Academic literature on the topic 'Sketch formalization'

This paper sketches or signals some ideas, results, and proposals connected with the theoretical issues related to the categorial approach to language which originated from the first author (1985, 1989, 1991, 1998) and which form the basis for further research by the second author. The main aims are the following: 1) to bring into common use some Polish ideas concerned with classical categorial grammar; 2) to take into consideration a universal and simultaneously formal-logical perspective; 3) to consider Peirce's well-known differentiation of linguistic objects, i.e. their twofold ontological status as tokens (concretes) and types (abstract objects) and, according to this, to consider the biaspectual formalization of language dealing with the two main orientations in the controversy between nominalism and Platonism; 4) to characterize language according to Frege's ontological canons, according to which each expression of language corresponds to its denotation. All of these factors make possible not only the syntactic characterization of language but also the introduction of syntactic and semantic definitions of a true expression and its denotation. These notions correspond here to the old classical, but not necessarily standard, understanding of semantic concepts. The paper is divided into four sections: the first contains a brief characterization of the categorial approach to syntax; the second presents two strains of this approach; the third touches on certain general semantic issues connected with the notion of truth; and the last gives some final remarks.

“Appreciate the process, by taking a random walk” offers a basic introduction to random walks—a mathematical formalization for a path as an object wanders away from a starting point—with a particular focus on biased random walks, including a real-life example of a random walk of an E. coli bacterium. The discussion is illustrated with hand-drawn sketches. Mathematics students and enthusiasts are encouraged to build in a productive bias in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

This book is to be an accessible book on patterns, their representation, and inference. There are a small number of ideas and techniques that, when mastered, make the subject more accessible. This book has arisen from ten years of a research program which the authors have embarked upon, building on the more abstract developments of metric pattern theory developed by one of the authors during the 1970s and 1980s. The material has been taught over multiple semesters as part of a second year graduate-level course in pattern theory, essentially an introduction for students interested in the representation of patterns which are observed in the natural world. The course has attracted students studying biomedical engineering, computer science, electrical engineering, and applied mathematics interested in speech recognition and computational linguistics, as well as areas of image analysis, and computer vision. Now the concept of patterns pervades the history of intellectual endeavor; it is one of the eternal followers in human thought. It appears again and again in science, taking on different forms in the various disciplines, and made rigorous through mathematical formalization. But the concept also lives in a less stringent form in the humanities, in novels and plays, even in everyday language. We use it all the time without attributing a formal meaning to it and yet with little risk of misunderstanding. So, what do we really mean by a pattern? Can we define it in strictly logical terms? And if we can, what use can we make of such a definition? These questions were answered by General Pattern Theory, a discipline initiated by Ulf Grenander in the late 1960s [1–5]. It has been an ambitious effort with the only original sketchy program having few if any practical applications, growing in mathematical maturity with a multitude of applications having appeared in biology/medicine and in computer vision, in language theory and object recognition, to mention but a few. Pattern theory attempts to provide an algebraic framework for describing patterns as structures regulated by rules, essentially a finite number of both local and global combinatory operations. Pattern theory takes a compositional view of the world, building more and more complex structures starting from simple ones. The basic rules for combining and building complex patterns from simpler ones are encoded via graphs and rules on transformation of these graphs.

The doctrine of double effect (DDE) is a long-studied ethical principle that governs when actions that have both positive and negative effects are to be allowed. The goal in this paper is to automate DDE. We briefly present DDE, and use a first-order modal logic, the deontic cognitive event calculus, as our framework to formalize the doctrine. We present formalizations of increasingly stronger versions of the principle, including what is known as the doctrine of triple effect. We then use our framework to simulate successfully scenarios that have been used to test the presence of the principle