You seem to throw together two interesting, but distinct topics:
- The question about the existence of social facts.
- The question about what kind of semantics one should adopt when understanding how everyday concepts work (or the more narrow question about which semantics works best in the case of social facts).
1) The existence of social facts
If you believe that there actually are "brute facts" out there in the world, which would also exist if there were no human beings (say, a mountain), then a very basic way to phrase the puzzle is: There seem to be things which wouldn't exist without human beings recognizing them as such; at the same time, they are not subjective in the sense that if you wouldn't believe in them, they would therefore cease to exist. Such things are five-dollar bills, driver's licenses, being married to someone, etc. In John Searle's parlance they are epistemically objective (they are not a matter of individual preference or opinion), but may be ontologically subjective (they depend for their existence on being agreed upon). I may suggest that Mona Lisa is one if these things.
There is a whole field dedicated to this question called social ontology.
You may want to read John Searle's The Construction of Social Reality as an easy introductory text.
2) The semantics of concepts
Aristotle codified a view which became the major (only?) theory of concepts: Concepts are categories characterized by a set of properties which are shared by their members. The set of properties set both the necessary and sufficient conditions to include or exclude some item from the category.
This view led in the 20th century to extensional or intensional semantics, in their set-theoretic approaches.
This view was first (as far as I know) challenged as a model of how to think about ordinary language by Ludwig Wittgenstein. He observed that concepts are vague in their application and that a better analogy - he never construed a theoretical model - might be family resemblance:
I can think of no better expression to characterize these similarities than "family resemblances"; for the various resemblances between members of a family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and criss-cross in the same way. […] For instance the kinds of number form a family in the same way. Why do we call something a "number"? Well, perhaps because it has a direct relationship with several things that have hitherto been called number; and this can be said to give it an indirect relationship to other things we call the same name. And we extend our concept of number as in spinning a thread we twist fibre on fibre. And the strength of the thread does not reside in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres. (Philosophical Investigations, §67)
I can give the concept 'number' rigid limits ... that is, use the word "number" for a rigidly limited concept, but I can also use it so that the extension of the concept is not closed by a frontier. And this is how we do use the word "game". For how is the concept of a game bounded? What still counts as a game and what no longer does? Can you give the boundary? No. You can draw one; for none has so far been drawn. (But that never troubled you before when you used the word "game".)
(Philosophical Investigations, §68)
Basically, even very basic and well-defined concepts like bachelor as "unmarried man" admit counterexamples, i.e. cases where conditions given by the definition do not readily include or exclude some items (think of the pope, a newborn male baby, etc.).
Wittgenstein's remarks eventually led on to new models in cognitive semantics, which departed from definition-based approaches, e.g. the pioneering work of Eleanor Rosch (who wrote her under-grad thesis on Wittgenstein) on a graded notion of categories; see Prototype theory.
You may want to read the book Women, Fire and Dangerous Things by another great cognitive linguist, Georg Lakoff, as an introductory text.
As to your question, you may want to read some work by Morris Weitz, who applied Wittgenstein's definition-less approach to the very case of art:
Weitz argued against the traditional essentialist methodology and proposed using Wittgenstein's family resemblance argument as an alternate method for identifying art objects. Weitz proposed that in asking "what is art?" aestheticians were really asking the wrong question altogether. The question he believed needed to be fundamentally addressed instead was "what kind of concept is 'art'?" Weitz used this question to propel both his defense of Wittgensteinian family resemblances, as well as his defense of art as an 'open concept.' (WP:Morris_Weitz)
