Qualitative Spatial Reasoning with Topological Information


Book Description

Spatial knowledge representation and reasoning with spatial knowledge are relevant issues for many application areas such as robotics, geographical information systems, and computer vision. Exceeding purely quantitative approaches, more recently initiated qualitative approaches allow for dealing with spatial information on a more abstract level that is closer to the way humans think and speak. Starting out with the qualitative, topological constraint calculus RCC8 proposed by Randell, Cui, and Cohn, this work presents answers to a variety of open questions regarding RCC8. The open issues concerning computational properties are solved by exploiting a broad variety of results and methods from logic and theoretical computer science. Questions concerning practical performance are addressed by large-scale empirical computational experiments. The most impressive result is probably the complete classification of computational properties for all fragments of RCC8.




Modal and Relevance Logics for Qualitative Spatial Reasoning


Book Description

Qualitative Spatial Reasoning (QSR) is an alternative technique to represent spatial relations without using numbers. Regions and their relationships are used as qualitative terms. Mostly peer qualitative spatial reasonings has two aspect: (a) the first aspect is based on inclusion and it focuses on the "part-of" relationship. This aspect is mathematically covered by mereology. (b) the second aspect focuses on topological nature, i.e., whether they are in "contact" without having a common part. Mereotopology is a mathematical theory that covers these two aspects. The theoretical aspect of this thesis is to use classical propositional logic with non-classical relevance logic to obtain a logic capable of reasoning about Boolean algebras i.e., the mereological aspect of QSR. Then, we extended the logic further by adding modal logic operators in order to reason about topological contact i.e., the topological aspect of QSR. Thus, we name this logic Modal Relevance Logic (MRL). We have provided a natural deduction system for this logic by defining inference rules for the operators and constants used in our (MRL) logic and shown that our system is correct. Furthermore, we have used the functional programming language and interactive theorem prover Coq to implement the definitions and natural deduction rules in order to provide an interactive system for reasoning in the logic.




Handbook of Spatial Logics


Book Description

The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject.










Spatial and Temporal Reasoning


Book Description

Qualitative reasoning about space and time - a reasoning at the human level - promises to become a fundamental aspect of future systems that will accompany us in daily activity. The aim of Spatial and Temporal Reasoning is to give a picture of current research in this area focusing on both representational and computational issues. The picture emphasizes some major lines of development in this multifaceted, constantly growing area. The material in the book also shows some common ground and a novel combination of spatial and temporal aspects of qualitative reasoning. Part I presents the overall scene. The chapter by Laure Vieu is on the state of the art in spatial representation and reasoning, and that by Alfonso Gerevini gives a similar survey on research in temporal reasoning. The specific contributions to these areas are then grouped in the two main parts. In Part II, Roberto Casati and Achille Varzi examine the ontological status of spatial entities; Anthony Cohn, Brandon Bennett, John Gooday, and Nicholas Gotts present a detailed theory of reasoning with qualitative relations about regions; Andrew Frank discusses the spatial needs of geographical information systems; and Annette Herskovits focuses on the linguistic expression of spatial relations. In Part III, James Allen and George Ferguson describe an interval temporal logic for the representation of actions and events; Drew McDermott presents an efficient way of predicting the outcome of plan execution; and Erik Sandewall introduces a semantics based on transitions for assessing theories of action and change. In Part IV, Antony Galton's chapter stands clearly between the two areas of space and time and outlines the main coordinates of an integrated approach.




Handbook of Knowledge Representation


Book Description

Handbook of Knowledge Representation describes the essential foundations of Knowledge Representation, which lies at the core of Artificial Intelligence (AI). The book provides an up-to-date review of twenty-five key topics in knowledge representation, written by the leaders of each field. It includes a tutorial background and cutting-edge developments, as well as applications of Knowledge Representation in a variety of AI systems. This handbook is organized into three parts. Part I deals with general methods in Knowledge Representation and reasoning and covers such topics as classical logic in Knowledge Representation; satisfiability solvers; description logics; constraint programming; conceptual graphs; nonmonotonic reasoning; model-based problem solving; and Bayesian networks. Part II focuses on classes of knowledge and specialized representations, with chapters on temporal representation and reasoning; spatial and physical reasoning; reasoning about knowledge and belief; temporal action logics; and nonmonotonic causal logic. Part III discusses Knowledge Representation in applications such as question answering; the semantic web; automated planning; cognitive robotics; multi-agent systems; and knowledge engineering. This book is an essential resource for graduate students, researchers, and practitioners in knowledge representation and AI. * Make your computer smarter* Handle qualitative and uncertain information* Improve computational tractability to solve your problems easily




Handbook of Modal Logic


Book Description

The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth




Neutrosophy in Arabic Philosophy (English language version)


Book Description

Examples of Neutrosophy used in Arabic philosophy:- While Avicenna promotes the idea that the world is contingent if it is necessitated by its causes, Averroes rejects it, and both of them are right from their point of view. Hence and have common parts.- Islamic dialectical theology (kalam) promoting creationism was connected by Avicenna in an extraordinary way with the opposite Aristotelian-Neoplatonic tradition.Much work by Avicenna is neutrosophic.- Averroes's religious judges (qadis) can be connected with atheists' believes.- al-Farabi's metaphysics and general theory of emanation vs. al-Ghazali's Sufi writings and mystical treatises [we may think about a coherence of al-Ghazali's "Incoherence of the Incoherence" book].- al-Kindi's combination of Koranic doctrines with Greek philosophy.- Islamic Neoplatonism + Western Neoplatonism. - Ibn ? Khaldun?s statements in his theory on the cyclic sequence of civilizations, says that: Luxury leads to the raising of civilization (because the people seek for comforts of life) but also Luxury leads to the decay of civilization (because its correlation with ethics corruption).- On the other hand, there?s the method of absent?by?present syllogism in jurisprudence, in which we find the same principles and laws of neutrosophy.- We can also function a lot of Arabic aphorisms, maxims, Koranic miracles (Ayat Al-Qur??n) and Sunna of the prophet, to support the theory of neutrosophy. Take the colloquial proverb that "The continuance of state is impossible" too, or "Everything, if it?s increased over its extreme, it will turn over to its opposite"!