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Allen's Interval Algebra
Allen's interval algebra is a calculus (other), calculus for spatial-temporal reasoning, temporal reasoning that was introduced by James F. Allen (computer scientist), James F. Allen in 1983. The calculus defines possible relations between time intervals and provides a composition table that can be used as a basis for reasoning about temporal descriptions of events. Formal description Relations The following 13 base relations capture the possible relations between two intervals. To see that the 13 relations are exhaustive, note that each point of X can be at 5 possible locations relative to Y: before, at the start, within, at the end, after. These give 5 + 4 + 3 + 2 + 1 = 15 possible relative positions for the start and the end of X. Of these, we cannot have X_0 = X_1 = Y_0 since X_0 < X_1, and similarly we cannot have , thus giving us 13 possible relations. In general, the number of different relations between ''n'' intervals, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Calculus (other)
Calculus (from Latin ''calculus'' meaning ‘pebble’, plural '' calculī'') in its most general sense is any method or system of calculation. Calculus may refer to: Biology * ''Calculus'' (spider), a genus of the family Oonopidae * '' Caseolus calculus'', a genus and species of small land snails Medicine * Calculus (dental), deposits of calcium phosphate salts on teeth, also known as tartar * Calculus (medicine), a stone formed in the body such as a gall stone or kidney stone Mathematics * Infinitesimal calculus (or simply calculus), which investigates motion and rates of change ** Differential calculus ** Integral calculus ** Non-standard calculus, an approach to infinitesimal calculus using Robinson's infinitesimals * Calculus of sums and differences ( difference operator), also called the finite-difference calculus, a discrete analogue of "calculus" * Functional calculus, a way to apply various types of functions to operators * Schubert calculus, a branch of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Overlapping Markup
In markup languages and the digital humanities, overlap occurs when a document has two or more structures that interact in a non-hierarchical manner. A document with overlapping markup cannot be represented as a tree. This is also known as concurrent markup. Overlap happens, for instance, in poetry, where there may be a metrical structure of feet and lines; a linguistic structure of sentences and quotations; and a physical structure of volumes and pages and editorial annotations. History The problem of non-hierarchical structures in documents has been recognised since 1988; resolving it against the dominant paradigm of text as a single hierarchy (an ''ordered hierarchy of content objects'' or ''OHCO'') was initially thought to be merely a technical issue, but has, in fact, proven much more difficult. In 2008, Jeni Tennison identified markup overlap as "the main remaining problem area for markup technologists". Markup overlap continues to be a primary issue in the digital stud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Commonsense Reasoning
In artificial intelligence (AI), commonsense reasoning is a human-like ability to make presumptions about the type and essence of ordinary situations humans encounter every day. These assumptions include judgments about the nature of physical objects, taxonomic properties, and peoples' intentions. A device that exhibits commonsense reasoning might be capable of drawing conclusions that are similar to humans' folk psychology (humans' innate ability to reason about people's behavior and intentions) and naive physics (humans' natural understanding of the physical world). Definitions and characterizations Some definitions and characterizations of common sense from different authors include: * "Commonsense knowledge includes the basic facts about events (including actions) and their effects, facts about knowledge and how it is obtained, facts about beliefs and desires. It also includes the basic facts about material objects and their properties." * "Commonsense knowledge differs from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Spatial Relation
A spatial relationD. M. Mark and M. J. Egenhofer (1994), "Modeling Spatial Relations Between Lines and Regions: Combining Formal Mathematical Models and Human Subjects Testing"PDF/ref> specifies how some object is located in space in relation to some reference object. When the reference object is much bigger than the object to locate, the latter is often represented by a point. The reference object is often represented by a bounding box. In Anatomy it might be the case that a spatial relation is not fully applicable. Thus, the degree of applicability is defined which specifies from 0 till 100% how strongly a spatial relation holds. Often researchers concentrate on defining the applicability function for various spatial relations. In spatial databases and geospatial topology the ''spatial relations'' are used for spatial analysis and constraint specifications. In cognitive development for walk and for catch objects, or for understand objects-behaviour; in robotic Natural F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Region Connection Calculus
The region connection calculus (RCC) is intended to serve for qualitative spatial representation and reasoning. RCC abstractly describes regions (in Euclidean space, or in a topological space) by their possible relations to each other. RCC8 consists of 8 basic relations that are possible between two regions: * disconnected (DC) * externally connected (EC) * equal (EQ) * partially overlapping (PO) * tangential proper part (TPP) * tangential proper part inverse (TPPi) * non-tangential proper part (NTPP) * non-tangential proper part inverse (NTPPi) From these basic relations, combinations can be built. For example, proper part (PP) is the union of TPP and NTPP. Axioms RCC is governed by two axioms. * for any region x, x connects with itself * for any region x, y, if x connects with y, y connects with x Remark on the axioms The two axioms describe two features of the connection relation, but not the characteristic feature of the connect relation. For example, we can say that an objec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Temporal Logic
In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I eat something"). It is sometimes also used to refer to tense logic, a modal logic-based system of temporal logic introduced by Arthur Prior in the late 1950s, with important contributions by Hans Kamp. It has been further developed by computer scientists, notably Amir Pnueli, and logicians. Temporal logic has found an important application in formal verification, where it is used to state requirements of hardware or software systems. For instance, one may wish to say that ''whenever'' a request is made, access to a resource is ''eventually'' granted, but it is ''never'' granted to two requestors simultaneously. Such a statement can conveniently be expressed in a temporal logic. Motivation Consider the statement "I am hungry". Though it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Semantic Reasoner
A semantic reasoner, reasoning engine, rules engine, or simply a reasoner, is a piece of software able to infer logical consequences from a set of asserted facts or axioms. The notion of a semantic reasoner generalizes that of an inference engine, by providing a richer set of mechanisms to work with. The inference rules are commonly specified by means of an ontology language, and often a description logic language. Many reasoners use first-order predicate logic to perform reasoning; inference commonly proceeds by forward chaining and backward chaining. There are also examples of probabilistic reasoners, including non-axiomatic reasoning systems, and probabilistic logic networks. Notable applications Notable semantic reasoners and related software: Free to use (closed source) * Cyc inference engine, a forward and backward chaining inference engine with numerous specialized modules for high-order logic. * KAON2 is an infrastructure for managing OWL-DL, SWRL, and F-L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Web Ontology Language
The Web Ontology Language (OWL) is a family of Knowledge representation and reasoning, knowledge representation languages for authoring Ontology (information science), ontologies. Ontologies are a formal way to describe Taxonomy, taxonomies and classification networks, essentially defining the structure of knowledge for various domains: the nouns representing classes of objects and the verbs representing relations between the objects. Ontologies resemble class hierarchies in object-oriented programming but there are several critical differences. Class hierarchies are meant to represent structures used in source code that evolve fairly slowly (perhaps with monthly revisions) whereas ontologies are meant to represent information on the Internet and are expected to be evolving almost constantly. Similarly, ontologies are typically far more flexible as they are meant to represent information on the Internet coming from all sorts of heterogeneous data sources. Class hierarchies on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Interval Tree
In computer science, an interval tree is a tree data structure to hold intervals. Specifically, it allows one to efficiently find all intervals that overlap with any given interval or point. It is often used for windowing queries, for instance, to find all roads on a computerized map inside a rectangular viewport, or to find all visible elements inside a three-dimensional scene. A similar data structure is the segment tree. The trivial solution is to visit each interval and test whether it intersects the given point or interval, which requires O(n) time, where n is the number of intervals in the collection. Since a query may return all intervals, for example if the query is a large interval intersecting all intervals in the collection, this is asymptotically optimal; however, we can do better by considering output-sensitive algorithms, where the runtime is expressed in terms of m, the number of intervals produced by the query. Interval trees have a query time of O(\log n + m) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Battle Of Hastings
The Battle of Hastings was fought on 14 October 1066 between the Norman-French army of William, Duke of Normandy, and an English army under the Anglo-Saxon King Harold Godwinson, beginning the Norman Conquest of England. It took place approximately northwest of Hastings, close to the present-day town of Battle, East Sussex, and was a decisive Norman victory. The background to the battle was the death of the childless King Edward the Confessor in January 1066, which set up a succession struggle between several claimants to his throne. Harold was crowned king shortly after Edward's death but faced invasions by William, his own brother Tostig, and the Norwegian king Harald Hardrada (Harold III of Norway). Hardrada and Tostig defeated a hastily gathered army of Englishmen at the Battle of Fulford on 20 September 1066. They were in turn defeated by Harold at the Battle of Stamford Bridge on 25 September. The deaths of Tostig and Hardrada at Stamford Bridge left William as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Harold Godwinson
Harold Godwinson ( – 14 October 1066), also called Harold II, was the last crowned Anglo-Saxon King of England. Harold reigned from 6 January 1066 until his death at the Battle of Hastings on 14 October 1066, the decisive battle of the Norman Conquest. He was succeeded by William the Conqueror, the victor at Hastings. Harold Godwinson was a member of the most powerful noble family in England, his father Godwin having been made Earl of Wessex by Cnut the Great. Harold, who served previously as Earl of East Anglia, was appointed to his father's earldom on Godwin's death. After his brother-in-law, King Edward the Confessor, died without an heir on 5 January 1066, the ''Witenagemot'' convened and chose Harold to succeed him; he was probably the first English monarch to be crowned in Westminster Abbey. In late September, he defeated an invasion by rival claimant Harald Hardrada of Norway in the Battle of Stamford Bridge near York before marching his army back south to meet Willi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
