Internal set theory - Wikipedia
Internal set theory (IST) is a mathematical theory of sets developed by Edward Nelson that provides an axiomatic basis for a portion of the nonstandard analysis introduced by Abraham Robinson. Instead of adding new elements to the real numbers, Nelson's approach modifies the axiomatic foundations through syntactic enrichment. Thus, the axioms introduce a new term, "standard", which can be used to
Non-well-founded set theory - Wikipedia
Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation. The study of non-well-founded sets was initiated by Dmitry Mirimanoff in a series of papers between 1917 and 1920, in which he fo
Fuzzy logic - Wikipedia
This article is about the scientific theory of that name. For other uses, see Fuzzy logic (disambiguation). Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false.[1] By contrast, in Boolean logic, the
Vector logic - Wikipedia
Vector logic[1][2] is an algebraic model of elementary logic based on matrix algebra. Vector logic assumes that the truth values map on vectors, and that the monadic and dyadic operations are executed by matrix operators. "Vector logic" has also been used to refer to the representation of classical propositional logic as a vector space,[3][4] in which the unit vectors are propositional variables.
Quantum logic - Wikipedia
In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipÂulation of propositions inspired by the structure of quantum theory. The formal system takes as its starting point an obsÂervation of Garrett Birkhoff and John von Neumann, that the structure of experimental tests in classical mechanics forms a Boolean algebra, but the str
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HPO formalism - Wikipedia
Universal set - Wikipedia
List of alternative set theories - Wikipedia
Fuzzy set - Wikipedia
Noncommutative logic - Wikipedia
Multiset - Wikipedia
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