answer the question “What can be expressed by language?”

It is an understatement to say that the Tractatus is difficult to read and understand. Accordingly, numerous introductory books and commentaries have been written. These texts are important contributions in philosophy but also are quite complex, even when described as being introductory.

In contrast, this book brings out the fundamental ideas of the Tractatus in simple, everyday language, with all concepts and conclusions illustrated by numerous examples taken from the natural sciences.
This  book is also available in German, see below.

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Einführung in Wittgensteins Tractatus Logico-Philosophicus

capturephilosophiebuchLudwig Josef Wittgenstein (1889-1951) veröffentlichte 1921 ein bahnbrechendes Buch der Philosophie: den Tractatus Logico-Philosophicus, oft kurz Tractatus genannt. Das Buch entwickelt eine tiefgreifende Theorie – heute Bildtheorie genannt – über die Bedeutung von Sprache und liefert damit eine allumfassende Antwort auf die Frage, was durch Sprache ausgedrückt werden kann.

Der Tractatus ist zweifellos schwierig zu lesen und zu verstehen. Aus dem Grunde sind eine Anzahl von Einführungen erschienen. Diese Einführungen sind wichtige Beiträge zur Philosophie, aber selber oft recht komplex.

Im Gegensatz dazu entwickelt das vorliegende Buch die fundamentalen Ideen des Tractatus in einfacher, nicht-technischer Sprache. Konzepte und Schlussfolgerungen werden anhand zahlreicher Beispiele aus den Naturwissenschaften erläutert.

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