The Knowledge Base Paradigm for

Decision & Process Management

Representation

DMN
- Decision Tables
- FEEL

BPMN
YAWL
DECLARE
Petri nets

Task

Enactment
Completeness/Exclusivity checking
...

Compliance checking
Conformance checking
Monitoring
Automation
...

DM & BPM

Representation

Deductive logic
Query languages (SQL, datalog)
Constraint programming
Abductive Logic Programming
Inductive Logic Programming
PDDL, strips
Answer set programming

Inference

Deduction
Query answering
Constraint solving
Abduction
Induction
Planning
Model generation

Declarative

Problem Solving

Deduction Example

No_Class(X) :- Day(X, wednesday), Time(X, afternoon).

Day(14:00-30/03/2016, wednesday).

Time(14:00-30/03/2016, afternoon).

Deduction: No_Class(14:00-30/03/2016).

Query Example

not(Class(X) and Date(X, wednesday) and Time(X, afternoon)).

Result: True if there is no class scheduled on a wednesday afternoon, false otherwise.

Declarative

Problem Solving

Focus on a single specific form of inference

=> One representation, one problem

Example

Class(15:00-30/03/2016).

Deduction: ¬Class(14:00-30/03/2016)

Query: False

\neg \exists X : \text{ Class(X) } \wedge \text{ Day(X, wednesday) } \wedge \text{ Time(X, afternoon) }

\neg \exists X : \text{ Class(X) } \wedge \text{ Day(X, wednesday) } \wedge \text{ Time(X, afternoon) }

Knowledge Base

Paradigm

Information

≠ Solution

≠ Problem description

= Passive, independent of specific problem

=> One representation, many problems

Knowledge Base

Paradigm

FO(.)

IDP's Representation Language
- Extension of first-order logic:
  - Types
  - Arithmetic
  - Aggregates
  - Inductive definitions
  - ...
- Formal Model Semantics

Decision Logic

Decision

Specification

Inference

Decision Management

Knowledge Base Paradigm

Modelling Business Decisions

An Example

Car Insurance

DMN - DRD

Potential Theft Rating

A car's theft rating is high if any of the following applies:
- The car is a convertible
- The car's price is over $45 000
- The car's model is on the High Theft Probability Auto list
If all of the following are true the car's theft rating is moderate:
- The car's price is between $20 000 and $45 000
- The car's model is not on the High Theft Probability Auto list
If all the following are true the car's theft rating if low:
- The car's price is lower than $20 000
- The car's model is not on the High Theft Probability Auto list

Decision Table

Potential Theft Rating

Definition

Potential Theft Rating

Some inferences

Completeness checking
Exclusivity checking
Compliance checking

Invokation

{

counter examples

Complete Input

Incomplete Input

Alternatives

Completeness

At least one outcome for every input value assignment

Violated if:

There exists a value assignment for which there is no outcome.

Exclusiveness

At most one outcome for every input value assignment

Violated if:

There exists a value assignment for which there is no outcome.

\exists \bar{X} : \neg \exists \bar{Y} : P(\bar{X}, \bar{Y})

\exists \bar{X} : \neg \exists \bar{Y} : P(\bar{X}, \bar{Y})

\exists \bar{X} : \exists_{>1} \bar{Y} : P(\bar{X}, \bar{Y})

\exists \bar{X} : \exists_{>1} \bar{Y} : P(\bar{X}, \bar{Y})

Stronger

Requires quantification over rules

=> rule reification

Compliance

Check whether the decision logic satisfies a certain property

"Minors can not be insured as drivers"

Violated if:

It is possible for someone younger than 18, to be insured.

\exists c ~ d : Covers(c, d) \wedge DriverAge(d) < 18 \wedge EligibleForInsurance(c, eligible)

\exists c ~ d : Covers(c, d) \wedge DriverAge(d) < 18 \wedge EligibleForInsurance(c, eligible)

Invokation

Invoke decision with
- all input values available
- some input values available
Determine input alternatives for desired outcome

Process Logic

Compliance checking

Conformance checking

Monitoring

Specification

Inference

Process Management

Knowledge Base Paradigm

Modelling Business Processes

Why are process miners so much more determined than data miners?

Their Wil is stronger.

An Example

Hotel charges

Current & Future

Research Questions

What is a decision?
- How to best represent the decision logic?
- Which types of decisions are there?
  - Which inferences are relevant?
Which knowledge is present in a process?
- How can this knowledge be represented?
- Which inferences are relevant?
How can decisions and processes be integrated?

Thank you

What is a decision?

The description of the decision logic required to determine an outcome from a given set of inputs

The act of determining an outcome from a given set of inputs using the decision logic

What is a decision?

DetermineResult(T, V_i, V_o, S_i) is an inference with:

Input:
- theory T
- set of input symbols V_i
- set of output symbols V_o
- partial structure S_i interpreting the symbols in V_i.
Output:
- If (T, V_i, V_o, S_i) is determinable:
  - a structure S_o over V_o, such that S_i ∪ S_o can be expanded to a model of T
- Otherwise:
  - "Not determinable"

What is a decision?

If T, V_i, V_o are fixed, DetermineResult(S_i) is a decision.