Computer system/server 12 may be described in the general context of computer system-executable instructions, such as program modules, being executed by a computer system. Generally, program modules may include routines, programs, objects, components, logic, data structures, and so on that perform particular tasks or implement particular abstract data types. Computer system/server 12 may be practiced in distributed cloud computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed cloud computing environment, program modules may be located in both local and remote computer system storage media including memory storage devices.

As shown in FIG. 1, computer system/server 12 in cloud computing node 10 is shown in the form of a general-purpose computing device. The components of computer system/server 12 may include, but are not limited to, one or more processors or processing units 16, a system memory 28, and a bus 18 that couples various system components including system memory 28 to processor 16.

Bus 18 represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnects (PCI) bus.

Computer system/server 12 typically includes a variety of computer system readable media. Such media may be any available media that is accessible by computer system/server 12, and it includes both volatile and non-volatile media, removable and non-removable media.

System memory 28 can include computer system readable media in the form of volatile memory, such as random-access memory (RAM) 30 and/or cache memory 32. Computer system/server 12 may further include other removable/non-removable, volatile/non-volatile computer system storage media. By way of example only, storage system 34 can be provided for reading from and writing to a non-removable, non-volatile magnetic media (not shown and typically called a “hard drive”). Although not shown, a magnetic disk drive for reading from and writing to a removable, non-volatile magnetic disk (e.g., a “floppy disk”), and an optical disk drive for reading from or writing to a removable, non-volatile optical disk such as a CD-ROM, DVD-ROM or other optical media can be provided. In such instances, each can be connected to bus 18 by one or more data media interfaces. As will be further depicted and described below, system memory 28 may include at least one program product having a set (e.g., at least one) of program modules that are configured to carry out the functions of embodiments of the invention.

Program/utility 40, having a set (at least one) of program modules 42, may be stored in system memory 28 by way of example, and not limitation, as well as an operating system, one or more application programs, other program modules, and program data. Each of the operating system, one or more application programs, other program modules, and program data or some combination thereof, may include an implementation of a networking environment. Program modules 42 generally carry out the functions and/or methodologies of embodiments of the invention as described herein.

Computer system/server 12 may also communicate with one or more external devices 14 such as a keyboard, a pointing device, a display 24, etc.; one or more devices that enable a user to interact with computer system/server 12; and/or any devices (e.g., network card, modem, etc.) that enable computer system/server 12 to communicate with one or more other computing devices. Such communication can occur via Input/Output (I/O) interfaces 22. Still yet, computer system/server 12 can communicate with one or more networks such as a local area network (LAN), a general wide area network (WAN), and/or a public network (e.g., the Internet) via network adapter 20. As depicted, network adapter 20 communicates with the other components of computer system/server 12 via bus 18. It should be understood that although not shown, other hardware and/or software components could be used in conjunction with computer system/server 12. Examples, include, but are not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data archival storage systems, etc.

Referring now to FIG. 2, illustrative cloud computing environment 50 is depicted. As shown, cloud computing environment 50 comprises one or more cloud computing nodes 10 with which local computing devices used by cloud consumers, such as, for example, personal digital assistant (PDA) or cellular telephone 54A, desktop computer 54B, laptop computer 54C, and/or automobile computer system 54N may communicate. Nodes 10 may communicate with one another. They may be grouped (not shown) physically or virtually, in one or more networks, such as Private, Community, Public, or Hybrid clouds as described hereinabove, or a combination thereof. This allows cloud computing environment 50 to offer infrastructure, platforms and/or software as services for which a cloud consumer does not need to maintain resources on a local computing device. It is understood that the types of computing devices 54A-N shown in FIG. 2 are intended to be illustrative only and that computing nodes 10 and cloud computing environment 50 can communicate with any type of computerized device over any type of network and/or network addressable connection (e.g., using a web browser).

Referring now to FIG. 3, a set of functional abstraction layers provided by cloud computing environment 50 (FIG. 2) is shown. It should be understood in advance that the components, layers, and functions shown in FIG. 3 are intended to be illustrative only and embodiments of the invention are not limited thereto. As depicted, the following layers and corresponding functions are provided:

Device layer 55 includes physical and/or virtual devices, embedded with and/or standalone electronics, sensors, actuators, and other objects to perform various tasks in a cloud computing environment 50. Each of the devices in the device layer 55 incorporates networking capability to other functional abstraction layers such that information obtained from the devices may be provided thereto, and/or information from the other abstraction layers may be provided to the devices. In one embodiment, the various devices inclusive of the device layer 55 may incorporate a network of entities collectively known as the “internet of things” (IoT). Such a network of entities allows for intercommunication, collection, and dissemination of data to accomplish a great variety of purposes, as one of ordinary skill in the art will appreciate.

Device layer 55 as shown includes sensor 52, actuator 53, “learning” thermostat 56 with integrated processing, sensor, and networking electronics, camera 57, controllable household outlet/receptacle 58, and controllable electrical switch 59 as shown. Other possible devices may include, but are not limited to various additional sensor devices, networking devices, electronics devices (such as a remote-control device), additional actuator devices, so called “smart” appliances such as a refrigerator or washer/dryer, and a wide variety of other possible interconnected objects.

Hardware and software layer 60 includes hardware and software components. Examples of hardware components include: mainframes 61; RISC (Reduced Instruction Set Computer) architecture-based servers 62; servers 63; blade servers 64; storage devices 65; and networks and networking components 66. In some embodiments, software components include network application server software 67 and database software 68.

Virtualization layer 70 provides an abstraction layer from which the following examples of virtual entities may be provided: virtual servers 71; virtual storage 72; virtual networks 73, including virtual private networks; virtual applications and operating systems 74; and virtual clients 75.

In one example, management layer 80 may provide the functions described below. Resource provisioning 81 provides dynamic procurement of computing resources and other resources that are utilized to perform tasks within the cloud computing environment. Metering and Pricing 82 provides cost tracking as resources are utilized within the cloud computing environment, and billing or invoicing for consumption of these resources. In one example, these resources may comprise application software licenses. Security provides identity verification for cloud consumers and tasks, as well as protection for data and other resources. User portal 83 provides access to the cloud computing environment for consumers and system administrators. Service level management 84 provides cloud computing resource allocation and management such that required service levels are met. Service Level Agreement (SLA) planning and fulfillment 85 provides pre-arrangement for, and procurement of, cloud computing resources for which a future requirement is anticipated in accordance with an SLA.

Workloads layer 90 provides examples of functionality for which the cloud computing environment may be utilized. Examples of workloads and functions which may be provided from this layer include: mapping and navigation 91; software development and lifecycle management 92; virtual classroom education delivery 93; data analytics processing 94; transaction processing 95; and, in the context of the illustrated embodiments of the present invention, various workloads and functions 96 for automatic reasoning with real-valued first order logic (e.g., executing a probabilistic inference operation using real-valued first order logic) and probability intervals in a computing environment (e.g., in a neural network architecture). In addition, workloads and functions 96 for automatic reasoning with real-valued first order logic and probability intervals in a computing environment may include such operations as analytics, deep learning, and as will be further described, user and device management functions. One of ordinary skill in the art will appreciate that the workloads and functions 96 for automatic reasoning with real-valued first order logic and probability intervals in a computing environment may also work in conjunction with other portions of the various abstractions layers, such as those in hardware and software 60, virtualization 70, management 80, and other workloads 90 (such as data analytics processing 94, for example) to accomplish the various purposes of the illustrated embodiments of the present invention.

Turning now to FIG. 4, a block diagram depicting exemplary functional components of system 400 for automatic reasoning with real-valued first order logic and probability intervals in a computing environment (e.g., in a neural network architecture) according to various mechanisms of the illustrated embodiments is shown. In one aspect, one or more of the components, modules, services, applications, and/or functions described in FIGS. 1-3 may be used in FIG. 4. As will be seen, many of the functional blocks may also be considered “modules” or “components” of functionality, in the same descriptive sense as has been previously described in FIGS. 1-3.

An intelligent reasoning service 410 is shown, incorporating processing unit 420 (“processor”) to perform various computational, data processing and other functionality in accordance with various aspects of the present invention. In one aspect, the processor 420 and memory 430 may be internal and/or external to the intelligent reasoning service 410, and internal and/or external to the computing system/server 12. The intelligent reasoning service 410 may be included and/or external to the computer system/server 12, as described in FIG. 1. The processing unit 420 may be in communication with the memory 430. The intelligent reasoning service 410 may include a reasoning learning component 440, a probabilistic inference component 450, a query component 460, and a machine learning component 470.

In one aspect, the system 400 may provide virtualized computing services (i.e., virtualized computing, virtualized storage, virtualized networking, etc.). More specifically, the system 400 may provide virtualized computing, virtualized storage, virtualized networking and other virtualized services that are executing on a hardware substrate.

The intelligent reasoning service 410, in association with the reasoning learning component 440, the probabilistic inference component 450, the query component 460, and the machine learning component 470, may convert all first-order logic formulas into real-valued logic formulas; and reason with 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.

Said differently, the intelligent reasoning service 410, in association with the reasoning learning component 440, the probabilistic inference component 450, the query component 460, and the machine learning component 470, may execute machine learning logic to convert all first-order logic formulas into real-valued logic formulas, wherein the real-valued logic formulas are input as training data into a logical neural network (“LNN”); and generate the LNN by using the training data to execute a probabilistic inference 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.

The intelligent reasoning service 410, in association with the reasoning learning component 440, the probabilistic inference component 450, the query component 460, and the machine learning component 470, may represent a truth value of each of the real-valued logic formulas as a zero or a one value.

The intelligent reasoning service 410, in association with the reasoning learning component 440, the probabilistic inference component 450, the query component 460, and the machine learning component 470, may receive a set of the first-order logic formulas, and a set of intervals representing upper and lower bounds on one or more truth values of a set of ground predicates from the first-order logic formulas.

The intelligent reasoning service 410, in association with the reasoning learning component 440, the probabilistic inference component 450, the query component 460, and the machine learning component 470, may set upper and lower bounds on one or more truth values of the real-valued logic formulas in a knowledge base.

The intelligent reasoning service 410, in association with the reasoning learning component 440, the probabilistic inference component 450, the query component 460, and the machine learning component 470, may determine a probability of a ground predicate being true based on an alternative ground predicate being true.

The intelligent reasoning service 410, in association with the reasoning learning component 440, the probabilistic inference component 450, the query component 460, and the machine learning component 470, may ground a first-order logic based on a knowledge domain of a plurality of variables; construct a Logical Neural Network (LNN) representation of the grounded first-order logic; and construct a credal network (CN) associated with the LNN.

The intelligent reasoning service 410, in association with the reasoning learning component 440, the probabilistic inference component 450, the query component 460, and the machine learning component 470, may apply a probabilistic inference to determine a set of solutions to one or more queries.

In one aspect, the machine learning component 470 may receive, identify, and/or select a machine learning model and/or machine learning pipeline, a dataset for a data set (e.g., a time series data set) used for testing the machine learning model and/or machine learning pipeline.

In one aspect, the machine learning component 470 as described herein, may perform various machine learning operations using a wide variety of methods or combinations of methods, such as supervised learning, unsupervised learning, temporal difference learning, reinforcement learning and so forth. Some non-limiting examples of supervised learning which may be used with the present technology include AODE (averaged one-dependence estimators), artificial neural network, backpropagation, Bayesian statistics, naive bays classifier, Bayesian network, Bayesian knowledge base, case-based reasoning, decision trees, inductive logic programming, Gaussian process regression, gene expression programming, group method of data handling (GMDH), learning automata, learning vector quantization, minimum message length (decision trees, decision graphs, etc.), lazy learning, instance-based learning, nearest neighbor algorithm, analogical modeling, probably approximately correct (PAC) learning, ripple down rules, a knowledge acquisition methodology, symbolic machine learning algorithms, sub symbolic machine learning algorithms, support vector machines, random forests, ensembles of classifiers, bootstrap aggregating (bagging), boosting (meta-algorithm), ordinal classification, regression analysis, information fuzzy networks (IFN), statistical classification, linear classifiers, fisher's linear discriminant, logistic regression, perceptron, support vector machines, quadratic classifiers, k-nearest neighbor, hidden Markov models and boosting. Some non-limiting examples of unsupervised learning which may be used with the present technology include artificial neural network, data clustering, expectation-maximization, self-organizing map, radial basis function network, vector quantization, generative topographic map, information bottleneck method, IBSEAD (distributed autonomous entity systems based interaction), association rule learning, apriori algorithm, eclat algorithm, FP-growth algorithm, hierarchical clustering, single-linkage clustering, conceptual clustering, partitional clustering, k-means algorithm, fuzzy clustering, and reinforcement learning. Some non-limiting example of temporal difference learning may include Q-learning and learning automata. Specific details regarding any of the examples of supervised, unsupervised, temporal difference or other machine learning described in this paragraph are known and are within the scope of this disclosure. Also, when deploying one or more machine learning models, a computing device may be first tested in a controlled environment before being deployed in a public setting. Also even when deployed in a public environment (e.g., external to the controlled, testing environment), the computing devices may be monitored for compliance.

FIG. 5 is a block flow diagram 500 depicting reasoning with real-valued first order logic and probability intervals in a computing environment according to an embodiment of the present invention. In one aspect, one or more of the components, modules, services, applications, and/or functions described in FIGS. 1-4 may be used in FIG. 5. As will be seen, many of the functional blocks may also be considered “modules” or “components” of functionality, in the same descriptive sense as has been previously described in FIGS. 1-4.

Starting in block 502, a knowledge base may contain a set of first-order logic (FOL) formula. In a real world scenario, the knowledge is likely to be noisy, namely the truth value of some formula may be unknown with certainty (for example, when this knowledge is extracted automatically from text sources). That is, a set of FOL formulas (“K”), truth value bounds for one or more ground observations (“O”) (i.e., ground predicates from FOL formulas K), a query (e.g., Q(A|B) where A and B are ground predicates in FOL formulas K.

In block 510, a FOL formulas K may be grounded based on a knowledge domain of a plurality of variables. That is, the output of block 510 is a probabilistic inference such as, for example, Pr(A|B). In other words, the interval conditional probability Pr(A|B) is determined/computed, where A and B are set to true. The knowledge base FOL formulas K is grounded into FOL formulas K′ by grounding every FOL predicate using the domains of the variables obtained from the ground observations.

In block 520, a Logical Neural Network (LNN) L representation of K′ is created. For example, a directed acyclic graph (“DAG”) LNN L may be created comprising the syntax trees of the formulae in K′. In one aspect, input truth value bounds may be attached to the nodes in the bottom layer of L (e.g., ground predicates). The truth value bounds for the connector nodes in LNN L (upper layers).

In block 530, a credal network (“CN”) C with the same structure as L, where the nodes in LNN L correspond to propositions (e.g., bottom layers) or connectors (e.g., upper layers) and an interval probability tables may be determined for each node.

In block 540, a probabilistic inference engine may determine/compute Pr(A|B) by setting B=true as evidence in C and running a standard probabilistic inference operation for credal network (“CN”) C (e.g., the Loopy 2U operation can be used as embodiment). In block 550, a probabilistic inference may return Pr(A|B) for a set of answers 560 based on a set of queries Q had.

This allows the truth value of a formula to be a real number between 0 and 1 instead of just either 0 (false) or 1 (true). In addition, to account for uncertainty in the estimates of the truth values, the upper and lower bounds may be set on the truth values of the formula in the knowledge base. Subsequently, aspects of this disclosure may answer any query of the form Pr(f(x)|g(y)) i.e., what is the probability of grounded predicate f(x) being true given that another ground predicate g(y) is true and solving these kinds of queries is translated into probabilistic reasoning over an equivalent credal network. Thus, the credal network 530 can revitalize reasoning under conditions of uncertainty especially in case of imprecise probability estimates as well as real-valued logic operators. The credal network 530 may be applied to other domains that require reasoning over FOL.

For further explanation, assume that we have a knowledge base containing first-order logic (FOL) formulae (e.g., formula). In a real-world situation, this knowledge is likely to be noisy, namely the truth value of some formulae may not be known with certainty (for example, when this knowledge is extracted automatically from text sources). Moreover, reasoning with classical logic formulae is quite brittle. Therefore, aspects of this disclosure converts all first-order logic formulae into real-valued logic formulae (e.g., Lukasiewicz logic). This allows the truth value of a formulae to be a real number between 0 and 1 instead of just either 0 (false) or 1 (true). In addition, to account for uncertainty in the estimates of the truth values, we set upper and lower bounds on the truth values of the formulae in the knowledge base. Subsequently, aspects of this disclosure may answer any query of the form Pr(f(x)|g(y)) i.e., what is the probability of grounded predicate f(x) being true given that another ground predicate g(y) is true. Thus, a variety of queries may be solved and then translated into probabilistic reasoning over an equivalent credal network.

To further illustrate, assume there is text data containing the following pieces of knowledge: (1) Smoking(“Sm”) causes cancer (“Ca”) (e.g., Sm(x)→Ca(x)). If two people (e.g., “x, y”) are friends (“Fr”), then either or both are smoking; and (2) A and B are friends (“Fr”), B and C are friends and B smokes. Thus, aspects of this disclosure may formalize this knowledge by automatically extracting the following FOL formulae: (a) allow probability upper/lower bounds on observation predicates (2) as depicted in FIG. 6A, and (b) use real-valued logical connectors in FOL formulae (1) as illustrated below and in as depicted in FIG. 6A:

{

Sm
⁢

(
x
)

→

C
⁢
a
⁢

(
x
)

Fr
⁢

(

x
,
y

)

→

(

s
⁢
m
⁢

(
x
)

⊕

S
⁢
m
⁢

(
y
)

.

(
1
)

For further explanation, FIG. 6A is a diagram 600 depicting a logical neural network (LNN) associated with the grounded formulas in a computing environment in which aspects of the present invention may be realized. In one aspect, one or more of the components, modules, services, applications, and/or functions described in FIGS. 1-5 may be used in FIG. 6A. As will be seen, many of the functional blocks may also be considered “modules” or “components” of functionality, in the same descriptive sense as has been previously described in FIGS. 1-5.

In one aspect, the logical neural network (LNN) 600 a directed acyclic graph 603, where the square nodes (e.g., nodes having shapes) correspond to the grounded predicates and the internal nodes correspond to the logical connectors in the formulas. These logical connectors are real-valued logical connectors and their associated rules are given above the graph. For example, the symbol (e.g., →) is the real-valued implication connector, and the circled plus sign (e.g., “+”) is the real-valued or connector.

In some implementation, the real-valued implication connector may be a real-valued connector defined by the Lukasiewicz real-valued logic. The square nodes are associated with lower and upper bounds on their truth values and the logical connectors compute lower and upper bounds on the truth values of the corresponding formulas.

Moreover, given the formal knowledge base, a query necessary to answer may be a query such as, for example: (“what is the probability that C has cancer given that A is a smoker?”) and furthermore, the current board HOA's to bound the truth value instead of giving point estimates such as, for example, example 1:

P(Ca(C)|Sm(A))∈[l,u] (1),

where, Ca represents a disease (e.g., cancer and (C) is a person has the disease, Sm represents a predicate engages in an activity (e.g., smoking(A) where A is a person doing the activity), and in this scenario, aspects of this disclosure determine/calculate the probability that person (C) given that person (A) is a smoker (e.g., P(Ca(C)|Sm(A))). Thus, aspects of this disclosure compute a probability interval [l, u] for P(Ca(C)|Sm(A)).

Thus, aspects of this disclosure first grounds the FOL given the domains of the variables (observations), constructs a Logical Neural Network (“LNN”) representation of the ground FOL, constructs an equivalent credal network (CN), and subsequently answers the query by means of probabilistic inference in the CN (e.g., using the Loopy 2U (“L2U”) belief propagation algorithm).

For further explanation, FIG. 6B is a diagram 615 depicting a logical neural network (LNN) associated with propositional formulas (e.g., “formulae”) in a computing environment, in which aspects of the present invention may be realized. In one aspect, one or more of the components, modules, services, applications, and/or functions described in