DEVICE AND COMPUTER-IMPLEMENTED METHOD FOR PROVIDING, TESTING, VERIFYING, OR VALIDATING A FACT IN A DATABASE STRUCTURE, FOR LEARNING A WEIGHT FOR PROVIDING, TESTING, VERIFYING, OR VALIDATING A FACT IN A DATABASE STRUCTURE WITH LINEAR REGRESSION, OR PROVIDING THE DATABASE MANAGEMENT SYSTEM WITH THE LEARNED WEIGHT

Abstract

Device and computer-implemented method for providing, testing, verifying, or validating a fact in a database structure. The method including providing symbolic rules that are configured to predict the fact depending on one of the two entities and the relation, or depending on the two entities, wherein the symbolic rules are associated with a respective weight, determining a score for the fact depending on the weights with a linear function for determining the score depending on the weights, wherein the score indicates whether the fact belongs to the database structure or not, and providing, testing, verifying, or validating the fact in the database structure depending on the score.

Description

CROSS REFERENCE

The present application claims the benefit under 35 U.S.C. § 119 of German Patent Application No. DE 10 2023 210 529.2 filed on Oct. 25, 2023, which is expressly incorporated herein by reference in its entirety.

FIELD

The present invention relates to a device and a computer-implemented method for providing, testing, verifying, or validating a fact in a database structure, a computer-implemented method for learning a weight for providing, testing, verifying, or validating a fact in a database structure with linear regression, and a computer-implemented method for providing the database management system with the learned weight.

SUMMARY

According to an example embodiment of the present invention, a computer-implemented method for providing, testing, verifying, or validating a fact in a database structure, in particular a knowledge graph that is stored in a database, with linear regression, wherein the database structure, in particular the knowledge graph, comprises entities and relations, wherein the fact comprises two entities, and a relation, wherein the method comprises providing symbolic rules that is configured to predict the fact depending on one of the two entities and the relation, or depending on the two entities, wherein the symbolic rules are associated with a respective weight, determining a score for the fact depending on the weights with a linear function for determining the score depending on the weights, wherein the score indicates whether the fact belongs to the database structure or not, and providing, testing, verifying, or validating the fact in the database structure depending on the score. The score that depends on the linear function of the weights has a better learning dynamic than a score that depends on a non-linear function of confidences that are associated with the symbolic rules.

According to an example embodiment of the present invention, the method may comprise determining the score for a plurality of facts for the database structure, in particular the knowledge graph, wherein the facts of the plurality of facts respectively comprise two entities and a relation of the database structure, wherein the plurality of facts comprises the fact, and wherein the method comprises selecting the fact from the plurality of facts depending on the scores that are determined for the plurality of facts, wherein the score that is determined for the selected fact indicates a higher probability that the fact belongs into the database structure, or a higher probability that the fact not belongs to the database structure, than the score that is determined for at least one other fact of the plurality of facts, in particular indicates the highest probability that is determined for the facts of the plurality of facts.

According to an example embodiment of the present invention, providing the fact may comprise adding the fact to the database structure, in particular when the score that is determined for the fact indicates that the fact belongs into the database structure. Testing, verifying, or validating the fact may comprise searching the fact in the database structure, and either confirming the fact in the database structure in case the fact is found, in particular when the score that is determined for the fact indicates that the fact belongs into the database structure, or invalidating the fact in the database structure or removing the fact from the database structure, in particular when the score that is determined for the fact indicates that the fact not belongs into the database structure.

According to an example embodiment of the present invention, a computer-implemented method for learning weights for providing, testing, verifying, or validating a fact in a database structure, in particular a knowledge graph, with linear regression, wherein the database structure, in particular the knowledge graph, comprises entities and relations, wherein the fact comprises two entities, and a relation, wherein the method comprises providing symbolic rules that are configured to predict the fact depending on one of the two entities and the relation, or depending on the two entities, wherein the symbolic rules are associated with a respective weight, and learning the weights depending on a loss, wherein the loss comprises a linear function for determining a score depending on the weights, wherein the score indicates whether the fact belongs to the database structure or not. The weights are learned with linear regression directly due to a simple linear scoring function.

According to an example embodiment of the present invention, the method for learning may comprise providing a plurality of symbolic rules that are configured to map an entity and a relation of the database structure to an entity of the database structure, or to map two entities of the database structure to a relation of the database structure, wherein the symbolic rules of the plurality of symbolic rules are associated with a respective weight, determining selected symbolic rules that predict the fact from the plurality of symbolic rules, and learning the weights that are associated with the selected symbolic rules depending on the loss, wherein the function in the loss depends on the respective weights that are associated with the selected symbolic rules. The selected symbolic rules actually predict the fact. The ruleset comprising the plurality of symbolic rules is improved depending on the weights of the rules that actually predict the fact. Symbolic rules not predicting the fact are ignored.

According to an example embodiment of the present invention, the method for learning may comprise providing, for at least one function in the loss, a reference, wherein the reference indicates whether the fact belongs to the database structure or not, wherein the loss depends on the reference for the at least one function. The reference provides supervised learning.

According to an example embodiment of the present invention, the loss may comprise for a plurality of facts a respective function, or in that the method comprises providing the reference for a plurality of facts, wherein the loss comprises for a plurality of facts a respective function, and depends on the reference for the plurality of facts.

According to an example embodiment of the present invention, a computer-implemented method for providing a database management system for managing a database structure, wherein the method for providing the database management system comprises learning weights for providing, testing, verifying, or validating a fact in the database structure, in particular a knowledge graph, in particular with the method for learning the weights for providing, testing, verifying, or validating a fact in the database structure, and providing the database management system with the learned weights and with means for providing, testing, verifying, or validating a fact in a database structure with the method for providing, testing, verifying, or validating a fact in a database structure.

According to an example embodiment of the present invention, a device comprises at least one processor and at least one memory, wherein the at least one processor is configured to execute instructions that, when executed by the at least one processor, cause the device to execute, method for providing, testing, verifying, or validating the fact in the database structure, method for learning the weights for providing, testing, verifying, or validating the fact in the database structure, the method for providing the database management system for managing the database structure, wherein the at least one memory stores the instructions.

According to an example embodiment of the present invention, a database structure, in particular knowledge graph, that is stored in a database, comprises entities, and relations, and facts, wherein a fact comprises two entities, and a relation, wherein the database structure comprises symbolic rules that are configured to predict the fact depending on one of the two entities and the relation, or depending on the two entities, wherein the database structure comprises weights, and wherein the symbolic rules are associated with a respective weight, wherein the database structure comprises a loss for learning the weights, wherein the loss comprises a linear function for determining a score depending on the weights, wherein the score indicates whether the fact belongs to the database structure or not.

According to an example embodiment of the present invention, a computer program comprises computer-readable instructions that, when executed by a computer, cause the computer to execute the method for providing, testing, verifying, or validating a fact in a database structure, the method for learning and/or the method for providing a database management system, according to the present invention.

Further embodiments of the present invention are derived from the following description and the figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically depicts a device, according to an example embodiment of the present invention.

FIG. 2 schematically depicts a data base structure, according to an example embodiment of the present invention.

FIG. 3 depicts a flow chart comprising steps of a method for providing, testing, verifying, or validating a fact in the database structure, according to an example embodiment of the present invention.

FIG. 4 depicts a flow chart comprising steps of a method for learning a weight for providing, testing, verifying, or validating the fact in the database structure, according to an example embodiment of the present invention.

FIG. 5 depicts a flow chart comprising steps of a method for providing a database management system, according to an example embodiment of the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

FIG. 1 schematically depicts a device 100.

The device 100 comprises at least one processor 102 and at least one memory 104.

The at least one processor 102 is configured to execute instructions.

The instructions, when executed by the at least one processor 102, may cause the device 100 to execute a method for providing, testing, verifying, or validating a fact in a database structure.

The instructions, when executed by the at least one processor 102, may cause the device 100 to execute a method for learning weights for providing, testing, verifying, or validating the fact in the database structure.

The instructions, when executed by the at least one processor 102, may cause the device 100 to execute a method for providing a database management system.

The at least one memory 104 stores the instructions.

FIG. 2 schematically depicts an example 200 for a part of the data base structure.

The database structure in the example 200 comprises a knowledge graph G⊂{p (s, o)|p ∈ P, s, o ∈C} as a set of ground atoms or facts defined on top of a signature C, P, wherein C is a set of constants, i.e., entities, and P is a set of predicates, i.e., relations, and wherein a fact t=p (s, o), comprises two entities, i.e., a subject s, and an object o, and a relation, i.e., a predicate p.

The database structure, e.g., the knowledge graph, in the example is stored in a database. The at least one memory 104 in the example comprises the database.

FIG. 2 schematically depicts exemplary entities 202, and relations 204 or the database structure.

FIG. 2 depicts exemplary relations 204 labelled citizen, born, works, city, capital, married, and exemplary entities 202 labelled monica, paul, sarah, tom, camilla, john, switzerland, germany, austria, usa, geneva, bern, vienna, chicago, Washington. FIG. 2 depicts exemplary facts t:

• • works (monica, geneva),
  • city (geneva, switzerland),
  • citizen (paul, switzerland),
  • born (paul, switzerland),
  • married (paul, sarah),
  • citizen (sarah, switzerland),
  • born (sarah, switzerland),
  • works (sarah, bern),
  • city (bern, switzerland),
  • capital (bern, switzerland),
  • works (tom, bern),
  • works (tom, vienna),
  • born (tom, germany),
  • married (tom, camilla),
  • citizen (camilla, austria),
  • born (camilla, austria),
  • capital (vienna, austria),
  • works (camilla, vienna),
  • works (camilla, chicago),
  • works (john, chicago),
  • citizen (john, usa),
  • born (john, usa),
  • city (chicago, usa),
  • city (washington, usa),
  • capital (washington, usa),
  • works (john, washington).

The database structure may be incomplete. For example, the knowledge graph is incomplete. In FIG. 2, dashed edges correspond to the following examples for missing facts:

• • citizen (tom, austria),
  • citizen (tom, germany),
  • city (vienna, austria).

The problem of knowledge graph completion is concerned with defining an automated procedure for finding missing facts solely by analyzing a statistical distributions and regularities of the given knowledge graph.

Missing facts may be found with queries that comprise an entity and a relation or with queries that comprise two entities. In the example described herein, missing facts are found with queries that comprise a relation and an entity. Queries comprising two entities may be used accordingly.

Missing facts are for example found with queries p (s,?), e.g., such as citizen (tom,?) and/or queries p (?, o), e.g., such as citizen (?, Austria), wherein? is a placeholder for the entity of the missing fact.

A model may be used to predict answers in the form of candidate facts p (s, o), e.g., such as citizen (tom, germany), or citizen (tom, switzerland) and assigns plausibility scores to these answers. A ranking of the candidate facts may be formed, and the highest ranking candidate fact may be used as missing fact. The model for example predicts a score for ranking the candidate facts such that the higher the score for a candidate fact is, the more likely it is that the candidate fact is the missing fact.

The candidate facts may be found based on symbolic rules R. The symbolic rules R are configured to predict candidate facts t depending on two entities 202.

A symbolic rule r∈R in the example is configured to map a first entity 202 and a relation 204 of the database structure to a second entity 202 of the database structure. According to the example, the symbolic rule r comprises a condition that, when the first entity 202, the second entity 202 and the relation 204 meet the condition, maps the first entity 202, and the relation 204 to the second entity 202.

The symbolic rule r may be configured to map two entities 202 of the database structure to a relation 202 of the database structure. The symbolic rule r may be configured to map a plurality of entities 202 and/or a plurality of relations 204 to an entity 202. The symbolic rule r may comprise a condition that, when the first entity 202, the second entity 202 and the relation 204 meet the condition, maps the first entity 202, and the second entity 202 to the relation 204.

Rules may be determined depending on the database structure, e.g., the knowledge graph. An example for determining rules is described in Christian Meilicke, Melisachew Wudage Chekol, Daniel Ruffinelli, and Heiner Stuckenschmidt, “Anytime bottom-up rule learning for knowledge graph completion;” in Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, pages 3137-3143. Ijcai.org, 2019 (AnyBURL). An example for determining rules is described in in Luis Galarraga, Christina Teflioudi, Katja Hose, and Fabian M Suchanek, “Fast rule mining in ontological knowledge bases with AMIE+;” the VLDB Journal, 24 (6): 707-730, 2015 (AMIE).

According to an example, four rules r₁, r₂, r₃, r₄ are defined

r ₁ :a(X,Y)←b(X,Y)

r ₂ :a(X,Y)←c(X,A),d(A,Y)

r ₃ :a(X,Y)←c(X,A),e(A,Y)

r ₄ :a(X,Y)←f(X,A),a(A,Y)

wherein a, b, c, d, e, f, are relations 204, and X, Y, A are variables representing entities 202. The rule r_i comprise a head, e.g., the predicted fact t that comprises the first entity 202, the second entity 202, and the relation 204, left of the ←. The rule r_i comprises a tail right of the ←. The rule r_i maps the tail to the head, in case entities 202 are found for the variables, such that the relations in the tail exist in the database structure.

An example for the four rules r₁, . . . , r₄ for the example 200 may be:

r ₁:citizen(X,Y)←born(X,Y)

r ₂:citizen(X,Y)←works(X,A),city(A,Y)

r ₃:citizen(X,Y)<works(X,A),capital(A,Y)

r ₄:citizen(X,Y)<married(X,A),citizen(A,Y)

wherein a=citizen, b=born, c=works, d=city, e=capital, f=married.

The rules r_i are associated with a respective confidence c_i that indicates whether the fact t_i predicted by the respective rule r_i ∈R belongs to the database structure or not. According to an example, the confidence c_i ∈ [0,1] is used. The confidence c_i may be defined on a different set of values than [0,1]. The rules r are associated with a respective score s_i that indicates whether the fact predicted by the respective rule n belongs to the database structure or not. The score s_i for a respective fact t_i may be determined depending on the confidences c_j of the rules r_j ∈R.

According to an example, the confidences c_j for the rules r_j may be learned on training data D={(y_i, x_i)}_i=1^N, wherein N is the number of facts t_i predicted by rules in R, wherein the variable y_i=1 if the fact t_i is seen in the training data D and y_i=0 otherwise, and x_i=(x_i1, . . . , x_ij, . . . , x_iK) is a binary vector, wherein x_ij=1 if the rule r_i predicted the fact t_i and x_ij=0 otherwise.

According to the example, the score s_i for a respective fact t_i depends on the respective confidences c_j:

$s_i=\sum _{j=I}^K{\stackrel{\_}{w}}_j{x}_{\mathrm{ij}}$

wherein w_j=−log (1−x_ijc_j).

This means, the x_ijc_j are reparametrized with z=x_ijc_j and a function −log (−z+1) that is monotonically increasing for z<1. According to the example, instead of learning the confidences c_j, the weights w have been learned with a loss

$L\left(\stackrel{\_}{w}\right)=-\sum _{i=1}^N{y}_i·\log P\left(y_i|x_i;\stackrel{\_}{w}\right)+\left(1-y_i\right)\log \left(1-P\left(y_i|x_i;\stackrel{\_}{w}\right)\right)$

The loss L(w) comprises a function

$P\left(y_i|x_i;\stackrel{\_}{w}\right)=\sigma \left(\sum _{j=1}^K{\stackrel{\_}{w}}_j{x}_{\mathrm{ij}}+w_0\right)$

for determining the weights w_j directly, wherein o is the sigmoid function. The weights w_j are for example learned with an optimization with respect to the weights w_j and a bias term w₀. The bias term w₀=0 may be used.

The loss L(w) depends on respective reference y_i for the respective function P(y_i|x_i;w).

The loss in the example is smooth and differentiable with respect to the parameter w_j. The learning may employ gradient-based optimization techniques on the loss.

The model for example comprises the parameter w_j and is configured to predict the scores s_i.

FIG. 3 depicts a method for providing, testing, verifying, or validating a fact t in the database structure, in particular the knowledge graph.

The method comprises a step 302.

The step 302 comprises providing the symbolic rules R for predicting facts {t₁, . . . , t_N}. The symbolic rules R are determined for example on the database structure, e.g., the knowledge graph, with AnyBURL or AMIE.

A respective symbolic rule r_i ∈R is configured to predict a respective fact t ∈ {t₁, . . . , t_N}. A respective symbolic rule r_i ∈R is associated with a respective weight w_j.

The method comprises a step 304.

The step 304 comprises determining a plurality of facts {t₁, . . . , t_N} with the respective symbolic rules r_i ∈R, and a respective score s_i for a respective fact t_i.

The score s_i for the fact t_i is for example determined with a linear function for determining the score s_i depending on the weights w_j of the rules r_j that predicted the fact t_i:

$s_i=\sum _{j=1}^K{\stackrel{\_}{w}}_j{x}_{\mathrm{ij}}$

wherein x_i=(x_i1, . . . , x_ij, . . . , x_iK) is a binary vector, wherein x_ij=1 if the rule r_j predicted the fact t_i and x_ij=0 otherwise.

The weights w_j in the example are learned weights w_j. According to an example, the scores s_i are determined with the model depending on the learned weights w_j.

The score s_i indicates whether the fact t_i belongs to the database structure or not.

The method comprises a step 306.

The step 306 comprises providing, testing, verifying, or validating the fact t_i in the database structure depending on the score.

Providing the fact t_i may comprise selecting the fact t_i from the plurality of facts depending on the scores that are determined for the plurality of facts.

Providing the fact t_i may comprise selecting the fact t_i that has the highest score. Providing the fact t_i may comprise selecting the fact t_i that has a higher score than other facts of the plurality of facts. Providing the fact t_i may comprise selecting facts that have the highest score or that have a higher score than other facts of the plurality of facts.

In the example, the score that is determined for the selected fact indicates a higher probability that the fact belongs into the database structure than the score that is determined for at least one other fact of the plurality of facts.

Providing the fact may comprise adding the fact to the database structure, in particular when the score that is determined for the fact indicates that the fact belongs into the database structure. According to the example, the fact or the facts associated with the highest score or with a higher score than other facts is added.

The example is not limited to the case wherein a higher probability indicates that the fact belongs into the database structure. According to an example, a higher probability may indicate that the fact not belongs to the database structure. Accordingly, the fact or the facts associated with the lowest score or with a lower score than other facts may be added.

Testing, verifying, or validating the fact may comprises searching the fact in the database structure, and either confirming the fact in the database structure in case the fact is found, in particular when the score that is determined for the fact indicates that the fact belongs into the database structure, or invalidating the fact in the database structure or removing the fact from the database structure, in particular when the score that is determined for the fact indicates that the fact not belongs into the database structure.

FIG. 4 depicts a flow chart comprising steps of a computer-implemented method for learning the weights w_i for providing, testing, verifying, or validating the fact in the database structure.

The method comprises a step 402.

The step 402 comprises providing the symbolic rules R.

The symbolic rules R are for example provided as described in step 302. The symbolic rules R are associated with a respective weight w_i that reparametrizes a respective confidence c_i.

The step 402 comprises providing respective references y_i for the scores s_i.

The reference y_i indicates for the fact t_i whether the fact t_i belongs to the database structure or not.

For example, the training data D is provided.

The reference y_i is for example the y_i=1 if the fact t_i is seen in the training data D and y_i=0 otherwise.

The method comprises a step 404.

The step 404 comprises determining selected symbolic rules r that predict the fact from the plurality of symbolic rules.

The selected symbolic rules are for example identified with the binary vector x_i=(x_i1, . . . , x_ij, . . . , x_iK), wherein x_ij=1 if the rule r predicted the fact t_i and x_ij=0 otherwise.

The method comprises a step 406.

The step 406 comprises learning the confidences c_i depending on the loss L(w).

The step 406 comprises learning the weights w_j that are associated with the selected symbolic rules r_j depending on the loss L(w), i.e., with linear regression depending on the linear function for the scores.

The loss depends on the respective functions that are associated with the selected symbolic rules r_j. The loss depends on the respective weights w_j that are associated with the selected symbolic rules r_j.

The learning for example employs gradient-based optimization techniques on the loss L(w). For example, the weights w_j are determined that minimize the loss L(w).

FIG. 5 schematically depicts a method for providing a database management system for managing the database structure.

The method for providing the database management system comprises a step 502.

The step 502 comprises learning the weights w_j, in particular with the method for learning the weights w_j.

The method for providing the database management system comprises a step 504.

The step 504 comprises providing the database management system with the learned weights w_j.

The step 504 comprises providing the database management system means for providing, testing, verifying, or validating a fact in the database structure with the method for providing, testing, verifying, or validating a fact in a database structure.

The means for providing, testing, verifying, or validating a fact in the database structure may comprise the at least one processor 102, and the at least one memory 104.

Claims

1. A computer-implemented method for providing, or testing, or verifying, or validating a fact in a database structure, the database structure including a knowledge graph that is stored in a database, with linear regression, the knowledge graph including entities and relations, and the fact includes two entities and a relation, the method comprising the following steps: providing symbolic rules that are configured to predict the fact depending on one of the two entities and the relation or depending on the two entities, wherein each of the symbolic rules is associated with a respective weight;determining a score for the fact depending on the respective weights with a linear function for determining the score depending on the respective weights, wherein the score indicates whether the fact belongs to the database structure or not; andproviding or testing or verifying or validating the fact in the database structure depending on the score.

2. The method according to claim 1, further comprising: determining a respective score for each of a plurality of facts for the database structure, wherein the facts of the plurality of facts respectively include two entities and a relation of the database structure, wherein the plurality of facts include the fact, and wherein the method further comprises selecting the fact from the plurality of facts depending on the respective scores that are determined for the plurality of facts, wherein the respective score that is determined for the selected fact indicates a higher probability that the fact belongs in the database structure or a higher probability that the fact not belongs to the database structure, than the respective score that is determined for at least one other fact of the plurality of facts, indicates a highest probability that is determined for the facts of the plurality of facts.

3. The method according to claim 2, wherein: the providing of the fact includes adding the fact to the database structure when the score that is determined for the fact indicates that the fact belongs into the database structure, orthe testing or verifying, or validating of the fact includes searching the fact in the database structuer, and either: (i) confirming the fact in the database structure in the case the fact is found, when the score that is determined for the fact indicates that the fact belongs into the database structure, or (ii) invalidating the fact in the database structure or removing the fact from the database structure, when the score that is determined for the fact indicates that the fact does not belong in the database structure.

4. A computer-implemented method for learning weights for providing or testing or verifying or validating a fact in a database structure including a knowledge graph, with linear regression, the knowledge graph including entities and relations, wherein the fact includes two entities and a relation, the method comprising the following steps: providing symbolic rules that are configured to predict the fact depending on one of the two entities and the relation, or depending on the two entities, wherein each of the symbolic rules is associated with a respective weight;learning the respective weights depending on a loss, wherein the loss includes a linear function for determining a score depending on the weights, wherein the score indicates whether the fact belongs to the database structure or not.

5. The method according to claim 4, further comprising: providing a plurality of symbolic rules that are configured to map an entity and a relation of the database structure to an entity of the database structure, or to map two entities of the database structure to a relation of the database structure, wherein each of the symbolic rules of the plurality of symbolic rules are associated with a respective weight;determining selected symbolic rules that predict the fact from the plurality of symbolic rules; andlearning the respective weights that are associated with the selected symbolic rules depending on the loss, wherein a function in the loss depends on the respective weights that are associated with the selected symbolic rules.

6. The method according to claim 4, further comprising providing, for at least one function in the loss, a reference, wherein the reference indicates whether the fact belongs to the database structure or not, wherein the loss depends on the reference for the at least one function.

7. The method according to claim 5, wherein: the loss includes for a plurality of facts a respective function, orthe method further comprises providing the reference for a plurality of facts, wherein the loss includes for a plurality of facts a respective function, and depends on the reference for the plurality of facts.

8. A computer-implemented method for providing a database management system for managing a database structure, the method comprising: learning weights for providing or testing or verifying or validating a fact in the database structure, including a knowledge graph, wherein the database structure includes entities and relations, and wherein the fact includes two entities and a relation the learning of the weights including: providing symbolic rules that are configured to predict the fact depending on one of the two entities and the relation, or depending on the two entities, wherein each of the symbolic rules is associated with a respective weight, andlearning the respective weights depending on a loss, wherein the loss includes a linear function for determining a score depending on the weights, wherein the score indicates whether the fact belongs to the database structure or not;providing the database management system with the learned weights, and with an arrangement for providing or testing or verifying or validating a fact in a database structure with a method for providing or testing or verifying or validating a fact in the knowledge graph including: providing symbolic rules that are configured to predict the fact depending on one of the two entities and the relation, or depending on the two entities, wherein each of the symbolic rules is associated with a respective weight,determining a score for the fact depending on the respective weights with a linear function for determining the score depending on the respective weights, wherein the score indicates whether the fact belongs to the database structure or not, and providing or testing or verifying or validating the fact in the database structure depending on the score.

9. A device, comprising: at least one processor; andat least one memory;wherein the at least one processor is configured to execute instructions that, when executed by the at least one processor, cause the device to perform steps for providing, or testing, or verifying, or validating a fact in a database structure, the database structure including a knowledge graph that is stored in a database, with linear regression, the database structure including entities and relations, and the fact includes two entities, and a relation, the steps including: providing symbolic rules that are configured to predict the fact depending on one of the two entities and the relation, or depending on the two entities, wherein each of the symbolic rules is associated with a respective weight,determining a score for the fact depending on the respective weights with a linear function for determining the score depending on the respective weights, wherein the score indicates whether the fact belongs to the database structure or not, andproviding or testing or verifying or validating the fact in the database structure depending on the score; andwherein the at least one memory stores the instructions.

10. A database structure including a knowledge graph that is stored in a database, the database structure comprising: entities;relations; andfacts, wherein each fact includes two entities and a relation;wherein the database structure includes: a first symbolic rule configured to predict the fact depending on one of the two entities and the relation, or depending on the two entities,weights, wherein each of the symbolic rules are associated with a respective weight;a loss for learning the weights, wherein the loss includes a linear function for determining a score depending on the weights, wherein the score indicates whether a fact belongs to the database structure or not.

11. A non-transitory computer-readable medium on which is stored a computer program including computer-readable instructions for providing, or testing, or verifying, or validating a fact in a database structure, the database structure including a knowledge graph that is stored in a database, with linear regression, the knowledge graph including entities and relations, and the fact includes two entities, and a relation, the instructions, when executed by a computer, causing the computer to perform the following steps: providing symbolic rules that are configured to predict the fact depending on one of the two entities and the relation, or depending on the two entities, wherein each of the symbolic rules is associated with a respective weight;determining a score for the fact depending on the respective weights with a linear function for determining the score depending on the respective weights, wherein the score indicates whether the fact belongs to the database structure or not; andproviding or testing or verifying or validating the fact in the database structure depending on the score.