The main aim of the present work is be to find the correlation between varying degrees of Specificity of different (nominal) expressions and their blocking effects in long-distance A-bar dependencies. To explain gradational effects in blocking A-bar extractions, I argue for an alternative notion of specificity. I suggest that specificity is a non-binary hierarchical relation among different noun phrases and propose the following correlation between A-bar dependency and specificity of intervening NPs: Between two noun phrases A and B, A is regarded as more specific than B iff the denotation of A comes from a more narrowly defined set than B. The more specific a noun phrase is, the stronger the blocking effects in A-bar dependency.