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Default Reasoning Using Maximum Entropy and Variable Strength Defaults
, 1999
"... The thesis presents a computational model for reasoning with partial information which uses default rules or information about what normally happens. The idea is to provide a means of filling the gaps in an incomplete world view with the most plausible assumptions while allowing for the retraction o ..."
Abstract

Cited by 5 (2 self)
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The thesis presents a computational model for reasoning with partial information which uses default rules or information about what normally happens. The idea is to provide a means of filling the gaps in an incomplete world view with the most plausible assumptions while allowing for the retraction of conclusions should they subsequently turn out to be incorrect. The model can be used both to reason from a given knowledge base of default rules, and to aid in the construction of such knowledge bases by allowing their designer to compare the consequences of his design with his own default assumptions. The conclusions supported by the proposed model are justified by the use of a probabilistic semantics for default rules in conjunction with the application of a rational means of inference from incomplete knowledgethe principle of maximum entropy (ME). The thesis develops both the theory and algorithms for the ME approach and argues that it should be considered as a general theory of default reasoning. The argument supporting the thesis has two main threads. Firstly, the ME approach is tested on the benchmark examples required of nonmonotonic behaviour, and it is found to handle them appropriately. Moreover, these patterns of commonsense reasoning emerge as consequences of the chosen semantics rather than being design features. It is argued that this makes the ME approach more objective, and its conclusions more justifiable, than other default systems. Secondly, the ME approach is compared with two existing systems: the lexicographic approach (LEX) and system Z + . It is shown that the former can be equated with ME under suitable conditions making it strictly less expressive, while the latter is too crude to perform the subtle resolution of default conflict which the ME...
Representation Results for Default Logics
"... Normal forms play an important role in computer science, for example in the areas of logic and databases. This paper provides a study of normal forms for some prominent logics for default reasoning. In particular we show that in Constrained and in Justified Default Logic, seminormal default theori ..."
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Normal forms play an important role in computer science, for example in the areas of logic and databases. This paper provides a study of normal forms for some prominent logics for default reasoning. In particular we show that in Constrained and in Justified Default Logic, seminormal default theories can represent arbitrary default theories. The main result for Justified Default Logic requires the signature (logical language) to be enhanced in order to obtain the desired outcome. 1 Introduction Normal forms play an important role in computer science. They help restrict the study of some properties to specific classes of items, and thus make the task at hand easier. Examples of areas where normal forms have proved fruitful include logic, where normal forms of formulae are used both for the proof of theoretical results and in theorem proving, and relational databases [2], where normal forms have been the driving force in the development of database theory and principles of good data mo...