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In mathematics, a ranked poset is a partially ordered set in which one of the following (non-equivalent) conditions hold: it is a graded poset, or; a poset with the property that for every element x, all maximal chains among those with x as greatest element have the same finite length, or; a poset in which all maximal chains have the same ...
The rank is consistent with the covering relation of the ordering, meaning that for all x and y, if y covers x then ρ(y) = ρ(x) + 1. The value of the rank function for an element of the poset is called its rank. Sometimes a graded poset is called a ranked poset but that phrase has other meanings; see Ranked poset.
A chatbot is a software application or web interface that is designed to mimic human conversation through text or voice interactions. [1] [2] [3] Modern chatbots are typically online and use generative artificial intelligence systems that are capable of maintaining a conversation with a user in natural language and simulating the way a human would behave as a conversational partner.
A convex set in a poset P is a subset I of P with the property that, for any x and y in I and any z in P, if x ≤ z ≤ y, then z is also in I. This definition generalizes the definition of intervals of real numbers. When there is possible confusion with convex sets of geometry, one uses order-convex instead of "convex".
Roblox allows users to create and publish their own games, which can then be played by other users, by using its game engine, Roblox Studio. [15] Roblox Studio includes multiple premade game templates [ 16 ] [ 17 ] as well as the Toolbox, which allows access to user-created models, plug-ins , audio, images, meshes, video, and fonts.
Lebeuf et al. [1] provide a faceted taxonomy to characterize bots based on a literature review. It is composed of 3 main facets: (i) properties of the environment that the bot was created in; (ii) intrinsic properties of the bot itself; and (iii) the bot's interactions within its environment.
A chatbot (originally chatterbot) [1] is a software application or web interface designed to have textual or spoken conversations. [2] [3] [4] Modern chatbots are typically online and use generative artificial intelligence systems that are capable of maintaining a conversation with a user in natural language and simulating the way a human would behave as a conversational partner.
An Internet bot, web robot, robot or simply bot, [1] is a software application that runs automated tasks on the Internet, usually with the intent to imitate human activity, such as messaging, on a large scale. [2] An Internet bot plays the client role in a client–server model whereas the server role is usually played by web servers. Internet ...