A dissertation submitted in a partial fulfillment of the requirements for the degree of Doctor of Engineering

Thesis (Ph.D.) - Asian Institute of Technology, 1997

This dissertation provides an abstract framework which accounts for the static aspect of deductive object-oriented representation paradigm, including deduction, in- heritance, implicit information, structured objects and complex object descriptions. For the sake of generality and simplicity, it uses Akama{u2019}s abstract theory of declara- tive programs as its primary logical basis. Interaction of deduction and nonmonotonic inheritance captured via specialization operation is discussed based on Dung's theory of argumentation. An appropriate semantics for declarative programs with nonmono- tonic inheritance is presented Relationship between this semantics and Dobbie and Topor{u2018}s perfect model (with overriding) semantics is investigated. It is shown that for inheritance-strati{uFB01}ed programs, the two kinds of semantics coincide. However, the proposed semantics also provides correct skeptical meanings for the programs which are not inheritance-strati{uFB01}ed. Interaction of deduction and implicit implication on an interpretation domain clue to taxonomic information is studied. Under the assumption that the implicit implica- tion can be determined in advance and represented by a preorder on the domain, an appropriate model-theoretic semantics for declarative programs along with its {uFB01}xpoint characterization is described. Based on Kostler et.a1.{u2018}s foundation of {uFB01}xpoint with subsumption, it is shown that, if the implicit-implication relation is further assumed to be a partial order, then the meaning of a program can be obtained more elegantly by computation over reduced subsets of the interpretation domain. Moreover, implicit implication that cannot be determined beforehand but varies with interpretations is also investigated. Structural interrelationships among composite objects and object descriptions are studied based on Aczel's theory of structured objects. In order to specify the forms of required objects more precisely and concisely, Aczel{u2019}s theory is extended under the aSSumption that a structured object may belong to a sort and that these object sorts are partially ordered. The extension provides a general principle for the construction of order-sorted universes of structured objects. In addition, semantic interdependency between compound atoms (molecules) and constituent atoms is discussed.