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.
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 "e;Algebras and Orders"e; as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation.
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.
In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being.
Like the journal TOPOl, the TOPOl Library is based on the assumption that philosophy is a lively, provocative, delightful activity, which constantly challenges our inherited habits, painstakingly elaborates on how things could be different, in other stories, in counterfactual situations, in alternative possible worlds.
Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras.
Intensional logic has emerged, since the 1960' s, as a powerful theoretical and practical tool in such diverse disciplines as computer science, artificial intelligence, linguistics, philosophy and even the foundations of mathematics.
The purpose of this book is to provide the reader who is interested in applications of fuzzy set theory, in the first place with a text to which he or she can refer for the basic theoretical ideas, concepts and techniques in this field and in the second place with a vast and up to date account of the literature.
Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy.
Doing Worlds with Words throws light on the problem of meaning as the meeting point of linguistics, logic and philosophy, and critically assesses the possibilities and limitations of elucidating the nature of meaning by means of formal logic, model theory and model-theoretical semantics.
without a properly developed inconsistent calculus based on infinitesimals, then in- consistent claims from the history of the calculus might well simply be symptoms of confusion.
With the vision that machines can be rendered smarter, we have witnessed for more than a decade tremendous engineering efforts to implement intelligent sys- tems.
