Knowledge Representation and Inductive Reasoning using Conditional Logic and Sets of Ranking Functions

A core problem in Artificial Intelligence is the modeling of human reasoning. Classic-logical approaches are too rigid for this task, as deductive inference yielding logically correct results is not appropriate in situations where conclusions must be drawn based on the incomplete or uncertain knowledge present in virtually all real world scenarios.Since there are no mathematically precise and generally accepted definitions for the notions of plausible or rational, the question of what a knowledge base consisting of uncertain rules entails has long been an issue in the area of knowledge representation and reasoning. Different nonmonotonic logics and various semantic frameworks and axiom systems have been developed to address this question.The main theme of this book, Knowledge Representation and Inductive Reasoning using Conditional Logic and Sets of Ranking Functions, is inductive reasoning from conditional knowledge bases. Using ordinal conditional functions as ranking models for conditional knowledge bases, the author studies inferences induced by individual ranking models as well as by sets of ranking models. He elaborates in detail the interrelationships among the resulting inference relations and shows their formal properties with respect to established inference axioms. Based on the introduction of a novel classification scheme for conditionals, he also addresses the question of how to realize and implement the entailment relations obtained.In this work, “Steven Kutsch convincingly presents his ideas, provides illustrating examples for them, rigorously defines the introduced concepts, formally proves all technical results, and fully implements every newly introduced inference method in an advanced Java library (…). He significantly advances the state of the art in this field.” – Prof. Dr. Christoph Beierle of the FernUniversität in Hagen

A core problem in Artificial Intelligence is the modeling of human reasoning. Classic-logical approaches are too rigid for this task, as deductive inference yielding logically correct results is not appropriate in situations where conclusions must be drawn based on the incomplete or uncertain knowledge present in virtually all real world scenarios. Since there are no mathematically precise and generally accepted definitions for the notions of plausible or rational, the question of what a knowledge base consisting of uncertain rules entails has long been an issue in the area of knowledge representation and reasoning. Different nonmonotonic logics and various semantic frameworks and axiom systems have been developed to address this question. The main theme of this book, Knowledge Representation and Inductive Reasoning using Conditional Logic and Sets of Ranking Functions, is inductive reasoning from conditional knowledge bases. Using ordinal conditional functions as ranking models for conditional knowledge bases, the author studies inferences induced by individual ranking models as well as by sets of ranking models. He elaborates in detail the interrelationships among the resulting inference relations and shows their formal properties with respect to established inference axioms. Based on the introduction of a novel classification scheme for conditionals, he also addresses the question of how to realize and implement the entailment relations obtained. In this work, “Steven Kutsch convincingly presents his ideas, provides illustrating examples for them, rigorously defines the introduced concepts, formally proves all technical results, and fully implements every newly introduced inference method in an advanced Java library (…). He significantly advances the state of the art in this field.” – Prof. Dr. Christoph Beierle of the FernUniversität in Hagen