A tour d'horizon about last developments in Artifical Intelligence, my personal opinion about the future role of AI in ERP systems and a small application of established theories in Business Rules Management.

1. Logical Abduction and an
Application in Business Rules
Management
Tobias Trapp – AOK Systems GmbH
SAP Mentor

2. 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 statistical
dependencies but does not imply
causation
• abduction: we want to explain a
phenomenon in terms of
consequence in a formal model

3. Applications
Diagnosis of complex systems:
• medical diagnosis
• root cause of system failure in
computing centers
• analysis of rule systems
outcome

4. The Era of Cognitive Computing
just started
short 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 new
generation of expert systems with
disruptive properties
• one grand challenge of AI is solved: the
world‘s strongest Go player Lee Seedol is in
top condition and plays offensive modern
Go - Alpha Go plays „like a goddess“ and
won three times in a row

5. 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 new
foundations for mathematics that are accessible
for computers:
– proofs are programs
– With this and related theories new functional
programming languages like Coq & Agda have been
created which helped understanding complex proofs
• IMHO we need a similar bold approach to
understand Deep Learning

6. 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

7. History of Abductive Reasoning
• Charles Sanders Peirce is said to be one of
the founders of statistics, but also worked
on semiotic and logics
• every paper in the area of abduction
mentions him as first philosopher who did
research on this topic
• today different approaches, f.e.:
– probabilistic logic
– non-monotonic logic

8. 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 does
not 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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…

15. 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

16. 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