Extensions Of The Default Logic

Abstract Reiter's default logic is one of the most popular formalism for describing non-monotonic reasoning and is extensive investigated by the community of logical foundations of Artificial Intelligence, particularly, default extension is the hot issue. In symbol,to acheive some completeness, the extensions of default theory realize to expand the set W of worlds, using default rules add some acceptable or believe worlds or conclusions to the set of worlds, and it requires them consistent each other, and have no contradict with the original worlds, (otherwise, it's inconsistent, it there exists with inconsistent extension, and this inconsistent extension is the only one.) that is , we only consider those adding worlds or conclusions are consistent with the original knowledage base. However, we know the set of worlds and the set of default rules all are complex and varied, and all methods of computing extensions are quasi-constructive, so the problem of computing extensions is hard.In this paper, from the simple synatic closed normal default theories without prequisite, we first discuss the classifications and properties etc of its consistent extension, then we respectively discuss the representation of default logic, that is, we can use the default theory that has the same extensions with it, but is simpler in synatic to represent it; to smplify compution, we can classify and simplify properly default rules before computing extensions and conclude the corresponding simpli-cation and classification priniciple. We systematically investigates the properties of Roos-extensions that is modified the defect of default logic, and the properties , compution of the extension of cumulative default logic(CDL). At last, we discuss the properties and computation of the statistical default logic, at the same time, we define and study the properties and proof theory of the normal statistical default logic. There are five chapters in this paper.Chatcer 1 is the basic knowledage that is used in this paper.Chapter 2 systematically investigates the consistent extensions of the finiteclosed normal default theories without prerequisite. First, a classification theorem of consistent extensions is proven; Second, certain characterization theorems forextensions are provided; Third, a quasi-constructive method for constructing extensions is proposed; moreover, possible numbers of different extensions of a default theory is estimated.In Chapter 3. First, we use the set of default extensions of default theory to investigate the representability of theories as the set of extensions of a default theory. we give some properties of equivalence of default theories; We show the default theories of having finite pairwise inconsistent extensions can be represented by a (prerequisite-free) (semi-) normal default theory. Also there is result that every default theory â–³ = (D, W) is representable in the class of default theories â–³ = (D~', W~' = (?)) ,we will point W~' = (?) is not necessary. At the same time , we give some examples for further explaining this. Second, In this present paper ,by the definition of default extensions, some default rules can not be considered that have no effect to compute extension and can be classified whose justification are inconsistent each other before computing the extensions of default theory. That is, this paper classifies and simplifies properly default rules before computing extension, and gives some classification and simplification principles. Finally, one important defect of Reiter's default logic is inability to reason by cases, to overcome the defect definition of Reiter's extension. Roos presents a modified definition of a default extension that solves the problem. In this chapter, we will discuss the properties of Roos-extension that similar to Reiter-extension, and will find some properties of Reiter-extension can not still correct to Roos-extension, for example, Roos-inconsistent extensions may be not the only one. We point out the difference of them and explain these using examples.Chapter 4 using Crigoris Antonion's semantic opertional theory algorithms and V.W.Marek & M.Fruszcyuski's synatic algorithms to compute the extensions of cumulative default logic(CDL) and systemically discusses the extensions of CDL and its two new variarits CADL,QDL.As a result,it systematries the extensions of cumulative default logic, and points these two methods can be used to compute extensions of others default theories, without generality, we use these two methods for the extensions of the prioritied default theories.Chapter 5 discusses statistical extensions of statistical default logic , an expansion of classical(i.e.Reiter' s )default logic that allows us to model common inference patterns found in standard inferential statistics, which is an expansion by means...