completeness assumption
1Completeness (knowledge bases) — A knowledge base KB is complete if there is no formular α such that KB ⊭ α and KB ⊭ ¬α. Example of knowledge base with incomplete knowledge: KB := { A ∨ B } Then we have KB ⊭ A and KB ⊭ ¬A. In some cases, you can make a consistent knowledge… …
2Original proof of Gödel's completeness theorem — The proof of Gödel s completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a rewritten version of the dissertation, published as an article in 1930) is not easy to read today; it uses concepts and formalism that are… …
3Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …
4Robinson's joint consistency theorem — is an important theorem of mathematical logic. It is related to Craig interpolation and Beth definability.The classical formulation of Robinson s joint consistency theorem is as follows:Let T 1 and T 2 be first order theories. If T 1 and T 2 are… …
5Method of analytic tableaux — A graphical representation of a partially built propositional tableau In proof theory, the semantic tableau (or truth tree) is a decision procedure for sentential and related logics, and a proof procedure for formulas of first order logic. The… …
6mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …
7Axiom — This article is about logical propositions. For other uses, see Axiom (disambiguation). In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self evident or to define and… …
8Propositional calculus — In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules… …
9Pythagoreans and Eleatics — Edward Hussey PYTHAGORAS AND THE EARLY PYTHAGOREANS Pythagoras, a native of Samos, emigrated to southern Italy around 520, and seems to have established himself in the city of Croton. There he founded a society of people sharing his beliefs and… …
10T-norm fuzzy logics — are a family of non classical logics, informally delimited by having a semantics which takes the real unit interval [0, 1] for the system of truth values and functions called t norms for permissible interpretations of conjunction. They are mainly …
