Foundations Of The Formal Sciences Ii

"Foundations of the Formal Sciences" (FotFS) is a series of interdisciplinary conferences in mathematics, philosophy, computer science and linguistics. The main goal is to reestablish the traditionally strong links between these areas of research that have been lost in the past decades. The second conference in the series had the subtitle "Applications of Mathematical Logic in Philosophy and Linguistics" and brought speakers from all parts of the Formal Sciences together to give a holistic view of how mathematical methods can improve our philosophical and technical understanding of language and scientific discourse, ranging from the theoretical level up to applications in language recognition software. Audience: This volume is of interest to all formal philosophers and theoretical linguists. In addition to that, logicians interested in the applications of their field and logic students in mathematics, computer science, philosophy and linguistics can use the volume to broaden their knowledge of applications of logic.

This volume takes a reflective position with respect to the conference series "Foundations of the Formal Sciences" (FotFS) and asks: * What are the Formal Sciences? * Can we develop a theoretical classification of the sciences that juxtaposes the formal sciences to the natural sciences, social sciences, and humanities? Can we do this solely by identifying common methodological features? * Can we identify changes of the notion of formal sciences over time? How were the areas that we now conceived as the "Foundations of the Formal Sciences" classified throughout history? Investigating the "History of the Concept of the Formal Sciences" to find answers to an array of questions with this wide scope, you need an enthusiastic group of researchers interested in going beyond the traditional boundaries of their subjects covering at once the philosophical, historical and logical issues at hand, like the authors of this volume. The papers in this volume stand witness to our success in touching the mentioned questions. It will be of interest to philosophers, sociologists, historians, and logicians, and covers many aspects of the history of the formal sciences from the Bronze Age to the early XXIst century.

Probabilistic methods are increasingly becoming an important tool in a variety of disciplines including computer science, mathematics, artificial intelligence, epistemology, game and

Philosophy and sociology of science aim at understanding the workings of scientific endeavour. Despite their different emphasis and methodology, they deal with the same subject matter; and yet, they seem to be worlds apart. In the course of the last few decades, steps have been taken towards a (partial) reconciliation. The conference FotFS VII was part of this process, bringing sociological aspects into philosophy of science and philosophical aspects into sociology of science. Since the FotFS conference series focusses on the formal sciences, the conference had a certain, but non-exclusive focus on the role of mathematics as one of the sciences covered by philosophy and sociology. FotFS VII was organized by the research network PhiMSAMP Philosophy of Mathematics: Sociological Aspects and Mathematical Practice. A volume documenting the work of this network has already been published in the series Texts in Philosophy and covers specific questions linking philosophical issues in mathematics to mathematical practice. The present volume provides the general methodological background for the work done by the PhiMSAMP network. It contains fully refereed versions of papers presented at the seventh installment of the conference series Foundations of the Formal Sciences (FotFS).

This book provides foundations for software specification and formal software development from the perspective of work on algebraic specification, concentrating on developing basic concepts and studying their fundamental properties. These foundations are built on a solid mathematical basis, using elements of universal algebra, category theory and logic, and this mathematical toolbox provides a convenient language for precisely formulating the concepts involved in software specification and development. Once formally defined, these notions become subject to mathematical investigation, and this interplay between mathematics and software engineering yields results that are mathematically interesting, conceptually revealing, and practically useful. The theory presented by the authors has its origins in work on algebraic specifications that started in the early 1970s, and their treatment is comprehensive. This book contains five kinds of material: the requisite mathematical foundations; traditional algebraic specifications; elements of the theory of institutions; formal specification and development; and proof methods. While the book is self-contained, mathematical maturity and familiarity with the problems of software engineering is required; and in the examples that directly relate to programming, the authors assume acquaintance with the concepts of functional programming. The book will be of value to researchers and advanced graduate students in the areas of programming and theoretical computer science.