How can I say the relationship / concept?

Firstly, you are wrong to think Mr.A is good friend is "strange"
A native speaker would understand this as Mr.A is good friend of mine.

Secondly you are wrong to think your reference to the verb "thank" is a philosophical point. It is a grammatical one in which the verb "to thank" is defined as transitive (requiring one or more objects).

Thirdly, the traditional philosophical analysis of "concepts" involves considerations of ontology (existence) and epistemology (theories of knowledge). It is true that modern philosophers such as Derrida and Wittgenstein have pointed out that such traditional analysis may be heavily subservient to language usage. In that respect your question may make some sense, but I do not recommend that you pursue such philosophical developments with your current level of English because even native speakers find the writings of those authors difficult.

Ignore Fresky, Max. No matter what the topic, he will try to turn it into a forum for his solipsistic, pseudo-intellectual bullshit.

If I understand you correctly, you are looking for general terms which convey the same meaning as would appear in a particular (or personalized) context.

You might say: "I am thankful." This doesn't say what you are thankful for, or who, in particular, you might want to thank, but it doesn't have to. It just expresses your general sentiments.

Likewise, you could simply say you are "friendly with" Mr. A, or more generally that you are a "friendly person."

Heh, Fresky. You continue to out-do even your own sorry self when it comes to trying prove your "superiority" by way of irrelevant bombast. You really have no sense of self-restraint or discretion whatsoever, do you? Being a chump, I guess it's only natural for you to think everyone else is also, but, still....

- Mr.A is good friend.
This sentence points to you as being the person that Mr. A is friend with.

"Mr. A is a good friend" is as equally possible as "Mr. A is a good husband/father." Mentioning the other people involved is not necessary.