The development of new and improved proof systems, proof formats and
proof search methods is one of the most essential goals of Logic. But
what is a proof? What makes a proof better than another? H...
Abstract algebraic logic is the more general and abstract side of algebraic logic, the branch of mathematics that studies the connections between logics and their algebra-based semantics. This emer...
What exactly is artificial intelligence?
This book is for all those who are curious to learn what artificial intelligence (AI) is. It is a purposely brief introduction to t...
Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy ...
This book presents an overview of the development of the
Axiom of Choice since its introduction by Zermelo at the
beginning of the last century. The book surveys the Axiom of
Choice from three pers...
This volume is dedicated to the memory of Paulo A. S. Veloso (1944-2020), a distinguished Brazilian logician. Veloso's scientific contributions are disseminated in the most important areas ...
Set theory, initially built on the Cantorian extension of number into the infinite and the Zermelian axiomatization affirming a foundation for mathematics, is today a rich and soph...
This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability, classification of complete types, elementary extensions, cat...
This book is a monograph on the topic of Proof-Theoretic Semantics, a theory of meaning constituting an alternative to the more traditional Model-Theoretic Semantics. The latter regards meaning as ...
Mathematics originates with intuition. But intuition alone can only go so far and formalism develops to handle the more difficult problems. Formalism, however, has its inherent dangers. There are ...
Honey bees collect two types of food material; nectar and pollen. With the collection of nectar there is no evidence that there is any selection based on its nutrient value, other than as a sour...
Epistemic logic and, more generally, logics of knowledge and belief, originated with philosophers such as Jaakko Hintikka and David Lewis in the early 1960s. Since then, such logics have played a s...