Reasoning with real-valued first order logic and probability intervals
View Patent ↗Embodiments are provided for providing enhanced reasoning in a computing system by a processor. All first-order logic formulas may be converted into real-valued logic formulas. A probabilistic inference is executed using the real-valued logic formulas and one or more probability intervals associated with an atomic formulae in a knowledge base to provide an interval conditional probability indicating that a first predicate condition is true based one or more alternative predicates being true.
1 . A method for providing enhanced automated reasoning in a computing environment by one or more processors comprising:
executing machine learning logic to convert a set of first-order logic statements into a set of real-valued logic representations, wherein the set of real-valued logic representations are input as training data into a logical neural network (“LNN”); and
generating the LNN by using the training data, wherein the LNN is configured to execute a probabilistic inference using the set of real-valued logic representations and one or more probability intervals associated with an atomic statement in a knowledge base to provide an interval conditional probability indicating that a first predicate condition is true based one or more alternative predicates being true, wherein the probabilistic inference comprises performing iterative message passing across nodes of a credal network representation of the LNN to update lower and upper probability bounds at the nodes, and terminating the iterative message passing responsive to detecting a convergence condition or expiration of a time limit.
2 . The method of claim 1 , further including representing a truth value of each of the set of real-valued logic representations as a zero or a one value.
3 . The method of claim 1 , further including receiving the set of first-order logic statements, and a set of intervals representing upper and lower bounds on one or more truth values of a set of ground predicates from the set of first-order logic statements.
4 . The method of claim 1 , further including setting upper and lower bounds on one or more truth values of the set of real-valued logic representations in the knowledge base.
5 . The method of claim 1 , further including determining a probability of a ground predicate being true based on an alternative ground predicate being true.
6 . The method of claim 1 , further including:
grounding a first-order logic based on a knowledge domain of a plurality of variables, wherein the LNN is a representation of the grounded first-order logic; and
constructing the credal network representation associated with the LNN.
7 . The method of claim 1 , further including applying the probabilistic inference to determine a set of solutions to one or more queries.
8 . A system for providing enhanced automated reasoning in a computing environment, comprising:
one or more computers with executable instructions that when executed cause the system to:
execute machine learning logic to convert a set of first-order logic statements into a set of real-valued logic representations, wherein the set of real-valued logic representations are input as training data into a logical neural network (“LNN”); and
generate the LNN by using the training data, wherein the LNN is configured to execute a probabilistic inference using the set of real-valued logic representations and one or more probability intervals associated with an atomic statement in a knowledge base to provide an interval conditional probability indicating that a first predicate condition is true based one or more alternative predicates being true, wherein the probabilistic inference comprises performing iterative message passing across nodes of a credal network representation of the LNN to update lower and upper probability bounds at the nodes, and terminating the iterative message passing responsive to detecting a convergence condition or expiration of a time limit.
9 . The system of claim 8 , wherein the executable instructions when executed cause the system to represent a truth value of each of the set of real-valued logic representations as a zero or a one value.
10 . The system of claim 8 , wherein the executable instructions when executed cause the system to receive the set of first-order logic statements, and a set of intervals representing upper and lower bounds on one or more truth values of a set of ground predicates from the set of first-order logic statements.
11 . The system of claim 8 , wherein the executable instructions when executed cause the system to set upper and lower bounds on one or more truth values of the set of real-valued logic representations in the knowledge base.
12 . The system of claim 8 , wherein the executable instructions when executed cause the system to determine a probability of a ground predicate being true based on an alternative ground predicate being true.
13 . The system of claim 8 , wherein the executable instructions when executed cause the system to:
ground a first-order logic based on a knowledge domain of a plurality of variables, wherein the LNN is a representation of the grounded first-order logic; and
construct the credal network representation associated with the LNN.
14 . The system of claim 8 , wherein the executable instructions when executed cause the system to apply the probabilistic inference to determine a set of solutions to one or more queries.
15 . A computer program product for providing enhanced automated reasoning in a computing environment, the computer program product comprising:
one or more computer readable storage media, and program instructions collectively stored on the one or more computer readable storage media, the program instruction comprising:
program instructions to execute machine learning logic to convert a set of first-order logic statements into a set of real-valued logic representations, wherein the set of real-valued logic representations are input as training data into a logical neural network (“LNN”); and
program instructions to generate the LNN by using the training data, wherein the LNN is configured to execute a probabilistic inference using the set of real-valued logic representations and one or more probability intervals associated with an atomic statement in a knowledge base to provide an interval conditional probability indicating that a first predicate condition is true based one or more alternative predicates being true, wherein the probabilistic inference comprises performing iterative message passing across nodes of a credal network representation of the LNN to update lower and upper probability bounds at the nodes, and terminating the iterative message passing responsive to detecting a convergence condition or expiration of a time limit.
16 . The computer program product of claim 15 , further including program instructions to represent a truth value of each of the set of real-valued logic representations as a zero or a one value.
17 . The computer program product of claim 15 , further including program instructions to receive the set of first-order logic statements, and a set of intervals representing upper and lower bounds on one or more truth values of a set of ground predicates from the set of first-order logic statements.
18 . The computer program product of claim 15 , further including program instructions to set upper and lower bounds on one or more truth values of the set of real-valued logic representations in the knowledge base.
19 . The computer program product of claim 15 , further including program instructions to determine a probability of a ground predicate being true based on an alternative ground predicate being true.
20 . The computer program product of claim 15 , further including program instructions to:
ground a first-order logic based on a knowledge domain of a plurality of variables, wherein the LNN is a representation of the grounded first-order logic; and
construct the credal network representation associated with the LNN.