Un algoritmo gen´ etico para el modelo Media-Varianza

Thefirst subsection of the BNA deals with acquisition of citizenship by virtue of birth in the United Kingdom after commencement (1 January 1983, the date on which the Act took effect):

1.-(1) A person born in the United Kingdom after commencement shall be a British citizen if at the time of the birth his father or mother is -

(a) a British citizen; or

(b) settled in the United Kingdom.

The English of this clause can be considered an informal variant of CL form, even to the extent of expressing its conclusion before (most of) its conditions, which is the conventional syntax for logic programs used to reason backwards. The biggest difference from CL syntax is that it inserts the logical conditions born in the United Kingdom after commencementinto the middle of its logical conclusiona person shall be a British citizen. Syntactically, these conditions are a variant of the restrictive relative clausewho is born in the United Kingdom after commencement.

Restrictive relative clauses are similar in syntax to non-restrictive relative clauses, but their semantics is entirely different. Restrictive relative clauses add extra conditions to conditionals. Non-restrictive relative clauses add extra con- clusions. Grammatically, non-restrictive clauses are supposed to be set apart from the rest of the sentence by commas, but restrictive clauses are supposed to be tied to the phrase they qualify without any commas. But most of the time, it seems that writers and readers ignore the rules of grammar, and rely instead upon their background knowledge to determine the intended meaning.

For example, the following two sentences are punctuated correctly. The relative clause is restrictive in thefirst sentence, and non-restrictive in the second sentence: A British citizen who obtains citizenship by providing false information may be deprived of British citizenship.

A British citizen, who is an EU citizen, is entitled to vote in EU elections.

In CL, the logical form of the two clauses is dramatically different: a person may be deprived of British citizenship

if the person obtains citizenship by providing false information. a person is entitled to vote in EU elections

if the person is a British citizen.

a person is an EU citizen if the person is a British citizen.

Some grammarians also insist that the correct relative pronoun for restrictive relative clauses is that rather than which or who. According to them, thefirst sentence in the pair of sentences above should be written:

A British citizen that obtains citizenship by providing false information may be deprived of British citizenship.

But in British English, this rule is largely ignored these days. In any case, if it is important that your readers understand what you write, then it is better not to rely on such subtle grammatical devices as the presence or absence of commas, and the supposed differences of meaning between that and which, which few readers know or care about. It is better to express yourself in an English form that more closely resembles the logical form of the thought you wish to convey. For example, do not write:

A British citizen, who has the right of abode in the UK, owes loyalty to the Crown.

or

A British citizen that has the right of abode in the UK owes loyalty to the Crown.

But, depending on what you mean, write:

All British citizens have the right of abode in the UK and owe loyalty to the Crown.

or

A British citizen owes loyalty to the Crown if the citizen has the right of abode in the UK.

The use of relative clauses is one way in which the syntax of English differs from the syntax of conditionals in logical form. Another difference is the way in which it represents variables. Symbolic forms of CL use symbols, like X and Y for variables, which range over classes of individuals. Variables are distinct from constants, which represent unique individuals.

English uses the combination of an article, like a and the, and a common noun, like person, animal, object and thing, as a sorted or typed variable. It uses the

articles a and an, as in an animal and a person, for thefirst use of a variable; and it uses the article the, as in the animal and the person, for subsequent uses of the same variable. It uses proper nouns, like Mary, Felix and Venus, which are usually capitalised, as constants, to represent individuals. Individuals can also be repre- sented by definite descriptions, as in the phrase the strongest man on earth.

Putting all these considerations about relative clauses and variables together, and taking the liberty to introduce one or two other refinements, we obtain the follow- ing more precise, but still relatively informal CL representation of subsection 1.1:1

X acquires british citizenship by subsection 1.1 at time T if X is a person

and X is born in the uk at time T and T is after commencement and Y is a parent of X

and Y is a british citizen at time T or Y is settled in the uk at time T

Notice that the condition X is a person prevents cats and dogs from claiming British Citizenship. However, it is unnecessary to add the condition Y is a person, because if X is a person then any parent of X is also a person. Notice also that the condition Y is a parent of X is short for Y is a mother of X or Y is a father of X.

This representation uses the Prolog convention in which capitalised words or letters, such as X, Y and T, stand for variables, which is why british and uk have been written in lower case. This is the opposite of the English convention in which upper case is used for proper nouns and names, and lower case is used for common nouns. Just for the record, this is one of the ways a die-hard mathe- matical logician might write 1.1:

∀X(∀T(∃Y(b(X, uk, T) ∧ c(T) ∧ d(Y, X) ∧ (e(Y, T) ∨ f(Y,T )))→ a(X, 1.1, T ))).