I just skimmed through this article
http://plato.stanford.edu/entries/logic-paraconsistent/ on paraconsistent logic. I'd not come across it before, although I'd had vague thoughts along those lines. It seems quite reasonable, maybe not as an accurate representation of the world but certainly as a model of how we interact with the world. It looks like it could (and probably does) have good applications in branches of A.I because of this.