This is from a newspaper headline. It seems ungrammatical. But perhaps it is a short newspaper-style way of saying "Koizumi and Bush talk about beef"?

In fact, this headline is intertextually connected to sentences like this, "Mr A and Mr B talked turkey". Looking in Kenkyusha's Luminous, I find this translation of "talk turkey":（商談などで）まじめに[率直に]話す. The "turkey" expression is an idiom. The "beef" expression is not an idiom, but is intertextually connected to the "turkey" expression.

When we realize this, we can then understand that the meaning of the headline is something like, "Koizumi and Bush had a frank talk about (importing American) beef".

Idioms, proverbs, jokes, etc. are all included within the idea of intertextuality. But the concept of intertextuality is much wider than this. Intertextuality is concerned with how language echoes in society and through time, and how one use of language may be related to other uses of language.

If you look at the headlines of English-language newspapers published in Japan, you will find that the level of intertextuality is very low. This is because the readers of these newspapers are not necessarily native-speakers of English.

If you look at such headlines in countries in which English is the native language, you will find that the level of intertextuality become much higher.

Intertextuality is a huge challenge to learners of a foreign language. It is a far greater challenge than learning English idioms.

Sometimes I hear learners of English say "He is my lover". The nuance of this is of rather a hot sexual relationship. It might also suggest an illicit relationship.

It is therefore not an expression which we can use lightly.

One common way of expressing a romantic relationship, not necessarily a sexual relationship, with a member of the opposite sex is:

John [Mary] is my boyfriend [girlfriend].

However, I feel that one cannot use this if you are over, say, 30 years of age.

With a similar meaning we can say any of the following:

John and Mary are dating.
John and Mary are seeing each other.
John and Mary are going out together.

If the couple have been going out for quite some time, and things are getting serious, we can say:

John and Mary are going steady.

Slightly more adult expressions are:

John and Mary have a serious relationship.
John and Mary are in a relationship.

These days, since it has become more or less acceptable to live together without getting married, we can say:

John and Mary are living together.

If the couple regard themselves, more or less, as husband and wife, but have not actually got married, the following expression can be used:

John [Mary] is Mary's [John's] partner.

There is also the expression "Mary is John's common-law wife". We can also say "John is Mary's common-law husband". However, these have a strong legal nuance, just like their Japanese translation equivalents.

The Christmas season has now arrived. This season in Japan has almost no connection with its real and original religious meaning, but is more or less completely commercial.

During this time of the year we see, almost everywhere, the word "X'mas", which people presumably think is a way of writing "Christmas". This is definitely very strange, and very definitely wrong.

If you do want to abbreviate the word "Christmas", please write it as "Xmas".

In Greek, there is a letter called "chi", which is used as an abbreviation of "Christ". This letter is very similar to the letter "X" of the Roman alphabet. Thus writing "Xmas" is an abbreviation for "Christmas".

The symbol ' (an apostrophe) is often used to show that a letter (or letters) has been omitted ("gov't" for "government"; "the '70s" for "the 1970s", etc.).

Since, in the case of "Xmas", nothing has been omitted, it is not correct to write "X'mas".

If the chances of rain this evening are quite low, I can say, "It may/might rain this evening." I think readers know that the "might" sentence suggests that the chance of rain is lower than in the case of "may".

If I am almost 100% certain that it is going to rain, I can say the following:

It will (certainly) rain this evening.
It is (certainly) going to rain this evening.

What about "must"? "Must" is used for strong assumptions, so can I use it if I am almost 100% sure that it is going to rain in the future? Actually, the following sentence is not correct English:

（×）It must rain this evening.

Generally speaking, "must", when it has the meaning of "strong assumption", can only be used about a present situation:

It must be raining outside now.

The following sentences are not exceptions to this rule, although they seem to be sentences about the future:

I was born, and I must eventually die.
Sooner or later, the world must come to an end.

However, these sentences are not about a real, concrete, imaginable future. Rather, they are about Fate, or the Natural Order of Things, or the Flow of Time, or What is Always True, etc. In such cases, the use of "must" is perfectly all right.