In predicate calculus there is no distinction between properties and relations---they are both just predicates. A property is a 1-ary predicate, and an n-ary relation is just an n-ary predicate. However, many analytic philosophers continue to speak of properties and relations rather than just using the combined terminology of predicates. What is the reason for this? Is it merely convenient terminology or are there principled reasons to distinguish properties from relations?
In first-order logic, it is possible to reduce n-ary predicates to (n-1)-ary predicates for n greater than two. But it is not possible to reduce binary predicates to unary predicates.
However, if you are willing to step beyond first-order logic, there are resources for accomplishing this. The problem is that there is no obvious way to specify a general semantics for higher order logics. One could at a pinch say that the relation 'loves' in "John loves Mary" is a unary attribute of the ordered pair <John, Mary>. But it is problematic to generalise this. We could accomplish it using plural quantification and say that binary relations are equivalent to unary attributes of pluralities. But again, it is difficult to find a general way to specify the semantics of plural quantification over binary relations.
David Lewis had a go at addressing this problem using third-order logic and mereology (the logic of wholes and parts) in his book Parts of Classes (Blackwell, 1991).