## Theory and Applications of Relational Structures as Knowledge Instruments II: International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers, Volume 2Harrie de Swart, Ewa Orlowska, Gunther Schmidt, Marc Roubens 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. |

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### Contents

Social Software for Coalition Formation | 1 |

Investigating Finite Models of Nonclassical Logics with Relation Algebra and RelView | 31 |

On the Logic of Medical Decision Support | 50 |

Generalizing and Modifying the HoedeBakker Index | 60 |

Relational Presentation of Nonclassical Logics | 89 |

Relational Approach to OrderofMagnitude Reasoning | 105 |

Relational Logics and Their Applications | 125 |

An Algebraic Approach Based on Residuated Lattices | 162 |

General Representation Theorems for Fuzzy Weak Orders | 229 |

A Survey | 245 |

LatticeBased Relation Algebras II | 267 |

Some Aspects of Lattice and Generalized Prelattice Effect Algebras | 290 |

A Decision Procedure for Monotone Functions over Bounded and Complete Lattices | 318 |

The Dominance Relation on the Class of Continuous TNorms from an Ordinal Sum Point of View | 334 |

Aggregation on Bipolar Scales | 355 |

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Aggregation of Fuzzy Relations and Preservation of Transitivity | 185 |

Flexible Query Answering Using DistanceBased Fuzzy Relations | 207 |

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aggregation operators application assume atomic axioms binary operation binary relations BLmf Boolean algebras bounded lattice canonical frame coalition formation complete complex algebra Computer Science consider deﬁned Deﬁnition denote diﬀerent distributive lattices dominance relationship doubly ordered set eﬀect equivalence relation ER-lattice example exists filter-ideal pair ﬁnite ﬁrst ﬂexible formula fulﬁlls function fuzzy orderings fuzzy relations Fuzzy Sets fuzzy weak orders gd(Bi Hence Hoede-Bakker index idempotent implies inclination vectors isomorphic L-fuzzy language lattice effect algebra LCPR algebra Lemma modal logic MV-algebras MV-effect algebra negation non-classical logics obtain ordinal sum t-norms Orlowska orthomodular lattice partial order party player prelattice properties Proposition query Re(OM relation algebras relational proof system relational terms representation residuated lattices resp respect rules satisﬁed satisfying Section semantics speciﬁc subset Swart TARSKI Theorem theory Tl{X translation triangular norm variables