We dedicate this volume to Professor Parimala on the occasion of her 60th birthday. It contains a variety of papers related to the themes of her research. Parimala's rst striking result was a counterexample to a quadratic analogue of Serre's conjecture (Bulletin of the American Mathematical Society, 1976). Her in uence has cont- ued through her tenure at the Tata Institute of Fundamental Research in Mumbai (1976-2006),and now her time at Emory University in Atlanta (2005-present). A conference was held from 30 December 2008 to 4 January 2009, at the U- versity of Hyderabad, India, to celebrate Parimala's 60th birthday (see the conf- ence's Web site at http://mathstat.uohyd.ernet.in/conf/quadforms2008). The or- nizing committee consisted of J.-L. Colliot-Thel ' en ' e, Skip Garibaldi, R. Sujatha, and V. Suresh. The present volume is an outcome of this event. We would like to thank all the participants of the conference, the authors who have contributed to this volume, and the referees who carefully examined the s- mitted papers. We would also like to thank Springer-Verlag for readily accepting to publish the volume. In addition, the other three editors of the volume would like to place on record their deep appreciation of Skip Garibaldi's untiring efforts toward the nal publication.

Adaptive Resonance Theory Microchips describes circuit strategies resulting in efficient and functional adaptive resonance theory (ART) hardware systems. While ART algorithms have been developed in software by their creators, this is the first book that addresses efficient VLSI design of ART systems. All systems described in the book have been designed and fabricated (or are nearing completion) as VLSI microchips in anticipation of the impending proliferation of ART applications to autonomous intelligent systems. To accommodate these systems, the book not only provides circuit design techniques, but also validates them through experimental measurements. The book also includes a chapter tutorially describing four ART architectures (ART1, ARTMAP, Fuzzy-ART and Fuzzy-ARTMAP) while providing easily understandable MATLAB code examples to implement these four algorithms in software. In addition, an entire chapter is devoted to other potential applications for real-time data clustering and category learning.

Text Retrieval and Filtering: Analytical Models of Performance is the first book that addresses the problem of analytically computing the performance of retrieval and filtering systems. The book describes means by which retrieval may be studied analytically, allowing one to describe current performance, predict future performance, and to understand why systems perform as they do. The focus is on retrieving and filtering natural language text, with material addressing retrieval performance for the simple case of queries with a single term, the more complex case with multiple terms, both with term independence and term dependence, and for the use of grammatical information to improve performance. Unambiguous statements of the conditions under which one method or system will be more effective than another are developed. Text Retrieval and Filtering: Analytical Models of Performance focuses on the performance of systems that retrieve natural language text, considering full sentences as well as phrases and individual words. The last chapter explicitly addresses how grammatical constructs and methods may be studied in the context of retrieval or filtering system performance. The book builds toward solving this problem, although the material in earlier chapters is as useful to those addressing non-linguistic, statistical concerns as it is to linguists. Those interested in grammatical information should be cautioned to carefully examine earlier chapters, especially Chapters 7 and 8, which discuss purely statistical relationships between terms, before moving on to Chapter 10, which explicitly addresses linguistic issues. Text Retrieval and Filtering: Analytical Models of Performance is suitable as a secondary text for a graduate level course on Information Retrieval or Linguistics, and as a reference for researchers and practitioners in industry.

Mathematics is often considered as a body of knowledge that is essen tially independent of linguistic formulations, in the sense that, once the content of this knowledge has been grasped, there remains only the problem of professional ability, that of clearly formulating and correctly proving it. However, the question is not so simple, and P. Weingartner's paper (Language and Coding-Dependency of Results in Logic and Mathe matics) deals with some results in logic and mathematics which reveal that certain notions are in general not invariant with respect to different choices of language and of coding processes. Five example are given: 1) The validity of axioms and rules of classical propositional logic depend on the interpretation of sentential variables; 2) The language dependency of verisimilitude; 3) The proof of the weak and strong anti inductivist theorems in Popper's theory of inductive support is not invariant with respect to limitative criteria put on classical logic; 4) The language-dependency of the concept of provability; 5) The language dependency of the existence of ungrounded and paradoxical sentences (in the sense of Kripke). The requirements of logical rigour and consistency are not the only criteria for the acceptance and appreciation of mathematical proposi tions and theories.

This book presents the general theory of categorical closure operators to gether with a number of examples, mostly drawn from topology and alge bra, which illustrate the general concepts in several concrete situations. It is aimed mainly at researchers and graduate students in the area of cate gorical topology, and to those interested in categorical methods applied to the most common concrete categories. Categorical Closure Operators is self-contained and can be considered as a graduate level textbook for topics courses in algebra, topology or category theory. The reader is expected to have some basic knowledge of algebra, topology and category theory, however, all categorical concepts that are recurrent are included in Chapter 2. Moreover, Chapter 1 contains all the needed results about Galois connections, and Chapter 3 presents the the ory of factorization structures for sinks. These factorizations not only are essential for the theory developed in this book, but details about them can not be found anywhere else, since all the results about these factorizations are usually treated as the duals of the theory of factorization structures for sources. Here, those hard-to-find details are provided. Throughout the book I have kept the number of assumptions to a min imum, even though this implies that different chapters may use different hypotheses. Normally, the hypotheses in use are specified at the beginning of each chapter and they also apply to the exercise set of that chapter."

Industrial development is essential to improvement of the standard of living in all countries. People's health and the environment can be affected, directly or indirectly by routine waste discharges or by accidents. A series of recent major industrial accidents and the effect of pollution highlighted, once again, the need for better management of routine and accidental risks. Moreover, the existence of natural hazards complicate even more the situation in any given region. In the past effort to cope with these risks, if made at all, have been largely on a plant by plant basis; some plants are well equipped to manage environmental and health hazards, while others are not. Managing the hazards of modern technological systems has become a key activity in highly industrialised countries. Decision makers are often confronted with complex issues concerning economic and social development, industrialisation and associated infrastructure needs, population and land use planning. Such issues have to be addressed in such a way that ensures that public health will not be disrupted or substantially degraded. Due to the increasing complexity of technological systems and the higher geographical density of punctual hazard sources, new methodologies and a novel approach to these problems are challenging risk managers and regional planers. Risks from these new complex technological systems are inherently different form those addressed by the risk managers for decades ago.

The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson, Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within the framework of this theory, algorithmic properties of abstract models are investigated by constructing representations on the set of natural numbers and studying relations between algorithmic and structural properties of these models. This book is a very readable exposition of the modern theory of constructive models and describes methods and approaches developed by representatives of the Siberian school of algebra and logic and some other researchers (in particular, Nerode and his colleagues). The main themes are the existence of recursive models and applications to fields, algebras, and ordered sets (Ershov), the existence of decidable prime models (Goncharov, Harrington), the existence of decidable saturated models (Morley), the existence of decidable homogeneous models (Goncharov and Peretyat'kin), properties of the Ehrenfeucht theories (Millar, Ash, and Reed), the theory of algorithmic dimension and conditions of autostability (Goncharov, Ash, Shore, Khusainov, Ventsov, and others), and the theory of computable classes of models with various properties. Future perspectives of the theory of constructive models are also discussed. Most of the results in the book are presented in monograph form for the first time. The theory of constructive models serves as a basis for recursive mathematics. It is also useful in computer science, in particular, in the study of programming languages, higher level languages of specification, abstract data types, and problems of synthesis and verification of programs. Therefore, the book will be useful for not only specialists in mathematical logic and the theory of algorithms but also for scientists interested in the mathematical fundamentals of computer science. The authors are eminent specialists in mathematical logic. They have established fundamental results on elementary theories, model theory, the theory of algorithms, field theory, group theory, applied logic, computable numberings, the theory of constructive models, and the theoretical computer science.

Geometric properties and relations play central roles in the description and processing of spatial data. The properties and relations studied by mathematicians usually have precise definitions, but verbal descriptions often involve imprecisely defined concepts such as elongatedness or proximity. The methods used in soft computing provide a framework for formulating and manipulating such concepts. This volume contains eight papers on the soft definition and manipulation of spatial relations and gives a comprehensive summary on the subject.

Reasoning and Unification over Conceptual Graphs is an exploration of automated reasoning and resolution in the expanding field of Conceptual Structures. Designed not only for computing scientists researching Conceptual Graphs, but also for anyone interested in exploring the design of knowledge bases, the book explores what are proving to be the fundamental methods for representing semantic relations in knowledge bases. While it provides the first comprehensive treatment of Conceptual Graph unification and reasoning, the book also addresses fundamental issues of graph matching, automated reasoning, knowledge bases, constraints, ontology and design. With a large number of examples, illustrations, and both formal and informal definitions and discussions, this book is excellent as a tutorial for the reader new to Conceptual Graphs, or as a reference book for a senior researcher in Artificial Intelligence, Knowledge Representation or Automated Reasoning.

Domain theory is a rich interdisciplinary area at the intersection of logic, computer science, and mathematics. This volume contains selected papers presented at the International Symposium on Domain Theory which took place in Shanghai in October 1999. Topics of papers range from the encounters between topology and domain theory, sober spaces, Lawson topology, real number computability and continuous functionals to fuzzy modelling, logic programming, and pi-calculi. This book is a valuable reference for researchers and students interested in this rapidly developing area of theoretical computer science.

Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are quite common. In Fuzzy Data Analysis the authors collect their recent results providing the reader with ideas, approaches and methods for processing such data when looking for sub-structures in knowledge bases for an evaluation of functional relationship, e.g. in order to specify diagnostic or control systems. The modelling presented uses ideas from fuzzy set theory and the suggested methods solve problems usually tackled by data analysis if the data are real numbers. Fuzzy Data Analysis is self-contained and is addressed to mathematicians oriented towards applications and to practitioners in any field of application who have some background in mathematics and statistics.

Formal Languages and Applications provides a comprehensive study-aid and self-tutorial for graduates students and researchers. The main results and techniques are presented in an readily accessible manner and accompanied by many references and directions for further research. This carefully edited monograph is intended to be the gateway to formal language theory and its applications, so it is very useful as a review and reference source of information in formal language theory.

The importance of having ef cient and effective methods for data mining and kn- ledge discovery (DM&KD), to which the present book is devoted, grows every day and numerous such methods have been developed in recent decades. There exists a great variety of different settings for the main problem studied by data mining and knowledge discovery, and it seems that a very popular one is formulated in terms of binary attributes. In this setting, states of nature of the application area under consideration are described by Boolean vectors de ned on some attributes. That is, by data points de ned in the Boolean space of the attributes. It is postulated that there exists a partition of this space into two classes, which should be inferred as patterns on the attributes when only several data points are known, the so-called positive and negative training examples. The main problem in DM&KD is de ned as nding rules for recognizing (cl- sifying) new data points of unknown class, i. e. , deciding which of them are positive and which are negative. In other words, to infer the binary value of one more attribute, called the goal or class attribute. To solve this problem, some methods have been suggested which construct a Boolean function separating the two given sets of positive and negative training data points.

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, a trilattice of truth values - a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi.

From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data." There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.

Chapter 1 The algebraic prerequisites for the book are covered here and in the appendix. This chapter should be used as reference material and should be consulted as needed. A systematic treatment of algebras, coalgebras, bialgebras, Hopf algebras, and represen tations of these objects to the extent needed for the book is given. The material here not specifically cited can be found for the most part in [Sweedler, 1969] in one form or another, with a few exceptions. A great deal of emphasis is placed on the coalgebra which is the dual of n x n matrices over a field. This is the most basic example of a coalgebra for our purposes and is at the heart of most algebraic constructions described in this book. We have found pointed bialgebras useful in connection with solving the quantum Yang-Baxter equation. For this reason we develop their theory in some detail. The class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras. We note the quantized enveloping algebras described Hopf algebras. Thus for many reasons pointed bialgebras are elsewhere are pointed of fundamental interest in the study of the quantum Yang-Baxter equation and objects quantum groups.

This book presents a unifying framework for using priority arguments to prove theorems in computability. Priority arguments provide the most powerful theorem-proving technique in the field, but most of the applications of this technique are ad hoc, masking the unifying principles used in the proofs. The proposed framework presented isolates many of these unifying combinatorial principles and uses them to give shorter and easier-to-follow proofs of computability-theoretic theorems. Standard theorems of priority levels 1, 2, and 3 are chosen to demonstrate the framework's use, with all proofs following the same pattern. The last section features a new example requiring priority at all finite levels. The book will serve as a resource and reference for researchers in logic and computability, helping them to prove theorems in a shorter and more transparent manner.

This book collects the papers presented at the 4th International Workshop on Logic, Rationality and Interaction/ (LORI-4), held in October 2013 at the /Center for the Study of Language and Cognition, Zhejiang University, Hangzhou, China. LORI is a series that brings together researchers from a variety of logic-related fields: Game and Decision Theory, Philosophy, Linguistics, Computer Science and AI. This year had a special emphasis on Norms and Argumentation. Out of 42 submissions, 23 full papers and 11 short contributions have been selected through peer-review for inclusion in the workshop program and in this volume. The quality and diversity of these contributions witnesses a lively, fast-growing, and interdisciplinary community working at the intersection of logic and rational interaction.

Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications range from a proof of the rationality of certain Poincare series associated to varieties over p-adic fields, to a proof of the Mordell-Lang conjecture for function fields in positive characteristic. In some cases (such as the latter) it is the most abstract aspects of model theory which are relevant. This book, originally published in 2000, arising from a series of introductory lectures for graduate students, provides the necessary background to understanding both the model theory and the mathematics behind these applications. The book is unique in that the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations) is covered and diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) are introduced and discussed, all by leading experts in their fields.

Quantitative Evaluation of Fire and EMS Mobilization Times presents comprehensive empirical data on fire emergency and EMS call processing and turnout times, and aims to improve the operational benchmarks of NFPA peer consensus standards through a close examination of real-world data. The book also identifies and analyzes the elements that can influence EMS mobilization response times. Quantitative Evaluation of Fire and EMS Mobilization Times is intended for practitioners as a tool for analyzing fire emergency response times and developing methods for improving them. Researchers working in a related field will also find the book valuable.

Compactness in topology and finite generation in algebra are nice properties to start with. However, the study of compact spaces leads naturally to non-compact spaces and infinitely generated chain complexes; a classical example is the theory of covering spaces. In handling non-compact spaces we must take into account the infinity behaviour of such spaces. This necessitates modifying the usual topological and algebraic cate gories to obtain "proper" categories in which objects are equipped with a "topologized infinity" and in which morphisms are compatible with the topology at infinity. The origins of proper (topological) category theory go back to 1923, when Kere kjart6 [VT] established the classification of non-compact surfaces by adding to orien tability and genus a new invariant, consisting of a set of "ideal points" at infinity. Later, Freudenthal [ETR] gave a rigorous treatment of the topology of "ideal points" by introducing the space of "ends" of a non-compact space. In spite of its early ap pearance, proper category theory was not recognized as a distinct area of topology until the late 1960's with the work of Siebenmann [OFB], [IS], [DES] on non-compact manifolds.

Henkin-Keisler models emanate from a modification of the Henkin construction introduced by Keisler to motivate the definition of ultraproducts. Keisler modified the Henkin construction at that point at which 'new' individual constants are introduced and did so in a way that illuminates a connection between Henkin-Keisler models and ultraproducts. The resulting construction can be viewed both as a specialization of the Henkin construction and as an alternative to the ultraproduct construction. These aspects of the Henkin-Keisler construction are utilized here to present a perspective on ultraproducts and their applications accessible to the reader familiar with Henkin's proof of the completeness of first order logic and naive set theory. This approach culminates in proofs of various forms of the Keisler-Shelah characterizations of elementary equivalence and elementary classes via Henkin-Keisler models. The presentation is self-contained and proofs of more advanced results from set theory are introduced as needed. Audience: Logicians in philosophy, computer science, linguistics and mathematics.

The theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology, linguistics, mathematics, sociology, physics. The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original Aristotelian theory.

The square of opposition from its origin in antiquity to the present day continues to exert a profound impact on the development of deductive logic. Since 10 years there is a new growing interest for the square due to recent discoveries and challenging interpretations. This book presents a collection of previously unpublished papers by high level specialists on the square from all over the world.

This is the first book on cut-elimination in first-order predicate logic from an algorithmic point of view. Instead of just proving the existence of cut-free proofs, it focuses on the algorithmic methods transforming proofs with arbitrary cuts to proofs with only atomic cuts (atomic cut normal forms, so-called ACNFs). The first part investigates traditional reductive methods from the point of view of proof rewriting. Within this general framework, generalizations of Gentzen's and Sch\"utte-Tait's cut-elimination methods are defined and shown terminating with ACNFs of the original proof. Moreover, a complexity theoretic comparison of Gentzen's and Tait's methods is given.

The core of the book centers around the cut-elimination method CERES (cut elimination by resolution) developed by the authors. CERES is based on the resolution calculus and radically differs from the reductive cut-elimination methods. The book shows that CERES asymptotically outperforms all reductive methods based on Gentzen's cut-reduction rules. It obtains this result by heavy use of subsumption theorems in clause logic. Moreover, several applications of CERES are given (to interpolation, complexity analysis of cut-elimination, generalization of proofs, and to the analysis of real mathematical proofs). Lastly, the book demonstrates that CERES can be extended to nonclassical logics, in particular to finitely-valued logics and to G\"odel logic.