\contentsline {section}{\numberline {1}Introduction}{5}
\contentsline {section}{\numberline {2}Basic Notions and Notation}{6}
\contentsline {subsection}{\numberline {2.1}Specifying Rules and their Theories}{6}
\contentsline {subsection}{\numberline {2.2}Secondary Aspects of our Logic}{7}
\contentsline {subsection}{\numberline {2.3}Global Parameters for the Given Specification}{8}
\contentsline {subsection}{\numberline {2.4}Formalization of Arguments}{8}
\contentsline {subsection}{\numberline {2.5}Quasi-Orderings}{9}
\contentsline {section}{\numberline {3}Motivating Examples}{10}
\contentsline {section}{\numberline {4}Toward an Intuitive Notion of Specificity}{12}
\contentsline {subsection}{\numberline {4.1}The Common-Sense Concept of Specificity}{12}
\contentsline {subsection}{\numberline {4.2}Arguments as an Intuitive Abstraction}{12}
\contentsline {subsection}{\numberline {4.3}The Intuitive R\^ole\ of Activation Sets in the Definition of Specificity}{13}
\contentsline {subsubsection}{\numberline {4.3.1}Modulo Which Theory are Activation Sets to be Compared?}{13}
\contentsline {subsubsection}{\numberline {4.3.2}A first Sketch of a Notion of Specificity}{14}
\contentsline {subsection}{\numberline {4.4}Isolation of the Defeasible Parts of a Derivation}{15}
\contentsline {subsubsection}{\numberline {4.4.1}Isolation of Actual Defeasible Parts in And-Trees}{15}
\contentsline {subsubsection}{\numberline {4.4.2}A first approximation of Activation Sets}{16}
\contentsline {subsubsection}{\numberline {4.4.3}Growth of the Defeasible Parts toward the Leaves}{16}
\contentsline {subsubsection}{\numberline {4.4.4}First Effect: Simplified Second Sketch of a Notion of Specificity}{17}
\contentsline {subsubsection}{\numberline {4.4.5}Second Effect: Preference of the ``More Concise''}{17}
\contentsline {subsubsection}{\numberline {4.4.6}Preference of the ``More Precise''}{19}
\contentsline {subsubsection}{\numberline {4.4.7}Conclusion on the Preferences}{19}
\contentsline {section}{\numberline {5}Requirements Specification of \\Specificity in Positive-Conditional Specification}{20}
\contentsline {section}{\numberline {6}Formalizations of Specificity}{21}
\contentsline {subsection}{\numberline {6.1}Activation Sets}{21}
\contentsline {subsection}{\numberline {6.2}{\sc Poole}'s Specificity Relation P1; its Minor Corrections P2, P3}{23}
\contentsline {subsection}{\numberline {6.3}Main Negative Result: Not Transitive!}{26}
\contentsline {subsection}{\numberline {6.4}Our Novel Specificity Ordering CP1}{27}
\contentsline {subsection}{\numberline {6.5}Relation between the Specificity Relations P3 and CP1}{29}
\contentsline {subsection}{\numberline {6.6}Checking Up the Previous Examples}{30}
\contentsline {section}{\numberline {7}Putting Specificity to Test w.r.t.\ Human Intuition}{32}
\contentsline {subsection}{\numberline {7.1}Monotonicity of the Specificity Relations w.r.t.\ Conjunction}{32}
\contentsline {subsection}{\numberline {7.2}Implementation of the Preference of the ``More Precise''}{34}
\contentsline {subsection}{\numberline {7.3}Conflict between the ``More Concise'' and the ``More Precise''}{36}
\contentsline {subsection}{\numberline {7.4}Global Effect matters more than Fine Structure}{37}
\contentsline {section}{\numberline {8}Efficiency Considerations and\\the Specificity Ordering CP2}{38}
\contentsline {subsection}{\numberline {8.1}A Slight Gain in Efficiency}{38}
\contentsline {subsection}{\numberline {8.2}Comparing Derivations}{38}
\contentsline {subsubsection}{\numberline {8.2.1}No Pruning Required}{38}
\contentsline {subsubsection}{\numberline {8.2.2}Sets of Derivations have to be Compared}{38}
\contentsline {subsubsection}{\numberline {8.2.3}Path Criteria?}{39}
\contentsline {subsection}{\numberline {8.3}Toward a More Efficiently Realizable Notion of {\sc Poole}-Style Specificity}{41}
\contentsline {subsubsection}{\numberline {8.3.1}Immediate Activation Sets}{41}
\contentsline {subsubsection}{\numberline {8.3.2}Special Cases with Simple Activation-Set Computation}{47}
\contentsline {subsubsection}{\numberline {8.3.3}A Step Toward Operationalization of Immediate Activation Sets}{49}
\contentsline {subsubsection}{\numberline {8.3.4}A Specificity Relation Based on Given And-Trees}{53}
\contentsline {section}{\numberline {9}Conclusion}{56}
\contentsline {subsection}{\numberline {9.1}Summary}{56}
\contentsline {subsection}{\numberline {9.2}Application Context}{57}
\contentsline {subsection}{\numberline {9.3}Critical Assessment}{58}
\contentsline {section}{Acknowledgments}{59}
\contentsline {section}{References}{59}