Logical Abduction and an

Application in Business Rules

Management

Tobias Trapp – AOK Systems GmbH

SAP Mentor

No Aliens and no Fitness Tips

in this Talk about Abduction!

• deduction means inference in which the conclusion is of no greater generality than the premises

• correlation describes statisticaldependencies but does not implycausation

• abduction: we want to explain a phenomenon in terms ofconsequence in a formal model

Applications

Diagnosis of complex systems:

• medical diagnosis

• root cause of system failure in

computing centers

• analysis of rule systems

outcome

The Era of Cognitive Computing

just startedshort history of artificial intelligence:

• great hopes in the 80s - but limited success

• in some areas huge success – now imple-mented everywhere: machine learning, speech and pattern recognition…

• with Watson IBM wants to establish a newgeneration of expert systems withdisruptive properties

• one grand challenge of AI is solved: theworld‘s strongest Go player Lee Seedol is in top condition and plays offensive modern Go - Alpha Go plays „like a goddess“ andwon three times in a row

The Next Challenge for Human Mind:

Understanding Advanced Algorithms• We don‘t understand why Neural Networks are

successful – we need new mathematical toolset

• In other branches logicians started to create newfoundations for mathematics that are accessiblefor computers:

– proofs are programs

– With this and related theories new functionalprogramming languages like Coq & Agda have beencreated which helped understanding complex proofs

• IMHO we need a similar bold approach tounderstand Deep Learning

My Belief

• cognitive computing will come – apps will get smarter and

will become personal assistants

• users will expect that ERP applications will become smarter

• IT systems using this technology have disruptive potential

since they exploit the data and knowledge within ERP

implementations and usage simpler

• developers should start to learn how to use the different

techniques in AI

History of Abductive Reasoning

• Charles Sanders Peirce is said to be one ofthe founders of statistics, but also workedon semiotic and logics

• every paper in the area of abductionmentions him as first philosopher who didresearch on this topic

• today different approaches, f.e.:

– probabilistic logic

– non-monotonic logic

Formal Definition from Wikipedia

• we would like to restrict to „simple“ explanations – i.e. minimal or minimum models(inspired by Occam‘s razor)

• this principle means that we should not make unneccessary assumptions – but it doesnot means that the simplest explanation is always true

• non-monotic logic if we introduce a preference relation between explanantions

• abduction can be defined for other logics like decidable fragments of First Order Logic

A Tidbit for Theorists:

Abduction is Harder than Deduction

• we restrict to propositional logic

• verifiying a deduction is a satisfiability problem

• checking whether an explanation is correct is at a

higher level of the Polynomial Hierarchy:

– The complexity of logic-based abduction, Thomas

Eiter & Georg Gottlob, Journal of the ACM, Volume

42 Issue 1, Jan. 1995, Pages 3-42

– What makes propositional abduction

tractable, Gustav Nordh & Bruno Zanuttini,

Artificial Intelligence, Volume 172, Issue 10,

June 2008, Pages 1245–1284

• Experience says that most real world use cases are

solvable!

abduction

satisfiability

A Use Case for Abduction

• we are using rule systems implemented in BRFplus to

automate business problems

• when checking SAP business objects often dozens of

conspicious features are detected

• we want to support the official in charge to understand the

root cause

Decision Table

#procure-

ments A

#procure-

ments B

#procure-

ments C

#procure-

ments D

#procure-

ments D

Age : 3 Error

> 10 < 6 <12

> 4 < 1

> 5 > 0

> 5 > 0

< 8 < 6

Instance

#procure-

ments A : 20

#procure-

ments B : 2

#procure-

ments C : 0

#procure-

ments D : 0

#procure-

ments D : 2

Age : 3 Error

> 10 < 6 <12 detected

> 4 < 1 detected

> 5 > 0 detected

> 5 > 0

< 8 < 6 detected

Explanation Using Classical Abduction

#procure-

ments A : 20

#procure-

ments B : 2

#procure-

ments C : 0

#procure-

ments D : 0

#procure-

ments D : 2

Age : 3 Error

> 10 < 6 <12 detected

> 4 < 1 detected

> 5 > 0 detected

> 5 > 0

< 8 < 6 detected

Rectification as Minimum

Hitting Set Problem• which attributes of a business object have to

be altered so that the object passes all checks

• we are looking to a minimum set which with

these properties which is equivalent to a

Hitting Set Problem

• Hitting Set is well understood and one of

„easier“ NP-hard problems and there are

many approaches like kernelization…

Rectification

#procure-

ments A : 20

#procure-

ments B : 2

#procure-

ments C : 0

#procure-

ments D : 0

#procure-

ments D : 2

Age : 3 Error

> 10 < 6 <12 detected

> 4 < 1 detected

> 5 > 0 detected

> 5 > 0

< 8 < 6 detected

Summary

• Rectification as special case of abduction

• getting metadata and computation results from an BRFplus

decision table is simple due to API

• implementation in Python because implementation of data

structures for advanced algorithms is difficult in ABAP

• tests with random data promising

• ask me for a working draft of my work if you are interested in

details