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Ebook: Nonmonotonic Reasoning with Defeasible Rules on Feasible and Infeasible Worlds
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The modeling of intelligent behavior has been a central topic for researchers since artificial intelligence emerged as a research field. The use of classical logic in representing the knowledge and beliefs of an intelligent agent implies that inferences remain valid irrespective of additional information, and that the set of conclusions grows monotonically with the amount of available information. In reality, however, decisions must be made and planning actions must be taken in the presence of uncertain and incomplete information, meaning that previously obtained inferences may have to be withdrawn in the light of new information. Nonmonotonic logic provides the means to model such behavior.
This book, Nonmonotonic Reasoning with Defeasible Rules on Feasible and Infeasible Worlds, explores the area of nonmonotonic reasoning from conditional belief bases, in which postulates describe desirable properties of nonmonotonic reasoning, and many inference methods, differing in which of these postulates they satisfy, are applied. The author employs the notion of inductive inference operators, which map a belief base (a set of given conditionals) to an inference relation containing all the inferences an agent can draw from the set. Two notions of consistency – weak and strong – are contrasted, and the topic of inductive inference from weakly consistent belief bases is examined.
The book addresses the challenging problems of nonmonotonic reasoning from conditional belief bases with convincing and rigorously proven theoretical results, placed in a scientific context. It will be of interest to all those working in the area of logic-based knowledge representation.
Ever since the emergence of Artificial Intelligence as a research field, the modelling of intelligent behaviour has been a central topic in this area. Using classical logics for representing the knowledge and beliefs of an intelligent agent suffers from the fact that all inferences drawn remain valid under any additional information, i.e., the set of conclusions grows monotonically with the amount of available information. In realistic situations, however, conclusions for making decisions and for planning actions must be taken in the presence of uncertain and incomplete information. This leads to the requirement that previously obtained inferences may have to be withdrawn in the light of new information, and nonmonotonic logics provide the capability to model such a behaviour. In particular, given a belief base consisting of a set of defeasible conditionals of the form “If A, then usually B”, an inductive inference operator completes any such conditional belief base and maps is to a full nonmonotonic inference relation that can represent an agent’s epistemic state.
The dissertation presented by Jonas Haldimann is located in the area of nonmonotonic reasoning from conditional belief bases. While in classical logic there is a unique notion of deductive inference, in nonmonotonic reasoning there is no inference method that is generally accepted as “best”. Instead, there are various postulates that describe desirable properties of nonmonotonic reasoning, and there are many inference methods that differ in which of the postulates they satisfy. In his thesis, Haldimann explores and evaluates several inductive inference methods. Among these are the well-known p-entailment, which coincides with inferences based on system P, and system Z, which coincides with rational closure. A special focus is on the only recently introduced system W which extends both rational closure and c-inference. Haldimann shows that system W fully satisfies syntax splitting and also conditional syntax splitting, and he develops several upper and lower approximations of system W.
For all addressed inference operators, Haldimann examines whether they are able to deal with, or how they can be extended to deal with contradictions that may arise from a belief base and can lead to the complete implausibility of possible worlds, an aspect that has often been neglected before. For these investigations, the central notions of strong and weak consistency of conditional belief bases and the concepts of feasible and infeasible worlds are introduced, allowing for a precise and conclusive formalization of nonmonotonic inferences even in the presence of local inconsistencies. All considered inductive inference operators and their extended versions are inserted in a comprehensive landscape showing the arising interrelationships among them.
Overall, Jonas Haldimann has presented a very successful dissertation; all theoretical results are convincingly and rigorously proven and placed in the scientific context. In the area of logic-based knowledge representation, he has delved deeply into challenging problems of non-monotonic reasoning from conditional belief bases and has achieved insightful and significant results that mark considerable scientific progress.
Hagen, May 2024
Christoph Beierle
