Rational Reasoning With Finite Conditional Knowledge Bases
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Rational Reasoning with Finite Conditional Knowledge Bases
Nonmonotonic reasoning is a discipline of computer science, epistemology, and cognition: It models inferences where classical logic is inadequate in symbolic AI, defines normative models for reasoning with defeasible information in epistemology, and models human reasoning under information change in cognition. Its building blocks are defeasible rules formalised as DeFinetti conditionals. In this thesis, Christian Eichhorn examines qualitative and semi-quantitative inference relations on top said conditionals, using the conditional structure of the knowledge base and Spohn’s Ordinal Conditional Functions, using established properties. Converting network approaches from probabilistics, he shows how to approach the relations with regard to implementation.
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
Adaptive Logics for Defeasible Reasoning
Author: Christian Straßer
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-11-29
This book presents adaptive logics as an intuitive and powerful framework for modeling defeasible reasoning. It examines various contexts in which defeasible reasoning is useful and offers a compact introduction into adaptive logics. The author first familiarizes readers with defeasible reasoning, the adaptive logics framework, combinations of adaptive logics, and a range of useful meta-theoretic properties. He then offers a systematic study of adaptive logics based on various applications. The book presents formal models for defeasible reasoning stemming from different contexts, such as default reasoning, argumentation, and normative reasoning. It highlights various meta-theoretic advantages of adaptive logics over other logics or logical frameworks that model defeasible reasoning. In this way the book substantiates the status of adaptive logics as a generic formal framework for defeasible reasoning.