Cyc is a long-term artificial intelligence project that aims to assemble a comprehensive ontology and knowledge base that spans the basic concepts and rules about how the world works. Hoping to capture common sense knowledge, Cyc focuses on implicit knowledge that other AI platforms may take for granted. This is contrasted with facts one might find somewhere on the internet or retrieve via a search engine or Wikipedia. Cyc enables semantic reasoners to perform human-like reasoning and be less "brittle" when confronted with novel situations.
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.
Knowledge representation and reasoning is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can utilize to solve complex tasks such as diagnosing a medical condition or having a dialog in a natural language. Knowledge representation incorporates findings from psychology about how humans solve problems and represent knowledge in order to design formalisms that will make complex systems easier to design and build. Knowledge representation and reasoning also incorporates findings from logic to automate various kinds of reasoning, such as the application of rules or the relations of sets and subsets.
Truth is the property of being in accord with fact or reality. In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences.
Douglas Bruce Lenat is the CEO of Cycorp, Inc. of Austin, Texas, and has been a prominent researcher in artificial intelligence; he was awarded the biannual IJCAI Computers and Thought Award in 1976 for creating the machine learning program, AM. He has worked on machine learning, knowledge representation, "cognitive economy", blackboard systems, and what he dubbed in 1984 "ontological engineering". He has also worked in military simulations, and numerous projects for US government, military, intelligence, and scientific organizations. In 1980, he published a critique of conventional random-mutation Darwinism. He authored a series of articles in the Journal of Artificial Intelligence exploring the nature of heuristic rules.
In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory, as it provides a useful method for constructing models of any set of sentences that is finitely consistent.
The problem of induction is the philosophical question of what are the justifications, if any, for any growth of knowledge understood in the classic philosophical sense—knowledge that goes beyond a mere collection of observations—highlighting the apparent lack of justification in particular for:
- Generalizing about the properties of a class of objects based on some number of observations of particular instances of that class or
- Presupposing that a sequence of events in the future will occur as it always has in the past. Hume called this the principle of uniformity of nature.
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 and naive physics.
In mathematics, given a collection of subsets of a set X, an exact cover is a subcollection of such that each element in is contained in exactly one subset in . One says that each element in is covered by exactly one subset in . An exact cover is a kind of cover.
Non-classical logics are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is done, including by way of extensions, deviations, and variations. The aim of these departures is to make it possible to construct different models of logical consequence and logical truth.
In information science, an upper ontology is an ontology which consists of very general terms that are common across all domains. An important function of an upper ontology is to support broad semantic interoperability among a large number of domain-specific ontologies by providing a common starting point for the formulation of definitions. Terms in the domain ontology are ranked under the terms in the upper ontology, e.g., the upper ontology classes are superclasses or supersets of all the classes in the domain ontologies.
In linguistics, an argument is an expression that helps complete the meaning of a predicate, the latter referring in this context to a main verb and its auxiliaries. In this regard, the complement is a closely related concept. Most predicates take one, two, or three arguments. A predicate and its arguments form a predicate-argument structure. The discussion of predicates and arguments is associated most with (content) verbs and noun phrases (NPs), although other syntactic categories can also be construed as predicates and as arguments. Arguments must be distinguished from adjuncts. While a predicate needs its arguments to complete its meaning, the adjuncts that appear with a predicate are optional; they are not necessary to complete the meaning of the predicate. Most theories of syntax and semantics acknowledge arguments and adjuncts, although the terminology varies, and the distinction is generally believed to exist in all languages. Dependency grammars sometimes call arguments actants, following Lucien Tesnière (1959).
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
In logic, the formal languages used to create expressions consist of symbols, which can be broadly divided into constants and variables. The constants of a language can further be divided into logical symbols and non-logical symbols.
Many-sorted logic can reflect formally our intention not to handle the universe as a homogeneous collection of objects, but to partition it in a way that is similar to types in typeful programming. Both functional and assertive "parts of speech" in the language of the logic reflect this typeful partitioning of the universe, even on the syntax level: substitution and argument passing can be done only accordingly, respecting the "sorts".
In mathematics, the Vitali covering lemma is a combinatorial and geometric result commonly used in measure theory of Euclidean spaces. This lemma is an intermediate step, of independent interest, in the proof of the Vitali covering theorem. The covering theorem is credited to the Italian mathematician Giuseppe Vitali. The theorem states that it is possible to cover, up to a Lebesgue-negligible set, a given subset E of Rd by a disjoint family extracted from a Vitali covering of E.
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.
In machine learning, first-order inductive learner (FOIL) is a rule-based learning algorithm.
Something and anything are concepts of existence in ontology, contrasting with the concept of nothing. Both are used to describe the understanding that what exists is not nothing without needing to address the existence of everything. The philosopher, David Lewis, has pointed out that these are necessarily vague terms, asserting that "ontological assertions of common sense are correct if the quantifiers—such words as "something" and "anything"—are restricted roughly to ordinary or familiar things."
In the Semantic Web and in knowledge representation, a metaclass is a class whose instances are themselves classes. Similar to their role in programming languages, metaclasses in Semantic Web languages can have properties otherwise applicable only to individuals, while retaining the same class's ability to be classified in a concept hierarchy. This enables knowledge about instances of those metaclasses to be inferred by semantic reasoners using statements made in the metaclass. Metaclasses thus enhance the expressivity of knowledge representations in a way that can be intuitive for users. While classes are suitable to represent a population of individuals, metaclasses can, as one of their feature, be used to represent the conceptual dimension of an ontology. Metaclasses are supported in the ontology language OWL and the data-modeling vocabulary RDFS.
