This book examines how epistemology was reinvented by Ibn Sina, an influential philosopher-scientist of the classical Islamic world who was known to the West by the Latinised name Avicenna.
This textbook addresses the mathematical description of sets, categories, topologies and measures, as part of the basis for advanced areas in theoretical computer science like semantics, programming languages, probabilistic process algebras, modal and dynamic logics and Markov transition systems.
This book provides an overview of the confluence of ideas in Turing's era and work and examines the impact of his work on mathematical logic and theoretical computer science.
This book offers an original contribution to the foundations of logic and mathematics and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry.
The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring.
This Brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of Lukasiewicz infinite-valued logic.
This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology and even the history of philosophy.
A group of 100 prisoners, all together in the prison dining area, are told that they will be all put in isolation cells and then will be interrogated one by one in a room containing a light with an on/off switch.
Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials.
This volume tackles Godel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained.
This is a comprehensive book on the life and works of Leon Henkin (1921-2006), an extraordinary scientist and excellent teacher whose writings became influential right from the beginning of his career with his doctoral thesis on "e;The completeness of formal systems"e; under the direction of Alonzo Church.
This book constitutes the refereed proceedings of the Joint 25th International Conference on Rewriting Techniques and Applications, RTA 2014, and 12th International Conference on Typed Lambda-Calculi and Applications, TLCA 2014, held as part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014.
In this new text, Steven Givant-the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski-develops three theories of duality for Boolean algebras with operators.
This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students.
This book brings together contributions by leading researchers in computational complexity theory written in honor of Somenath Biswas on the occasion of his sixtieth birthday.
This volume presents recent advances in philosophical logic with chapters focusing on non-classical logics, including paraconsistent logics, substructural logics, modal logics of agency and other modal logics.
This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics.
This volume celebrates the work of Petr Hajek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work.
This volume is the first systematic and thorough attempt to investigate the relation and the possible applications of mereology to contemporary science.
The problem of probability interpretation was long overlooked before exploding in the 20th century, when the frequentist and subjectivist schools formalized two conflicting conceptions of probability.
The first part of this book is of an epistemological nature and develops an original theory of scientific objectivity, understood in a weak sense (as intersubjective agreement among the specialists) and a strong sense (as having precise concrete referents).
This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena.
This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects.
While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light.
This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics.
This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Lesniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school.
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia.
