Collaborative　Reasoning　(CR)　aims　to　view　users＇　historical　behaviors　as　logical　expressions　to　generate　recommendations.　Existing　neural　CR　models　embed　users　and　items　as　points　in　a　latent　space　and　define　each　logical　operator　with　one　neural　network　constrained　by　many　logical　regularizers,　which　causes　difficulties　in　modelling　uncertainty　and　training　networks.　To　address　these　shortcomings,　this　paper　develops　a　probabilistic　embedding　based　CR　model　BeCR　for　recommendation　tasks.　In　BeCR,　we　encode　each　user　or　item　as　a　Beta　embedding　(each　element　follows　a　Beta　distribution)　and　then　define　probabilistic　logical　negation　and　conjunction　operators　on　these　embeddings.　The　proposed　model　can　naturally　characterize　the　uncertainty　and　satisfy　basic　logical　rules　without　any　logical　regularizer.　With　our　logical　operators,　the　embedding　of　a　user　is　capable　of　filling　the　gap　between　reasoning　and　personalization.　Based　on　it,　BeCR　is　extended　to　a　personalized　recommendation　model　BeCR4p.　Experimental　results　on　three　benchmark　datasets　demonstrate　that　our　models　achieve　competitive　performance　against　eight　state-of-the-art　baselines.