Knowledge agents via logic programming and fuzzy reasoning

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Julkaisu 655 Publication 655

Ossi Nykänen

Knowledge Agents via Logic Programming and Fuzzy Reasoning

Tampere 2007

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Tampereen teknillinen yliopisto. Julkaisu 655 Tampere University of Technology. Publication 655

Ossi Nykänen

Knowledge Agents via Logic Programming and Fuzzy Reasoning

Thesis for the degree of Doctor of Technology to be presented with due permission for public examination and criticism in Tietotalo Building, Auditorium TB111, at Tampere University of Technology, on the 2nd of April 2007, at 12 noon.

Tampereen teknillinen yliopisto - Tampere University of Technology Tampere 2007

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Custodian: Professor Keijo Ruohonen

Tampere University of Technology Tampere, Finland

Opponent: Dr. Ivan Herman

Centre for Mathematics and Computer Sciences Amsterdam, The Netherlands

ISBN 978-952-15-1727-3 (printed) ISBN 978-952-15-1774-7 (PDF) ISSN 1459-2045

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Errata for the PhD Thesis: "Knowledge Agents via Logic Programming and Fuzzy Reasoning"

Ossi Nykänen 1.4.2007, Tampere

Remark 1 (page 11, just above definition 2):

In the general case, it makes sense to define that if sup(A) = 1, then A is normal.

Remark 2 (page 13, Definition 5):

The inequality symbols are ambiguous in the definition of the case of a1 = a2. It should read x < a1 and a1 < x (instead of x ≤ a1 and a1 ≤ x).

Remark 3 (page 21, second last paragraph):

The text reads "we essentially get a recursive version of the well-known max-min composition". It should read: "we essentially get a recursive version of the well- known max-min rule composition". (The term "max-min composition"

unintentionally refers to a different, well-established concept of fuzzy relations.) Remark 4 (page 23, Proof for the Proposition 4):

The term "describe query" should be replaced with the term "ask query".

On the last paragraph, it reads: "…the smallest firing strength…". It should read:

"…the largest firing strength…"

Remark 5 (page 24, Proof for the Proposition 4):

On the first paragraph, it reads: "…both ω1 and ω2 must also be firing strengths." It should read: "…either ω1 or ω2 must also be a firing strength."

Remark 6 (page 27, the equation before subsection 2.6):

In the first line of the equation, the operator ⊗ is missing from the first term ("r₃))r₀∨"). It should read: "r₃))⊗r₀∨".

Remark 7 (page 40, first paragraph in subjection 3.4.1):

It reads: "...one ore more…" while it should read: "...one or more…".

Acknowledgements

The author wishes to thank Mr. Osmo Kaleva for pointing out the remarks 1 and 2.

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Tampereen teknillinen yliopisto PL 527

33101 Tampere

Tampere University of Technology P.O. Box 527

FIN-33101 Tampere, Finland