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Trillas, S. Cubillo, E. Castiñeira, On conjectures in orthocomplemented lattices, Artificial Intelligence 117 (2000) 255–275] recently proposed a mathematical model for conjectures, hypotheses and consequences (abbr. CHCs), and with this model we can execute certain mathematical reasoning and reformulate some important theorems in classical logic.
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Using data from those brain scans, the researchers built a computer program, or a statistical library of sorts, that uses mathematical reasoning in matching certain neural activity of the observer with certain facial features of the photo being observed.
The National Council of Teachers of Mathematics has pressed for more mathematical reasoning and less memorizing of facts and formulas.
Alternatively, Wittgenstein may mean that mathematical inferences (i.e., not substitutions) are in accord with, or make use of, logical inferences, and insofar as mathematical reasoning is logical reasoning, mathematics is a method of logic.
Barker-Plummer & Bailin (1997) present a case study in developing computers which can carry out the kind of analogical reasoning that humans perform when proving certain mathematical theorems.
Much of what earlier philosophers said of mathematical reasoning must, thus, be understood as applying to relational (first-order) reasoning.
There are certain mathematical problems that computers can't solve.
He is also the author of books that include "How the Other Half Thinks: Adventures in Mathematical Reasoning".
Such loose mathematical reasoning would have riled a punctilious logician like Dodgson.
In The Theory of Political Coalitions (1962), Riker demonstrated by mathematical reasoning why and how politicians form alliances.
It combines experiment with mathematical reasoning, even if it is generally used for validation rather than discovery.
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