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... [0; 0; −(x η − a η ); 0]. The errorcorrection algorithm will amend the weight vector, and, on the next iteration, the weight vector will be [P η ; ( η ; a η ; ) η ], and the error will be zero. See (=-=Komendantskaya, 2009-=-b). This example illustrates that some algorithms of computational logic have direct analogy with the learning algorithms of neurocomputing. This direct use of neural networks for implementations of c...

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...itts, in that logical information is given only by means of logical connectives and truth values; as opposed to encoding the higher-order syntax and logical structure of sentences in neural networks, =-=[7, 11]-=-. In this paper, we stretch the fundamental quest for correctness of computations from the area of Computational Logic to the area of Neuro-Symbolic computation. In particular, we examine the question...

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...required when machinelearning various logical structures, as e.g. in [7, 36, 43]. Another solution would be to enumerate the first-order syntax and implement proof-search in neural networks directly, =-=[26, 40]-=-. However, in such applications, statistical nature of learning often conflicts with logical soundness; [26]. The related work on using analysis of formula occurrences in big libraries of proofs [39] ...

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...itts, in that logical information is given only by means of logical connectives and truth values; as opposed to encoding the higher-order syntax and logical structure of sentences in neural networks, =-=[7, 11]-=-. In this paper, we stretch the fundamental quest for correctness of computations from the area of Computational Logic to the area of Neuro-Symbolic computation. In particular, we examine the question...