THIRTY FIVE YEARS OF AUTOMATING MATHEMATICS: DEDICATED TO 35 YEARS OF DE BRUIJN'S AUTOMATH N. G. de Bruijn was a well established mathematician before deciding in 1967 at the age of 49 to work on a new direction related to Automating Mathematics. By then, his contributions in mathematics were numerous and extremely influential. His book on advanced asymptotic methods, North- Holland 1958, was a classic and was subsequently turned into a book in the well known Dover book series. His work on combinatorics yielded influential notions and theorems of which we mention the de Bruijn-sequences of...
THIRTY FIVE YEARS OF AUTOMATING MATHEMATICS: DEDICATED TO 35 YEARS OF DE BRUIJN'S AUTOMATH N. G. de Bruijn was a well established mathematician before...
Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-application of functions was at the heart of Russell's paradox. This led Russell to introduce type theory in order to avoid the paradox. Since, the twentieth century has seen an amazing number of theories concerned with types and functions and many applications. Progress in computer science also meant more and more emphasis on the use of logic, types and functions to study the syntax, semantics, design and implementation of programming languages and theorem provers,...
Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-application of functions...
This monograph provides a new account of justified inference as a cognitive process. In contrast to the prevailing tradition in epistemology, the focus is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe and analyze such inferences.
Part 1 gives a purely system-theoretic explication of belief and...
This monograph provides a new account of justified inference as a cognitive process. In contrast to the prevailing tradition in epistemology, the f...
This is the first book on automated model building, a discipline of automated deduction that is of growing importance. Although models and their construction are important per se, automated model building has appeared as a natural enrichment of automated deduction, especially in the attempt to capture the human way of reasoning. The book provides an historical overview of the field of automated deduction, and presents the foundations of different existing approaches to model construction, in particular those developed by the authors. Finite and infinite model building techniques are...
This is the first book on automated model building, a discipline of automated deduction that is of growing importance. Although models and their co...
The creation of intelligent robots is surely one of the most exciting and ch- lenginggoals of Arti?cial Intelligence. A robot is, ?rst of all, nothing but an inanimate machine with motors and sensors. In order to bring life to it, the machine needs to be programmed so as to make active use of its hardware c- ponents. This turns a machine into an autonomous robot. Since about the mid nineties of the past century, robot programming has made impressive progress. State-of-the-art robots are able to orient themselves and move around freely in indoor environments or negotiate di?cult outdoor...
The creation of intelligent robots is surely one of the most exciting and ch- lenginggoals of Arti?cial Intelligence. A robot is, ?rst of all, nothing...
This book identifies important recent developments in intensional logic, a branch of logic with applications in linguistics, cognitive science, artificial intelligence, philosophy and computer science. The main themes of the book are proof theory, descriptive uses, applications, and foundations of intensional logic.
This book identifies important recent developments in intensional logic, a branch of logic with applications in linguistics, cognitive science, artifi...
This book is the most comprehensive description of the decades-long Non-Axiomatic Reasoning System (NARS) project, including its philosophical foundation, methodological consideration, conceptual design details, implications in the related fields, and its similarities and differences to many related works in cognitive science. While most current works in Artificial Intelligence (AI) focus on individual aspects of intelligence and cognition, NARS is designed and developed to attack the AI problem as a whole.
This book is the most comprehensive description of the decades-long Non-Axiomatic Reasoning System (NARS) project, including its philosophical foun...
Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature (for instance, two Hilbert calculi or a Hilbert calculus and a tableau calculus). The important issue of preservation of properties is extensively addressed. For instance,...
Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and de...
Hybrid Logic and its Proof-Theory demonstrates that hybrid-logical proof-theory remedies the lack of uniformity in ordinary modal-logical proof systems. Various versions and proof systems for hybrid logic are considered, providing a detailed overview of the topic.
Hybrid Logic and its Proof-Theory demonstrates that hybrid-logical proof-theory remedies the lack of uniformity in ordinary modal-logical proof system...
