It seems that most modern mathematicians tend to think in terms that are compatible with ZFC (which is ZF extended with the Axiom of Choice), but in practice they almost never write the full formal details. And it is quite rare for mathematicians to do their thinking while regarding a type...
Unique Names Axiom: If a1,… , an are all the constant symbols of ℒ, then ai ≠ aj for all 1 ≤ i < j ≤ n. • Domain Closure Axiom: If a1,… , an are all the constant symbols of ℒ, then ∀X (X = a1∨…∨ X = an). • Completion Axioms: If p(a11,… , ...
We added two axioms in Manchester OWL Syntax: for the entity ‘measurement data item’, the axiom “’part of’ (is) some ‘diagnostic finding’” is defined, and for the entity ‘diagnostic finding’ its inverse “’has part’ (is) some ‘measurement data item’” is defined. In ...
With the expansion of dermoscopy, its vocabulary has proliferated, but the rapid evolution of the vocabulary of dermoscopy without standardized control is counterproductive. We aimed to develop a domain-specific ontology to formally represent knowledge for certain dermoscopic features. Methods The first ...
A subset of 194 lines, including 24 founders and 170 randomly selected progenies, were further genotyped using the Affymetrix Axiom Maize Genotyping Array 200K (from Peking University, China). The Affymetrix Power Tools (APT) and SNPolisher package [45] were used to analyze the genotyping data ...
ontologies express relationships and allow users to connect or relate multiple concepts innovatively using the following elements: individuals/objects, classes, attributes, relations, and axioms3,21. They follow an open-world hypothetical knowledge representation style using the Web Ontology Language (OWL)...
Wheat (Triticum aestivum L.) is a major staple food for more than one-third of the world’s population. Tiller number is an important agronomic trait in wheat, but only few related genes have been cloned. Here, we isolate a wheat mutant, tiller number1 (tn1), with much fewer tillers....
Cubical Type Theory: a constructive interpretation of the univalence axiom- Cyril Cohen, Thierry Coquand, Simon Huber, Anders Mörtberg. The key difference is that the Kan composition operations are decomposed into homogeneous composition and generalized transport as in: ...
An easy and very convenient axiom is Bool 2.It says that if a Boolean term b is not equal to t, it must be equal to f or in other words that there are at most two Boolean values. Applying this axiom boils down to a case distinction, proving a statement for the values t and f,...
An extensive form game in game theory is a type of game where players make decisions sequentially, represented in the form of a game tree. Each player's actions are based on the actions taken by previous players, leading to a more complex and detailed analysis of strategic interactions. ...