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Attributional Calculus
Attributional calculus is a logic and representation system defined by Ryszard S. Michalski. It combines elements of predicate logic, propositional calculus Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations b ..., and multi-valued logic. Attributional calculus provides a formal language for natural induction, which is an inductive learning process whose outcomes are in human-readable forms. References Michalski, R.S., "ATTRIBUTIONAL CALCULUS: A Logic and Representation Language for Natural Induction," Reports of the Machine Learning and Inference Laboratory, MLI 04–2, George Mason University, Fairfax, VA, April, 2004. Artificial intelligence Systems of formal logic {{Compu-AI-stub ...
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Ryszard S
Ryszard () is the Polish equivalent of "Richard", and may refer to: * Ryszard Andrzejewski (born 1976), Polish rap musician, songwriter and producer * Ryszard Bakst (1926–1999), Polish and British pianist and piano teacher of Jewish/Polish/Russian origin * Ryszard Bartel (1897–1982), Polish engineer, aircraft designer, pioneer and aviator * Ryszard Bender (born 1932), Polish politician and historian, specialist in the history of the January Uprising * Ryszard Wincenty Berwiński (1817–1879), Polish poet, translator, folklorist, and nationalist * Ryszard Białous (1914–1992), Polish scoutmaster (harcmistrz) captain of the AK-Szare Szeregi *Ryszard Bober (born 1956), Polish politician, Vice-Chairperson of Kuyavian-Pomeranian Regional Assembly * Ryszard Bogusz (born 1951), Lutheran theologian, bishop of the diocese Wroclaw of the Evangelical Augsburg Church in Poland * Ryszard Bolesławski (1889–1937), Polish film director, actor and teacher of acting *Ryszard Bosek (born 1950 ...
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Predicate Logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists''"'' is a quantifier, while ''x'' is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set ...
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Propositional Calculus
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic. Explanation Logical connectives are found in natural languages. In English for example, some examples are "and" ( conjunction), "or" ( disjunction), "not" (negation) and ...
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Multi-valued Logic
Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false") for any proposition. Classical two-valued logic may be extended to ''n''-valued logic for ''n'' greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values "true", "false", and "unknown"), four-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic. History It is wrong that the first known classical logician who did not fully accept the law of excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of wo-valuedlogic"). In fact, Aristotle did not contest the univer ...
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Artificial Intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech recognition, computer vision, translation between (natural) languages, as well as other mappings of inputs. The ''Oxford English Dictionary'' of Oxford University Press defines artificial intelligence as: the theory and development of computer systems able to perform tasks that normally require human intelligence, such as visual perception, speech recognition, decision-making, and translation between languages. AI applications include advanced web search engines (e.g., Google), recommendation systems (used by YouTube, Amazon and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Tesla), automated decision-making and competing at the highest level in strategic game systems (such as chess and Go). ...
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