Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples, background knowledge and hypotheses. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples.
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modelling basic arithmetic. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "One cannot say of something that it is and that it is not in the same respect and at the same time."
Reliability in statistics and psychometrics is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions. "It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are accurate, reproducible, and consistent from one testing occasion to another. That is, if the testing process were repeated with a group of test takers, essentially the same results would be obtained. Various kinds of reliability coefficients, with values ranging between 0.00 and 1.00, are usually used to indicate the amount of error in the scores." For example, measurements of people's height and weight are often extremely reliable.
In computer science, consistency models are used in distributed systems like distributed shared memory systems or distributed data stores. The system is said to support a given model if operations on memory follow specific rules. The data consistency model specifies a contract between programmer and system, wherein the system guarantees that if the programmer follows the rules, memory will be consistent and the results of reading, writing, or updating memory will be predictable. This is different from coherence, which occurs in systems that are cached or cache-less, and is consistency of data with respect to all processors. Coherence deals with maintaining a global order in which writes to a single location or single variable are seen by all processors. Consistency deals with the ordering of operations to multiple locations with respect to all processors.
In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large". The proposition that such cardinals exist cannot be proved in the most common axiomatization of set theory, namely ZFC, and such propositions can be viewed as ways of measuring how "much", beyond ZFC, one needs to assume to be able to prove certain desired results. In other words, they can be seen, in Dana Scott's phrase, as quantifying the fact "that if you want more you have to assume more".
In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early part of the 20th century, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic.
Reason maintenance is a knowledge representation approach to efficient handling of inferred information that is explicitly stored. Reason maintenance distinguishes between base facts, which can be defeated, and derived facts. As such it differs from belief revision which, in its basic form, assumes that all facts are equally important. Reason maintenance was originally developed as a technique for implementing problem solvers. It encompasses a variety of techniques that share a common architecture: two components—a reasoner and a reason maintenance system—communicate with each other via an interface. The reasoner uses the reason maintenance system to record its inferences and justifications of the inferences. The reasoner also informs the reason maintenance system which are the currently valid base facts (assumptions). The reason maintenance system uses the information to compute the truth value of the stored derived facts and to restore consistency if an inconsistency is derived.
Consistency, in logic, is a quality of no contradiction.
Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents.
Newton Carneiro Affonso da Costa is a Brazilian mathematician, logician, and philosopher. He studied engineering and mathematics at the Federal University of Paraná in Curitiba and the title of his 1961 Ph.D. dissertation was Topological spaces and continuous functions.
Eventual consistency is a consistency model used in distributed computing to achieve high availability that informally guarantees that, if no new updates are made to a given data item, eventually all accesses to that item will return the last updated value. Eventual consistency, also called optimistic replication, is widely deployed in distributed systems, and has origins in early mobile computing projects. A system that has achieved eventual consistency is often said to have converged, or achieved replica convergence. Eventual consistency is a weak guarantee – most stronger models, like linearizability are trivially eventually consistent, but a system that is merely eventually consistent does not usually fulfill these stronger constraints.
In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa. In this case, they are, roughly speaking, "as consistent as each other".
The term "bootstrap model" is used for a class of theories that use very general consistency criteria to determine the form of a quantum theory from some assumptions on the spectrum of particles. It is a form of S-matrix theory.
In constraint satisfaction, local consistency conditions are properties of constraint satisfaction problems related to the consistency of subsets of variables or constraints. They can be used to reduce the search space and make the problem easier to solve. Various kinds of local consistency conditions are leveraged, including node consistency, arc consistency, and path consistency.
In mathematical logic, an ω-consistent theory is a theory that is not only (syntactically) consistent, but also avoids proving certain infinite combinations of sentences that are intuitively contradictory. The name is due to Kurt Gödel, who introduced the concept in the course of proving the incompleteness theorem.
Vivid knowledge refers to a specific kind of knowledge representation.
The term completeness as applied to knowledge bases refers to two different concepts.
