Examples of using Boolean algebra in English and their translations into French
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well known for founding digital circuit design theory in 1937, when-as a 21-year-old master's degree student at the Massachusetts Institute of Technology(MIT)-he wrote his thesis demonstrating that electrical applications of Boolean algebra could construct any logical numerical relationship.
Abstract algebraic logic Ampheck Boolean algebra(logic) Boolean domain Boolean function Boolean logic Causality Deductive reasoning Logic gate Logical graph Peirce's law Probabilistic logic Propositional calculus Sole sufficient operator Strict conditional Tautology(logic)
including Boolean algebra, gates, combinational
can indeed regain the original Boolean algebra(up to isomorphism)
The abbreviations BPI or PIT(for Boolean algebras) are sometimes used to refer to this additional axiom.
Boolean algebras are Stone algebras,
Examples of Ockham algebras include Boolean algebras, De Morgan algebras,
this is the essence of the duality pervading all Boolean algebras.
introduced Maharam algebras, complete Boolean algebras with continuous submeasures.
There are many known bases for all Boolean algebras and hence for 2.
On the other hand, it is known that the strong PIT for distributive lattices is equivalent to BPI i.e. to the MIT and PIT for Boolean algebras.
one can exploit the fact the dual orders of Boolean algebras are exactly the Boolean algebras themselves.
For example, the modal logic S4 is characterized by the class of topological boolean algebras-that is, boolean algebras with an interior operator.
nontrivial metatheorem states that any theorem of 2 holds for all Boolean algebras.
Summing up, for Boolean algebras, the weak and strong MIT,
The prototypical properties that were discussed for Boolean algebras in the above section can easily be modified to include more general lattices,
one ends up with a number of theorems that equally apply to Boolean algebras, but where every occurrence of ideal is replaced by filter.
the assertion that"PIT" holds is usually taken as the assertion that the corresponding statement for Boolean algebras(BPI) is valid.
where she earned her Ph.D. in 1997 with a dissertation on The Theory of Commuting Boolean Algebras.
Then I is contained in some prime ideal of B that is disjoint from F. The weak prime ideal theorem for Boolean algebras simply states: Every Boolean algebra contains a prime ideal.