According to the Dictionary of Philosophy and Religion: Eastern and Western Thought by W.L. Reese, "the principle Greek terms [for love] are philia, eros, and agape. Philia developed the connotation of the kind of love involved in friendship . . . and eros the type of love based on desire, . . . and agape the sense of a higher or selfless type of love." (New Jersey: Humanities Press, 1980), p. 316.
In philosophy useful definitions are those which provide genus (the larger category to which the concept belongs) and differentia (distinguishing features that pick out the concept from other concepts belonging to this larger category). One can typically find the genus by asking what type (or kind) of thing is this? In the case of Love, corresponding to the three Greek terms, one can find three differing larger categories. Love can be a kind of desire: erotic. Love can be a type of emotion: philia. Love can be a kind of commitment: agape. These three represent different and possibly independent senses of the word love. Thus a man might desire to have sex with a woman without feeling any emotional attachment or even liking her. And a woman might feel emotional attachment toward her mother without any desire to have sex with her. Also one may like (feel positive regard toward) someone without being willing to sacrifice one's own personal interest (say one's bank account) for that person. These examples are merely meant to show that these different senses can be independent of each other. It is also possible for these senses to coincide with each other as when a married couple still desire each other sexually, are friends (feel emotionally attached) and are committed to the point of being willing to make personal sacrifices for each other.
Once we realize that 'love' can have three differing senses or meanings, we can use that knowledge to analyse claims made about love. We would not normally analyse a parent's claim to love his or her child as an expression of desire to have sex with the child, but at the same time a young man's profession of love for his date is at least sometimes exactly that. Similarly a more philosophical claim such as that men are incapable of love, would be clearly false if interpreted as the erotic kind of love, but more plausible if interpreted as agape love. The question, "Do you believe in love at first sight?" is clearly ambiguous. If the question is about erotic love, how could one deny that sexual desire can arise at first sight? But if the question is about emotional attachment, this naturally would require some time to form, although parents form emotioinal attachments for their children quite quickly. Finally, if the question is about agape love, perhaps someone could choose to commit to someone at first sight, but would that be wise? Would you really want a commitment given out so frivolously? The question of whether there may be selfless commitment at first sight is perhaps the most interesting of the three possible interpretations of the question.