In this paper, we propose a novel method for semi-supervised learning of non-projective log-linear dependency parsers using directly expressed linguistic prior knowledge (e.g.~a noun's parent is often a verb). Model parameters are estimated using a generalized expectation (GE) objective function that penalizes the mismatch between model predictions and linguistic expectation constraints. In a comparison with two prominent "unsupervised" learning methods that require indirect biasing toward the correct syntactic structure, we show that GE can attain better accuracy with as few as 20 intuitive constraints. We also present positive experimental results on longer sentences in multiple languages.