Every normal logic program has a 2-valued semantics: theory, extensions, applications, implementations

Abstract

After a very brief introduction to the general subject of Knowledge Representation and Reasoning with Logic Programs we analyse the syntactic structure of a logic program and how it can influence the semantics. We outline the important properties of a 2-valued semantics for Normal Logic Programs, proceed to define the new Minimal Hypotheses semantics with those properties and explore how it can be used to benefit some knowledge representation and reasoning mechanisms. The main original contributions of this work, whose connections will be detailed in the sequel, are: • The Layering for generic graphs which we then apply to NLPs yielding the Rule Layering and Atom Layering — a generalization of the stratification notion; • The Full shifting transformation of Disjunctive Logic Programs into (highly nonstratified)NLPs; • The Layer Support — a generalization of the classical notion of support; • The Brave Relevance and Brave Cautious Monotony properties of a 2-valued semantics; • The notions of Relevant Partial Knowledge Answer to a Query and Locally Consistent Relevant Partial Knowledge Answer to a Query; • The Layer-Decomposable Semantics family — the family of semantics that reflect the above mentioned Layerings; • The Approved Models argumentation approach to semantics; • The Minimal Hypotheses 2-valued semantics for NLP — a member of the Layer-Decomposable Semantics family rooted on a minimization of positive hypotheses assumption approach; • The definition and implementation of the Answer Completion mechanism in XSB Prolog — an essential component to ensure XSB’s WAM full compliance with the Well-Founded Semantics; • The definition of the Inspection Points mechanism for Abductive Logic Programs;• An implementation of the Inspection Points workings within the Abdual system [21] We recommend reading the chapters in this thesis in the sequence they appear. However, if the reader is not interested in all the subjects, or is more keen on some topics rather than others, we provide alternative reading paths as shown below. 1-2-3-4-5-6-7-8-9-12 Definition of the Layer-Decomposable Semantics family and the Minimal Hypotheses semantics (1 and 2 are optional) 3-6-7-8-10-11-12 All main contributions – assumes the reader is familiarized with logic programming topics 3-4-5-10-11-12 Focus on abductive reasoning and applications.