No detailed description available for "A Model Theoretic Oriented Approach to Partial Algebras".

Nowadays algebra is understood basically as the general theory of algebraic oper ations and relations. It is characterised by a considerable intrinsic naturalness of its initial notions and problems, the unity of its methods, and a breadth that far exceeds that of its basic concepts. It is more often that its power begins to be displayed when one moves outside its own limits. This characteristic ability is seen when one investigates not only complete operations, but partial operations. To a considerable extent these are related to algebraic operators and algebraic operations. The tendency to ever greater generality is amongst the reasons that playa role in explaining this development. But other important reasons play an even greater role. Within this same theory of total operations (that is, operations defined everywhere), there persistently arises in its different sections a necessity of examining the emergent feature of various partial operations. It is particularly important that this has been found in those parts of algebra it brings together and other areas of mathematics it interacts with as well as where algebra finds applica tion at the very limits of mathematics. In this connection we mention the theory of the composition of mappings, category theory, the theory of formal languages and the related theory of mathematical linguistics, coding theory, information theory, and algebraic automata theory. In all these areas (as well as in others) from time to time there arises the need to consider one or another partial operation.

This book presents the main ideas of General Galois Theory as a generalization of Classical Galois Theory. It sketches the development of Galois connections through the last three centuries. Examples of Galois connections as powerful tools in Category Theory and Universal Algebra are given. Applications of Galois connections in Linguistic and Data Analysis are presented.

In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.

Theareaofgraphtransformationoriginatedinthelate1960sunderthename “graph grammars” – the main motivation came from practical considerations concerning pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph transformation has grown impressively. The areas include: software speci?cation and development, VLSI layout schemes, database design, modeling of concurrent systems, m- sively parallel computer architectures, logic programming, computer animation, developmentalbiology,musiccomposition,distributedsystems,speci?cationl- guages, software and web engineering, and visual languages. As a matter of fact, graph transformation is now accepted as a fundamental computation paradigm where computation includes speci?cation, programming, and implementation. Over the last three decades the area of graph transfor- tion has developed at a steady pace into a theoretically attractive research ?eld, important for applications. Thisvolume consistsofpapersselectedfromcontributionsto the Sixth Int- national Workshop on Theory and Applications of Graph Transformation that took place in Paderborn, Germany, November 16-20, 1998. The papers und- went an additional refereeing process which yielded 33 papers presented here (out of 55 papers presented at the workshop). This collection of papers provides a very broad snapshot of the state of the art of the whole ?eld today. They are grouped into nine sections representing most active research areas. Theworkshopwasthe sixth in a seriesof internationalworkshopswhich take place every four years. Previous workshops were called “Graph Grammars and Their Application to Computer Science”. The new name of the Sixth Workshop re?ectsmoreaccuratelythecurrentsituation,whereboththeoryandapplication play an equally central role.

This book describes the functional properties and the structural organization of the members of the thrombospondin gene family. These proteins comprise a family of extracellular calcium binding proteins that modulate cellular adhesion, migration and proliferation. Thrombospondin-1 has been shown to function during angiogenesis, wound healing and tumor cell metastasis.

The algebraic specification of abstract data types has been a flourishing research topic in computer science since 1974. The main goal of this work isto evolve theoretical foundations and a methodology to support the design and formal development of reliable software. This volume gives the proceedings of the Eighth Workshop on Specification of Abstract Data Types, held jointly with the Third COMPASS workshop near Paris in August 1991. The main topics covered by the joint workshop are: - specification languagesand program development - algebraic specification of concurrency - theorem proving - object-oriented specifications - order-sorted algebras - abstract implementation and behavioral semantics. The volume contains four invited surveys and twelve contributed papers, all of which underwent a careful refereeing process.