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Intuitionistic logic is related by duality to a paraconsistent logic known as Brazilian, anti-intuitionistic or dual-intuitionistic logic. [14] The subsystem of intuitionistic logic with the FALSE (resp. NOT-2) axiom removed is known as minimal logic and some differences have been elaborated on above.
Intuition in the context of decision-making is defined as a "non-sequential information-processing mode." [1] It is distinct from insight (a much more protracted process) and can be contrasted with the deliberative style of decision-making.
In mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, of intuitionistic logic was proposed by L. E. J. Brouwer and Arend Heyting, and independently by Andrey Kolmogorov. It is also sometimes called the realizability interpretation, because of the connection with the realizability theory of Stephen ...
A method of mathematical proof used to establish the truth of an infinite number of cases, based on a base case and an inductive step. proof theory The branch of mathematical logic that studies the structure and properties of mathematical proofs, aiming to understand and formalize the process of mathematical reasoning. proof-theoretic consequence
Process theories are important in management and software engineering. [3] Process theories are used to explain how decisions are made [4] how software is designed [5] [6] and how software processes are improved. [7] Motivation theories can be classified broadly into two different perspectives: Content and Process theories.
In intuitionistic analysis and in computable analysis, indecomposability or indivisibility (German: Unzerlegbarkeit, from the adjective unzerlegbar) is the principle that the continuum cannot be partitioned into two nonempty pieces.
In classical logic, intuitionistic logic, and similar logical systems, the principle of explosion [a] [b] is the law according to which any statement can be proven from a contradiction. [ 1 ] [ 2 ] [ 3 ] That is, from a contradiction, any proposition (including its negation ) can be inferred; this is known as deductive explosion .
A typical example is intuitionistic logic, where the law of excluded middle does not hold. [8] [9] Additionally, one can identify a variations (or variants), where the content of the system remains the same, while the notation may change substantially. For instance many-sorted predicate logic is considered a just variation of predicate logic. [6]