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searching for Axiomatic system 40 found (112 total)

Formalism (philosophy of mathematics) (1,316 words) [view diff] exact match in snippet view article

show that an axiomatic system was consistent was by formalizing it using a particular language. In order to formalize an axiomatic system, you must first

Ordinal logic (207 words) [view diff] exact match in snippet view article find links to article

incompleteness theorems. While Gödel showed that every recursively enumerable axiomatic system that can interpret basic arithmetic suffers from some form of incompleteness

Decision model (580 words) [view diff] no match in snippet view article find links to article

theory is the starting point for a decision method within a formal (axiomatic) system. Decision models contain at least one action axiom. An action is in

Melpathur Narayana Bhattathiri (1,112 words) [view diff] exact match in snippet view article find links to article

His most important scholarly work, Prakriya-sarvasvam, sets forth an axiomatic system elaborating on the classical system of Panini. However, he is most

Principle of explosion (1,162 words) [view diff] exact match in snippet view article find links to article

explosion, the existence of a contradiction (inconsistency) in a formal axiomatic system is disastrous; since any statement can be proven, it trivializes the

Temporal logic (3,819 words) [view diff] exact match in snippet view article find links to article

functions in the structure of Mill's concept. Having that, he provided his axiomatic system of logic that would fit as a framework for Mill's canons along with

Vectors in Three-dimensional Space (284 words) [view diff] exact match in snippet view article find links to article

on the other hand, pure mathematicians reduced vector algebra to an axiomatic system, and introduced wide generalisations of the concept of a three-dimensional

Quaternionic structure (236 words) [view diff] exact match in snippet view article find links to article

In mathematics, a quaternionic structure or Q-structure is an axiomatic system that abstracts the concept of a quaternion algebra over a field. A quaternionic

Algebra of communicating processes (1,754 words) [view diff] exact match in snippet view article find links to article

algebra of processes, and sought to create an abstract, generalized axiomatic system for processes, and in fact the term process algebra was coined during

Typographical Number Theory (798 words) [view diff] exact match in snippet view article find links to article

Typographical Number Theory (TNT) is a formal axiomatic system describing the natural numbers that appears in Douglas Hofstadter's book Gödel, Escher,

Hilbert's fourth problem (3,534 words) [view diff] exact match in snippet view article find links to article

it was to find — up to an isomorphism — all geometries that have an axiomatic system of the classical geometry (Euclidean, hyperbolic and elliptic), with

Brouwer–Hilbert controversy (4,441 words) [view diff] exact match in snippet view article find links to article

" In an address delivered in 1927, Hilbert attempted to defend his axiomatic system as having "important general philosophical significance." Hilbert views

Conjecture (3,046 words) [view diff] exact match in snippet view article find links to article

Euclid's parallel postulate can be taken either as true or false in an axiomatic system for geometry). In this case, if a proof uses this statement, researchers

BL (logic) (835 words) [view diff] exact match in snippet view article

\rightarrow A\end{array}}} The axioms (BL2) and (BL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005).

Reductionism (3,188 words) [view diff] exact match in snippet view article find links to article

Yet Gödel proved that, for any consistent recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers,

Number line (2,414 words) [view diff] exact match in snippet view article find links to article

R. This statement has been shown to be independent of the standard axiomatic system of set theory known as ZFC. The real line forms a metric space, with

Ernst Zermelo (1,195 words) [view diff] exact match in snippet view article find links to article

published his results despite his failure to prove the consistency of his axiomatic system. See the article on Zermelo set theory for an outline of this paper

Turtles all the way down (3,044 words) [view diff] exact match in snippet view article find links to article

in which one can never get rid of unprovable true statements in an axiomatic system. Axiom of foundation – Axiom of set theoryPages displaying short descriptions

Intuitionism (2,774 words) [view diff] exact match in snippet view article find links to article

this are said to be "uncountable". Cantor's set theory led to the axiomatic system of Zermelo–Fraenkel set theory (ZFC), now the most common foundation

Coordinative definition (993 words) [view diff] exact match in snippet view article find links to article

pure and the applied. The first part consists in an uninterpreted axiomatic system, or syntactic calculus, in which terms such as point, straight line

Abraham Fraenkel (1,420 words) [view diff] exact match in snippet view article find links to article

and 1925, he published two papers that sought to improve Zermelo's axiomatic system; the result is the Zermelo–Fraenkel axioms. Fraenkel worked in set

Internal set theory (2,325 words) [view diff] exact match in snippet view article find links to article

The approach for internal set theory is the same as that for any new axiomatic system—we construct a model for the new axioms using the elements of a simpler

Łukasiewicz logic (2,415 words) [view diff] exact match in snippet view article find links to article

logic can also be axiomatized by adding the following axioms to the axiomatic system of monoidal t-norm logic: Divisibility ( A ∧ B ) → ( A ⊗ ( A → B )

René Maurice Fréchet (1,424 words) [view diff] exact match in snippet view article find links to article

to that in group theory, proving theorems within a carefully chosen axiomatic system that can then be applied to a large array of particular cases. Here

Axiom of regularity (2,937 words) [view diff] exact match in snippet view article find links to article

implicit. [emphasis in original] In the same paper, Scott shows that an axiomatic system based on the inherent properties of the cumulative hierarchy turns

Gravitational interaction of antimatter (2,728 words) [view diff] exact match in snippet view article find links to article

Cabbolet, M. J. T. F. (2010). "Elementary Process Theory: a formal axiomatic system with a potential application as a foundational framework for physics

Bertram John Walsh (597 words) [view diff] exact match in snippet view article find links to article

equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of Brelot". Annales de l'Institut Fourier. 15 (2): 597–600. doi:10

Mathematics (15,930 words) [view diff] exact match in snippet view article find links to article

his incompleteness theorems, which show in part that any consistent axiomatic system—if powerful enough to describe arithmetic—will contain true propositions

Process philosophy (5,642 words) [view diff] exact match in snippet view article find links to article

mathematics was undertaken to develop mathematics as an airtight, axiomatic system in which every truth could be derived logically from a set of axioms

The Value of Science (2,132 words) [view diff] exact match in snippet view article find links to article

arithmetization of analysis, and ended with the revival of intuitive ideas in an axiomatic system, by the first (true) logicians. This historic intuition is therefore

Relevance logic (3,940 words) [view diff] exact match in snippet view article find links to article

deduction system for the logic, which he proved equivalent to the axiomatic system. Charlwood showed that his natural deduction system is equivalent to

John von Neumann (23,300 words) [view diff] exact match in snippet view article find links to article

measure theory. With the contributions of von Neumann to sets, the axiomatic system of the theory of sets avoided the contradictions of earlier systems

History of the Church–Turing thesis (8,282 words) [view diff] exact match in snippet view article find links to article

problem when one is approaching a notion "axiomatically", that is, an "axiomatic system" may have imbedded in it one or more tacit axioms that are unspoken

T-norm fuzzy logics (3,222 words) [view diff] exact match in snippet view article find links to article

classes of t-norms are axiomatizable. The completeness theorem of the axiomatic system with respect to the corresponding t-norm semantics on [0, 1] is then

History of logic (13,242 words) [view diff] exact match in snippet view article find links to article

the use of variables, a purely formal treatment, and the use of an axiomatic system. The other great school of Greek logic is that of the Stoics. Stoic

Romanian philosophy (11,686 words) [view diff] exact match in snippet view article find links to article

and The Polyvalent Logic, where he presents the Russell–Whitehead axiomatic system of Principia Mathematica, and C.I. Lewis' system of strict implication

Counterpart theory (4,529 words) [view diff] exact match in snippet view article find links to article

relation. This gives some neat formal machinery, mereology. This is an axiomatic system that uses formal logic to describe the relationship between parts and

Monoidal t-norm logic (3,717 words) [view diff] exact match in snippet view article find links to article

condition of prelinearity. The axioms (MTL2) and (MTL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005).

List of important publications in mathematics (10,127 words) [view diff] exact match in snippet view article find links to article

importance of establishing the consistency and completeness of an axiomatic system. H.S.M. Coxeter Regular Polytopes is a comprehensive survey of the

Models as Mediators: Perspectives on Natural and Social Science (1,402 words) [view diff] exact match in snippet view article find links to article

moved from the 'received view' - whereby a theory can be seen as an axiomatic system to be dealt with in the context of the discipline of logic, to a new