Harrie de Swart - Böcker

This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science.

This graduate textbook introduces to social choice theory, with a specific focus on elections and fair division, supported by mathematical theories and practical implications. Part I sheds light on the complexity of fair elections, and presents classical results from social choice theory, including May's, Arrow's, and Gibbard-Satterthwaite's theorems, and how they impact the organization of fair elections. They also discuss the measurement of voting power in such elections via the Penrose-Banzhaf index and the Shapley-Shubik index. Besides these more or less classical topics, the authors introduce Balinski and Laraki's transformative Majority Judgment framework.  Moreover, Part I concludes by critically addressing flaws in contemporary Western democracies and proposing an alternative political system.In Part II, the book dissects claims-based and preference-based fair division, explaining that the focus will be on the former. In particular, the focus will be on models that can elaborate on and make precise the thought that `fairness requires that claims are satisfied in proportion to their strength’,  as advocated for in the philosophical literature. The authors scrutinize various formal models, ranging from (weighted) bankruptcy problems to cooperative games, assessing their alignment with this claims-based conception of fairness. Part II concludes with a brief overview of preference-based fair division. This textbook is a crucial resource for graduate and advanced undergraduate students and scholars, bridging the worlds of mathematics, philosophy, political theory, and social justice.

Relational structures abound in our daily environment: relational databases, data mining, scaling procedures, preference relations, etc. As the documentation of scientific results achieved within the European COST Action 274, TARSKI, this book advances the understanding of relational structures and the use of relational methods in various application fields.The 12 revised full papers were carefully reviewed and selected for presentations. The papers are devoted to mechanization of relational reasoning, relational scaling and preferences, and algebraic and logical foundations of real world relations.

This book is a follow-up of LNCS volume 2929 with the same title, and presents the major results of COST action 274 (2002-2005), TARSKI: Theory and - plications of Relational Structures as Knowledge Instruments. Relational structures abound in the daily environment: relational databases, data-mining, scaling procedures, preference relations, etc. Reasoning about, and with, relations has a long-standing European tradition, which may be divided into three broad areas: 1. Algebraic Logic: algebras of relations, relational semantics, and algebras and logics derived from information systems. 2. Computational Aspects of Automated Relational Reasoning: decidability and complexity of algorithms, network satisfaction. 3. Applications: social choice, AI, linguistics, psychology, economics, etc. The main objective of the ?rst TARSKI book (LNCS 2929) was to advance the understanding of relational structures and the use of relational methods in applicable object domains. There were the following sub-objectives: 1. Tostudythesemanticalandsyntacticalaspectsofrelationalstructuresarising from ‘real world’ situations 2. To investigateautomatedinference for relationalsystems, and, wherepossible or feasible, develop deductive systems which can be implemented into industrial applications, such as diagnostic systems 3. To develop non-invasive scaling methods for predicting relational data 4. To make software for dealing with relational systems commonly available We are con?dent that the present book will further the understanding of int- disciplinary issues involving relational reasoning. This book consists of papers which give a clear and self-contained overview of the results obtained by the TARSKI action, typically obtained by di?erent persons from di?erent work - eas.