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Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance).
The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills. [2] [3] [4] The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.
The symbol grounding problem is a concept in the fields of artificial intelligence, cognitive science, philosophy of mind, and semantics.It addresses the challenge of connecting symbols, such as words or abstract representations, to the real-world objects or concepts they refer to.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
Arbitrary inference is a classic tenet of cognitive therapy created by Aaron T. Beck in 1979. [1] He defines the act of making an arbitrary inference as the process of drawing a conclusion without sufficient evidence, or without any evidence at all.
For example, "almost all real numbers are transcendental" because the algebraic real numbers form a countable subset of the real numbers with measure zero. One can also speak of "almost all" integers having a property to mean "all except finitely many", despite the integers not admitting a measure for which this agrees with the previous usage.
The inverse problem, of constructing the equation (with regular singularities), given a representation, is a Riemann–Hilbert problem. For a regular (and in particular Fuchsian) linear system one usually chooses as generators of the monodromy group the operators M j corresponding to loops each of which circumvents just one of the poles of the ...
The decision problem for the existential theory of the reals is the algorithmic problem of testing whether a given sentence belongs to this theory; equivalently, for strings that pass the basic syntactical checks (they use the correct symbols with the correct syntax, and have no unquantified variables) it is the problem of testing whether the ...