The PhD thesis consists of two parts. The first part describes an approach for reasoning with inconsistent knowledge. The approach was developed from 1987 until 1989, starting with the Master Thesis in 1987. The general idea is that, in case of inconsistencies, we accept conclusions entailed by all preferred maximally consistent subsets of the initial information given a partial preference ordering over the initial information. This idea is similar to the Preferred Subtheories, proposed by Brewka in IJCAI’89. The two approaches were developed in the same period independently of each other.
Unlike the Preferred Subtheories, the approach proposed in the PhD thesis specifies a preferential model semantics and a proof theory based on an assumption-based argumentation system.
The proposed assumption-based argumentation system derives arguments for propositions (called in-justifications) and uses arguments for inconsistencies to formulate undercutting arguments (called out-justifications) for assumptions. The stable semantics is used to determine the argument-extensions. Conclusions are propositions supported by every argument-extension (the skeptical approach).
The approach has been published in:
N. Roos, A preference logic for non-monotonic reasoning, Technical Report 88-94, Delft University of Technology, Faculty of Technical Mathematics and Informatics. ISSN 0922-5641, (1988). [pdf]
N. Roos, Preference Logic: a logic for reasoning with inconsistent knowledge, Technical Report 89-53, Delft University of Technology, Faculty of Technical Mathematics and Informatics. ISSN 0922-5641, (1989). [pdf]
A paper based on the report was rejected for the IJCAI’89 but was accepted by the AI journal after a review period of 3 years.
N. Roos, A preference logic for non-monotonic reasoning, Technical Report 88-94, Delft University of Technology, Faculty of Technical Mathematics and Informatics. ISSN 0922-5641, (1988). [pdf]
N. Roos, Een preferentie logika voor het redeneren met onvolledige kennis, NAIC’89 (1989).
N. Roos, A logic for reasoning with inconsistent knowledge, Artificial Intelligence 57 (1992) 69-103. [pdf]
The first idea of the approach dates back to the Master Thesis:
N. Roos, Geloofwaardig argumenteren – Formeel onderbouwd, Master Thesis, Delft University of Technology (Feb. 1987). [pdf]
The second part of the PhD thesis discusses how to derive probabilities of propositions based on the agent’s knowledge and information about the world. The idea is to construct mutually exclusive partial models for the agent’s knowledge and information. The probability of a proposition is determined by the faction of partial models supporting the proposition. The construction of the partial models is similar to the construction of a semantic tableau.
The approach has been published in:
N. Roos, How to reason with uncertain knowledge, in: Bouchon-Meurier, B., Yager, R. R., Zadeh, L. A. (eds), Uncertainty in Knowledge Bases, LNCS 521, Springer-Verlag (1991) 403-412.
N. Roos, Redeneren met onzekerheid door middel van de konstruktie van een partieel model, NAIC’91 (1991) 115-123.
N. Roos, Reasoning with partial models; Construction of partial models and management of uncertainty, in: Hoek, W. van der, Meyer, J.-J. Ch., Tan Y. H., Witteveen, C. (eds), Non-monotonic reasoning and partial semantics, Ellis Horwood (1992) 79-105.