Approximating the Semantics of Logic Programs by Recurrent Neural Networks

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DeepProbLog: Neural Probabilistic Logic Programming (2018, background): “However, they neither support probabilistic reasoning nor perception, and are often limited to non-recursive and acyclic logic programs [H¨olldobler et al., 1999].”
Dimensions of Neural-symbolic Integration - A Structured Survey (2005, background): “In [Blair, 1997] modiﬁcations were proposed to allow the storage of deeper and more complex data structures than before, but their applicability remains to be shown [Kalinke, 1997].”
Reasoning about Time and Knowledge in Neural Symbolic Learning Systems (2003, background): “ing (Holldobler & Kalinke, 1994) (see also ( Holldobler et al., 1999 )), a Translation Algorithm maps any logic program P into a single hidden layer neural network N such thatN computes the least flxed point ofP.”
Lifted Relational Neural Networks: Efficient Learning of Latent Relational Structures (2018, methodology): “…to neural-symbolic integration that rely on relational (and ﬁrst-order) representations (Bader & Hitzler, 2005), e.g. based on the CORE method (H¨olldobler, Kalinke, & St¨orr, 1999), they typically search for a neural network modelling a given logic program, and thus principally diﬀer from…”