They include the symbols for truth-functional connectives ( such as and, or, not, implies, and logical equivalence ) and the symbols for the quantifiers " for all " and " there exists ".
12.
In logically equivalent to " not ( not-A " ), or by the formula A a " ~ ( ~ A ) where the sign a " expresses logical equivalence and the sign ~ expresses negation.
13.
Therefore, instead of blindly assuming that no mistakes were made, a verification step is needed to check the logical equivalence of the final version of the netlist to the original description of the design ( golden reference model ).
14.
The logical equivalence between an empirical datum, which is a macroscopic phenomenon, and the result of a measurement, which is a quantum property, becomes clearer in the new approach, whereas it remained mostly tacit and questionable in the Copenhagen formulation.
15.
This means : " We assert the truth of the following : There exists a function " f " with the property that : given all values of " x ", their evaluations in function ? ( i . e ., resulting their matrix ) is logically equivalent to some " f " evaluated at those same values of " x " . ( and vice versa, hence logical equivalence ) ".
16.
"' RA "'can express any ( and up to logical equivalence, exactly the ) first-order logic ( FOL ) formulas containing no more than three variables . ( A given variable can be quantified multiple times and hence quantifiers can be nested arbitrarily deeply by " reusing " variables . ) Surprisingly, this fragment of FOL suffices to express Peano arithmetic and almost all undecidable . ( N . B . The Boolean algebra fragment of "'RA "'is complete and decidable .)
