Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Wolfram_axiom> ?p ?o. }
Showing items 1 to 38 of
38
with 100 items per page.
- Wolfram_axiom abstract "The Wolfram axiom is the result of a computer exploration undertaken by Stephen Wolfram in his A New Kind of Science looking for the shortest single axiom equivalent to the axioms of Boolean algebra (or propositional calculus). The result of his search was an axiom with six Nand's and three variables equivalent to Boolean algebra: ((a.b).c).(a.((a.c).a)) = cWith the dot representing the Nand logical operation (also known as the Sheffer stroke), with the following meaning: p Nand q is true if and only if not both p and q are true. It is named for Henry M. Sheffer, who proved that all the usual operators of Boolean algebra (Not, And, Or, Implies) could be expressed in terms of Nand. This means that logic can be set up using a single operator.Wolfram’s 25 candidates are precisely the set of Sheffer identities of length less or equal to 15 elements (excluding mirror images) that have no noncommutative models of size less or equal to 4 (variables).Researchers have known for some time that single equational axioms (i.e., 1-bases) exist for Boolean algebra, including representation in terms of disjunction and negation and in terms of the Sheffer stroke. Wolfram proved that there were no smaller 1-bases candidates than the axiom he found using the techniques described in his NKS book. The proof is given in two pages (in 4-point type) in Wolfram's book. Wolfram's axiom is therefore the single simplest axiom by number of operators and variables needed to reproduce Boolean algebra.Sheffer identities were independently obtained by different means and reported in a technical memorandum in June 2000 acknowledging correspondence with Wolfram in February 2000 in which Wolfram discloses to have found the axiom in 1999 while preparing his book. In is also shown that a pair of equations (conjectured by Stephen Wolfram) are equivalent to Boolean algebra.".
- Wolfram_axiom wikiPageExternalLink nand.html.
- Wolfram_axiom wikiPageExternalLink page-808.
- Wolfram_axiom wikiPageID "30159410".
- Wolfram_axiom wikiPageRevisionID "559270134".
- Wolfram_axiom hasPhotoCollection Wolfram_axiom.
- Wolfram_axiom title "Boolean algebra".
- Wolfram_axiom title "Huntington Axiom".
- Wolfram_axiom title "Robbins Axiom".
- Wolfram_axiom title "Wolfram Axiom".
- Wolfram_axiom urlname "Booleanalgebra".
- Wolfram_axiom urlname "HuntingtonAxiom".
- Wolfram_axiom urlname "RobbinsAxiom".
- Wolfram_axiom urlname "WolframAxiom".
- Wolfram_axiom subject Category:Boolean_algebra.
- Wolfram_axiom subject Category:History_of_logic.
- Wolfram_axiom subject Category:Logic_gates.
- Wolfram_axiom subject Category:Propositional_calculus.
- Wolfram_axiom type Artifact100021939.
- Wolfram_axiom type Circuit103033362.
- Wolfram_axiom type ComputerCircuit103084420.
- Wolfram_axiom type Device103183080.
- Wolfram_axiom type ElectricalDevice103269401.
- Wolfram_axiom type Gate103427656.
- Wolfram_axiom type Instrumentality103575240.
- Wolfram_axiom type LogicGates.
- Wolfram_axiom type Object100002684.
- Wolfram_axiom type PhysicalEntity100001930.
- Wolfram_axiom type Whole100003553.
- Wolfram_axiom comment "The Wolfram axiom is the result of a computer exploration undertaken by Stephen Wolfram in his A New Kind of Science looking for the shortest single axiom equivalent to the axioms of Boolean algebra (or propositional calculus).".
- Wolfram_axiom label "Wolfram axiom".
- Wolfram_axiom label "Аксиома Вольфрама".
- Wolfram_axiom sameAs m.0g53brn.
- Wolfram_axiom sameAs Q4059939.
- Wolfram_axiom sameAs Q4059939.
- Wolfram_axiom sameAs Wolfram_axiom.
- Wolfram_axiom wasDerivedFrom Wolfram_axiom?oldid=559270134.
- Wolfram_axiom isPrimaryTopicOf Wolfram_axiom.