Reasoning with Uncertainty

(2nd semester 2011/12)


Lecturer: PD Dr. Reinhard Blutner

ILLC, University of Amsterdam

Lectures: Block A: Wednesday 13-15, A1.06 (Science Park); Block B: Wednesday 13-15, G3.13 (Science Park)


Office Hours: by appointment



Reasoning with uncertainty and with probabilities is important for many fields of Artificial Intelligence, especially for expert systems, robotics, and neuronal networks. The course gives a representative overview of the various models and instruments that deal with uncertainty and vagueness, such as Bayesian networks, certainty factors, Dempster-Shafer theory, fuzzy logic, possibilistic logic, and quantum probabilities. The aim of the course is to look both for practical applications and to provide a basis that enables us to compare the different formalisms with each other.   


This course will be graded based on

Obligatory Homework:             (Questions concerning the homework can be asked at the beginning of the following lecture)
Hugin exercise: 20%                
(Final deadline for the Hugin exercise:  April 4. Grade is reduced if work is late: -1 per day!)
Test: 30%                                
(After the first 5 courses which  are based on the Halpern book)
Final exam: 50%

Final mark and final exam


Course Material 

Reasoning about Uncertainty 
Joseph Y. Halpern

Fuzzy Logic  
by Michiel van Lambalgen

Quantum Logic and Probability Theory
Alexander Wilce
The Stanford Encyclopedia of Philosophy (Spring 2006 Edition)

Hugin Exercises [pdf-file]

Exercises Part 1 [pdf-file]
Exercises Part 2 [pdf-file]


 Here you can find the solution for the special homework

4.1.Word meanings and LSA:  Perform a SVD for the course example ... [pdf]








P A R T   1


Representing Uncertainty 1  


ExercisesPart1: 1.3, 1.4, 1.6


No class on February 15


Representing Uncertainty 2   ExercisesPart1: 1.7, 1.8, 1.10(ii)&(iii), 1.11


Updating Beliefs


ExercisesPart1: 2.3. 2.4, 2.5, 2.7


Bayesian Networks 1

Bayesian [pdf]  [ppt]

ExercisesPart1: 3.1, 3.2, 3.3, 3.4


Bayesian Networks 2 / Explaining the Hugin Exercises

D-separation and noisy OR; Hugin Exercises

ExercisesPart1: 3.5, 3.6, 3.7


Rationality: the Dutch Book argument



Dutch book   


ExercisesPart2: 1.2,1.3

Writing the TEST: March 21.
Deadline for Hugin exercise: April 4

P A R T   2


Dempster Shafer Theory 1 & 2


ExercisesPart2: 2.2, 2.3, 2.5, 2.6, 2.7

Deadline for Hugin exercise!


Fuzzy sets 1


ExercisesPart2: 3.1 a&b, 3.3 c&d, 3.5


Fuzzy sets 2

ExercisesPart2: 3.8, 3.10, 3.11 c.


Quantum Probabilities 1

Quantum1 / Quantum2

ExercisesPart2: 4.1 a, 4.2, 4.3


No class on May 2nd



ExercisesPart2: 4.4, 4.6, 4.7


Quantum Probabilities 1/2


Quanten Probabilities 2


Applications of quantum probabilities


see a recent BBS target paper


    Written exam (closed book) on May 30 from 9-12 in G3.02 (Science Park)



Note concerning the origin of Hugin

"During an EU-sponsored research project (under the ESPRIT program) on diagnosing neuromuscular diseases, the Bayesian network MUNIN was constructed. A research group at Aalborg University worked on developing correct and efficient computation methods for the diagnosis problem. Some results had at that time been obtained by American researchers, but a very obstinate problem still remained, which prevented Bayesian networks from being used in the construction of expert systems. The problem was know as the rumour problem: you may hear the same story through several different channels; but still the story may originate from the same source. Without knowing whether or not your channels are independent, you cannot combine the statements correctly. In Bayesian networks the rumour problem appears when a cause can influence the same event through different paths in the network. The problem was solved and general methods were made available to be used in any domain which can be modeled by a Bayesian network. The methods were programmed into a general development and runtime system, which was easy to use for anyone wishing to construct an expert system based on Bayesian networks. The system was called Hugin. Over the years the system has been extended in various ways (e.g. influence diagrams, continuous variables, structural learning, adaptation, object-oriented specification of Bayesian networks and influence diagrams, etc.)." (cf. Hugin Help and Hugin Expert White Paper)


Related Websites 

Websites for Quantum Cognition


and some relevant articles and books:


Aerts, Diederik, Jan Broekaert & Liane Gabora (2006). A case for applying an abstracted quantum formalism to cognition. In Campbell, R.,M. H. Bickhard & S. O'Nuallain (Eds.), Mind in Interaction. Amsterdam: John Benjamins.

Aerts, Diederik, Marek Czachor & Bart D’Hooghe (2005?). Do We Think and Communicate in Quantum Ways? On the Presence of Quantum Structures in Language. In Gontier, N.,J. P. V. Bendegem & D. Aerts (Eds.), Evolutionary Epistemology, Language and Culture. Amsterdam: John Benjamins Publishing Company.

Atmanspacher, Harald, Hartmann Römer & Harald Walach (2002a). Weak Quantum Theory: Complementarity and Entanglement in Physics and Beyond. Foundations of Physics 32(3): 379-406.

Gabora, Liane & Dederik Aerts (2002). Contextalizing concepts using a mathematical generalization of the quantum formalism. Journal of Experimental and Theoretical Artificial Intelligence.

Jibu, Mari & Kunio Yasue (1995). Quantum Brain Dynamics and Consciousness. Amsterdam/Philadelphia: John Benjamins.

Lomonaco, Samuel J. Jr. (2000). A rosetta stone for quantum mechanics with an introduction to quantum computation.

Vedral, Vlatko (2006). Introduction to Quantum Information Science. Oxford University Press.

Widdows, Dominic & Stanley Peters (2003). Word Vectors and Quantum Logic: Experiments with negation and disjunction. Paper presented at the Eighth Mathematics of Language Conference, Bloomington, Indiana.