"e;In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual.
The thirty-one papers collected in this volume represent most of the arti- cles that I have published in the philosophy of science and related founda- tional areas of science since 1970.
The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science.
Domains are mathematical structures for information and approximation; they combine order-theoretic, logical, and topological ideas and provide a natural framework for modelling and reasoning about computation.
The present monograph is a slightly revised version of my Habilitations- schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997.
Proof theory and category theory were first drawn together by Lambek some 30 years ago but, until now, the most fundamental notions of category theory (as opposed to their embodiments in logic) have not been explained systematically in terms of proof theory.
During the last few decades the ideas, methods, and results of the theory of Boolean algebras have played an increasing role in various branches of mathematics and cybernetics.
Metric fixed point theory encompasses the branch of fixed point theory which metric conditions on the underlying space and/or on the mappings play a fundamental role.
This volume, the 6th volume in the DRUMS Handbook series, is part of the after- math of the successful ESPRIT project DRUMS (Defeasible Reasoning and Un- certainty Management Systems) which took place in two stages from 1989-1996.
This volume, the 7th volume in the DRUMS Handbook series, is part of the aftermath of the successful ESPRIT project DRUMS (Defeasible Reasoning and Uncertainty Management Systems) which took place in two stages from 1989- 1996.
Reasoning under uncertainty is always based on a specified language or for- malism, including its particular syntax and semantics, but also on its associated inference mechanism.
Fuzzy Sets, Logics and Reasoning about Knowledge reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning.
It took many decades for Peirce's coneept of a relation to find its way into the microelectronic innards of control systems of eement kilns, subway trains, and tunnel-digging machinery.
Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research.
Dynamic Fuzzy Pattern Recognition with Applications to Finance and Engineering focuses on fuzzy clustering methods which have proven to be very powerful in pattern recognition and considers the entire process of dynamic pattern recognition.
This book is devoted to some results from the classical Point Set Theory and their applications to certain problems in mathematical analysis of the real line.
The larger part of Yearbook 6 of the Institute Vienna Circle constitutes the proceedings of a symposium on Alfred Tarski and his influence on and interchanges with the Vienna Circle, especially those on and with Rudolf Carnap and Kurt Godel.
From the very beginning of their investigation of human reasoning, philosophers have identified two other forms of reasoning, besides deduction, which we now call abduction and induction.
Quantifiers: Logics, Models and Computation is the first concentrated effort to give a systematic presentation of the main research results on the subject, since the modern concept was formulated in the late '50s and early '60s.
This is the first of two volumes comprising the papers submitted for publication by the invited participants to the Tenth International Congress of Logic, Methodology and Philosophy of Science, held in Florence, August 1995.
The past fifteen years has witnessed an explosive growth in the fundamental research and applications of artificial neural networks (ANNs) and fuzzy logic (FL).
This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan- dardization of the mathematics of fuzzy sets established in the "e;Handbook"e;, namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish- ers, 1999).
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents.
This book is an example of fruitful interaction between (non-classical) propo- sitionallogics and (classical) model theory which was made possible due to categorical logic.
After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975).
At first glance, Robinson's original form of nonstandard analysis appears nonconstructive in essence, because it makes a rather unrestricted use of classical logic and set theory and, in particular, of the axiom of choice.
In the last years, it was observed an increasing interest of computer scientists in the structure of biological molecules and the way how they can be manipulated in vitro in order to define theoretical models of computation based on genetic engineering tools.
