Rational Reasoning with Finite Conditional Knowledge Bases: Theoretical and Implementational Aspects

Stuttgart: J.B. Metzler (2018)
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Abstract

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.

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2019

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9783476048233   9783476048240   3476048233

DOI

10.1007/978-3-476-04824-0
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Chapters

Summary and Final Remarks

In this chapter we sum up the thesis, comment on the research questions raised and indicate starting points for further work in the areas of this thesis.

Formal Inferences and Commonsense Reasoning: Connections to Psychology and Cognition

Humans reasoning about a single rule, presented with an additional fact and sometimes additional background information, are an objects of investigation in the disciplines of psychology and cognition, especially since the studies [Was68, Byr89].

Compact Representations of Conditional Knowledge and Implementational Aspects: Network Approaches to Ordinal Conditional Functions

From the definition of ordinal conditional functions in Section 3.3 we obtained that storing an OCF means to store the ranking value of every possible world, and therefore the space needed to store an OCF is exponentially large in the number of variables. Additionally, generating such an OCF from a ... see more

Normal Forms of Conditional Knowledge Bases

Conditionals are logical entities composed from the set of propositional formulas, and conditional knowledge bases are composed from sets of conditionals. Therefore it is possible to encode information in very different and even unclear or confusing ways. Conditional knowledge bases serve as base fo... see more

Reasoning with Sets of c-Representations

In Section 3.3.3.3 we recalled c-representations [KI01] as a technique to inductively obtain ranking models for a given conditional knowledge base. We also already discussed that other than ranking models obtained by System Z [Pea90], which are the unique Pareto minimal ranking models of the knowled... see more

Properties of Nonmonotonic Inference Relations

In the previous chapters we already recalled inference relations based on the consistency of knowledge bases, preference orderings, plausibilities and probabilities of the possible worlds. So far, we just juxtaposed these different inference relations, but neither compared them by means of inferenti... see more

Basic Techniques

In this section, we recall basic techniques which, on top of the formal preliminaries of the previous one, provide the formal and scientific groundwork for the dissertation. We start by recalling preferential models and preferential entailment as underlying formalism of the qualitative and semi-quan... see more

Preliminaries

This chapter recalls the formal background which provides the formal base this thesis is built upon. We start by introducing the running example, a variant of the iconic example from nonmonotonic reasoning speaking about birds and penguins with respect to their ability to fly. This example is then u... see more

Introduction

This section gives an overview over the topic of this thesis in its scientific context, motivates the work, phrases major research questions, and gives an outline over the structure of the thesis.

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