Abstract: According to one embodiment, a method, computer system, and computer program product for probabilistic inference from imprecise knowledge is provided. The embodiment may include identifying a knowledge base of one or more statements and first probability distributions corresponding to each of the one or more statements. The embodiment may also include identifying one or more queries. The embodiment may further include determining logical inferences about and second probability distributions for queries from the one or more queries or statements from the one or more statements based on information in the knowledge base.

Abstract: A computer-implemented method may include processors configured for receiving input data corresponding to a knowledge base comprising a plurality of propositional logic clauses, generating output data corresponding to a first set of logical rules and a first set of facts based on the plurality of propositional logic clauses, accumulating the first set of facts to generate accumulated facts, generating a model graph based on the accumulated facts and the first set of logical rules, alternating reasoning and learning passes at the model graph until convergence to generate a second set of logical rules and a second set of facts, and generating a third set of logical rules and a third set of facts, wherein the third set of logical rules and the third set of facts exceed a first predetermined threshold.

Abstract: Word sense disambiguation using a glossary layer embedded in a deep neural network includes receiving, by one or more processors, input sentences including a plurality of words. At least two words in the plurality of words are homonyms. The one or more processors convert the plurality of words associated with each input sentence into a first vector including possible senses for the at least two words. The first vector is then combined with a second vector including a domain-specific contextual vector associated with the at least two words. The combination of the first vector with the second vector is fed into a recurrent deep logico-neural network model to generate a third vector that includes word senses for the at least two words. A threshold is set for the third vector to generate a fourth vector including a final word sense vector for the at least two words.

Abstract: To improve the technological process of computerized answering of logical queries over incomplete knowledge bases, obtain a first order logic query; with a trained, computerized neural network, convert the first order logic query into a logic embedding; and answer the first order logic query using the logic embedding.

Abstract: Maximum expressivity can be received representing a ratio between maximum and minimum input weights to a neuron of a neural network implementing a weighted real-valued logic gate. Operator arity can be received associated with the neuron. Logical constraints associated with the weighted real-valued logic gate can be determined in terms of weights associated with inputs to the neuron, a threshold-of-truth, and a neuron threshold for activation. The threshold-of-truth can be determined as a parameter used in an activation function of the neuron, based on solving an activation optimization formulated based on the logical constraints, the activation optimization maximizing a product of expressivity representing a distribution width of input weights to the neuron and gradient quality for the neuron given the operator arity and the maximum expressivity. The neural network of logical neurons can be trained using the activation function at the neuron, the activation function using the determined threshold-of-truth.

Abstract: Word sense disambiguation using a glossary layer embedded in a deep neural network includes receiving, by one or more processors, input sentences including a plurality of words. At least two words in the plurality of words are homonyms. The one or more processors convert the plurality of words associated with each input sentence into a first vector including possible senses for the at least two words. The first vector is then combined with a second vector including a domain-specific contextual vector associated with the at least two words. The combination of the first vector with the second vector is fed into a recurrent deep logico-neural network model to generate a third vector that includes word senses for the at least two words. A threshold is set for the third vector to generate a fourth vector including a final word sense vector for the at least two words.

Abstract: A system for configuring and using a logical neural network including a graph syntax tree of formulae in a represented knowledgebase connected to each other via nodes representing each proposition. One neuron exists for each logical connective occurring in each formula and, additionally, one neuron for each unique proposition occurring in any formula. All neurons return pairs of values representing upper and lower bounds on truth values of their corresponding subformulae and propositions. Neurons corresponding to logical connectives accept as input the output of neurons corresponding to their operands and have activation functions configured to match the connectives' truth functions. Neurons corresponding to propositions accept as input the output of neurons established as proofs of bounds on the propositions' truth values and have activation functions configured to aggregate the tightest such bounds.

Abstract: Maximum expressivity can be received representing a ratio between maximum and minimum input weights to a neuron of a neural network implementing a weighted real-valued logic gate. Operator arity can be received associated with the neuron. Logical constraints associated with the weighted real-valued logic gate can be determined in terms of weights associated with inputs to the neuron, a threshold-of-truth, and a neuron threshold for activation. The threshold-of-truth can be determined as a parameter used in an activation function of the neuron, based on solving an activation optimization formulated based on the logical constraints, the activation optimization maximizing a product of expressivity representing a distribution width of input weights to the neuron and gradient quality for the neuron given the operator arity and the maximum expressivity. The neural network of logical neurons can be trained using the activation function at the neuron, the activation function using the determined threshold-of-truth.