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We study the cohomology properties of the singular foliation F determined by an action Φ : G×M → M where the abelian Lie group G preserves a riemannian metric on the compact manifold M . More precisely, we prove that the basic intersection cohomology IH * p (M/F ) is finite-dimensional and satisfies the Poincaré duality. This duality includes two well known situations: • Poincaré duality for basic cohomology (the action Φ is almost free). • Poincaré duality for intersection cohomology (thedoi:10.4064/ap89-3-1 fatcat:a6nsgq7sdfbb5ldfwzai3h556i