Examples of using Functionally complete in English and their translations into Portuguese
{-}
-
Colloquial
-
Official
-
Medicine
-
Financial
-
Ecclesiastic
-
Ecclesiastic
-
Computer
-
Official/political
These connectives are functionally complete.
There are no minimal functionally complete sets of more than three at most binary logical connectives.
The modular approach means manufacturing these subsystems or their components as functionally complete products.
Quine's preferred functionally complete set was conjunction and negation.
Different implementation of classical logic can choose different functionally complete subsets of connectives.
The following are the minimal functionally complete sets of logical connectives with arity≤ 2: One element{↑},{↓.
Another approach is to use on equal rights connectives of a certain convenient and functionally complete, but"not minimal" set.
The following are the minimal functionally complete sets of operators in classical logic whose arities do not exceed 2:;One element:{↑},{↓.
The formulations here use implication and negation{→,¬}{\displaystyle\{\to,\neg\}}as functionally complete set of basic connectives.
In other words,the set is functionally complete if every Boolean function that takes at least one variable can be expressed in terms of the functions ƒi.
A set of logical connectives associated with a formal system is functionally complete if it can express all propositional functions.
It is not functionally complete(because it lacks the ability to express falsity and negation) but it is however syntactically complete. .
The natural interpretation of"~" is negation; that of concatenation is any connective that, when combined with negation,forms a functionally complete set of connectives.
When a single logical connective orBoolean operator is functionally complete by itself, it is called a Sheffer function or sometimes a sole sufficient operator.
Minimal functionally complete operator sets==When a single logical connective or Boolean operator is functionally complete by itself, it is called a Sheffer function or sometimes a sole sufficient operator.
Because Sheffer's stroke(also known as NAND operator)is functionally complete, it can be used to create an entire formulation of propositional calculus.
However, the examples given above are not functionally complete in this stronger sense because it is not possible to write a nullary function, i.e. a constant expression, in terms of F if F itself does not contain at least one nullary function.
Based on available evidence, revascularization by MRS or PCI offers similar survival benefits; the intervention, however,should be at least functionally complete in patients who are non-diabetic, and have preserved left ventricle function, multivessel, and stable coronary artery disease.
Emil Post proved that a set of logical connectives is functionally complete if and only if it is not a subset of any of the following sets of connectives: The monotonic connectives; changing the truth value of any connected variables from F to T without changing any from T to F never makes these connectives change their return value from T to F, e.g.∨,∧,⊤,⊥{\displaystyle\vee,\wedge,\top,\bot.
Various subsets of the sixteen binary connectives e.g.,{∨{∨,~},{&,~},are themselves functionally complete in that they suffice to define the remaining connectives.
However, they do not form a minimal functionally complete set, as the conditional and biconditional may be defined as: :formula_6So formula_7 is also functionally complete. .
Given the Boolean domain B{0,1}, a set F of Boolean functions ƒi:Bni→ B is functionally complete if the clone on B generated by the basic functions ƒi contains all functions ƒ: Bn→ B, for all strictly positive integers n≥ 1.
They differ in the choice of basic connectives used,which in all cases have to be functionally complete(i.e. able to express by composition all n-ary truth tables), and in the exact complete choice of axioms over the chosen basis of connectives.
Since every Boolean function of at least one variable can be expressed in terms of binary Boolean functions,F is functionally complete if and only if every binary Boolean function can be expressed in terms of the functions in F. A more natural condition would be that the clone generated by F consist of all functions ƒ: Bn→ B, for all integers n≥ 0.
Characterization of functional completeness==Emil Post proved that a set of logical connectives is functionally complete if and only if it is not a subset of any of the following sets of connectives:* The monotonic connectives; changing the truth value of any connected variables from F to T without changing any from T to F never makes these connectives change their return value from T to F, e.g.
