Related papers: Foundations
In this report, a novel approach to intelligence and learning is introduced, this approach is based on what we call 'perception logic'. Based on this logic, a computing mechanism and automata are introduced. Multi-resolution analysis of…
The paper is an introduction to intuitionistic mathematics.
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
Mathematicians judge proofs to possess, or lack, a variety of different qualities, including, for example, explanatory power, depth, purity, beauty and fit. Philosophers of mathematical practice have begun to investigate the nature of such…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
We show that a proof in multiplicative linear logic can be represented as a decorated surface, such that two proofs are logically equivalent just when their surfaces are geometrically equivalent. This is an extended abstract for…
This article reformulates the theory of computable physical models, previously introduced by the author, as a branch of applied model theory in first-order logic. It provides a semantic approach to the philosophy of science that…
This paper presents a systematic survey on existing literature and seminal works relevant to the application of ontologies in different aspects of Cloud computing. Our hypothesis is that ontologies along with their reasoning capabilities…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
In this book we promote logical computational linguistics as opposed to statistical computational linguistics. In particular, we provide a logical semantic interface. This book assembles more than twenty years of research work on type…
Theoretical computer science has found fertile ground in many areas of mathematics. The approach has been to consider classical problems through the prism of computational complexity, where the number of basic computational steps taken to…
In this introductory chapter, we lay the groundwork for the rest of the book by providing a more detailed picture of the expected purpose, shape, and architecture of future grid systems. We structure the chapter in terms of six questions…
The intention of these notes is to give a mathematical account of how I believe students could be taught to think about functional programming languages and to explain how such languages work.
This soliloquy outlines some naive philosophical arguments underlying the thesis that mathematics ought to be viewed simply as a universal set of languages, some of precise expression, and some of effective communication.
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students'…
We apply a paraconsistent logic to reason about fractions.
In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the…