Theory Unification in Abstract Clause Graphs

Clause Graphs, as they were defined in the 1970s, are graphs representing first order formulas in conjunctive normal form together with the resolution possibilities. The nodes are labelled with literals and the edges (links) connect complementary unifiable literals. This report describes a generalization of this concept, called abstract clause graphs. The nodes of abstract clause graphs are still labelled with literals, the links however connect literals that are "unifiable" relative to a given relation between literals. This relation is not explicitely defined; only certain "abstract" properties are required. for instance the existence of a special purpose unification algorithm is assumed which computes substitutions, the application of which makes the relation hold for two literals. When instances of already existing literals are added to the graph (e.g. due to resolution or factoring), the links to the new literals are derived from the links of their ancestors. An inheritance mechanism for such links is presented which operates only on the attached substitutions and does not have to unify the literals. This solves a long standing open problem of connection graph calculi: how to inherit links (with several unifiers attached) such that no unifier has to be computed more than once

Set of support, demodulation, paramodulation: a historical perspective

This article is a tribute to the scientific legacy of automated reasoning pioneer and JAR founder Lawrence T. (Larry) Wos. Larry's main technical contributions were the set-of-support strategy for resolution theorem proving, and the demodulation and paramodulation inference rules for building equality into resolution. Starting from the original definitions of these concepts in Larry's papers, this survey traces their evolution, unearthing the often forgotten trails that connect Larry's original definitions to those that became standard in the field

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

Enhance DBMS capabilities using semantic data modelling approach.

by Yip Wai Man.Thesis (M.Phil.)--Chinese University of Hong Kong, 1990.Bibliography: leaves 132-135.ABSTRACTACKNOWLEDGEMENTSPART IChapter 1 --- OVERVIEW ON SEMANTIC DATA MODELLING APPROACH … --- p.1Chapter 2 --- SCOPE OF RESEARCH --- p.4Chapter 3 --- CONCEPTUAL STRUCTURE OF SAM* --- p.7Chapter 3.1 --- Concepts and Associations --- p.7Chapter 3.1.1 --- Membership Association --- p.8Chapter 3.1.2 --- Aggregation Association --- p.8Chapter 3.1.3 --- Generalization Association --- p.9Chapter 3.1.4 --- Interaction Association --- p.10Chapter 3.1.5 --- Composition Association --- p.11Chapter 3.1.6 --- Cross-Product Association --- p.12Chapter 3.1.7 --- Summary Association --- p.13Chapter 3.2 --- An Example --- p.14Chapter 3.3 --- Occurrences --- p.15PART IIChapter 4 --- SYSTEM OVERVIEW --- p.17Chapter 4.1 --- System Objectives --- p.17Chapter 4.1.1 --- Data Level --- p.17Chapter 4.1.2 --- Meta-Data Level --- p.18Chapter 4.2 --- System Characteristics --- p.19Chapter 4.3 --- Design Considerations --- p.20Chapter 5 --- IMPLEMENTATION CONSIDERATIONS --- p.23Chapter 5.1 --- Introduction --- p.23Chapter 5.2 --- Data Definition Language for Schema --- p.24Chapter 5.3 --- Construction of Directed Acyclic Graph --- p.27Chapter 5.4 --- Query Manipulation Language --- p.28Chapter 5.4.1 --- Semantic Manipulation Language --- p.29Chapter 5.4.1.1 --- Locate Concepts --- p.30Chapter 5.4.1.2 --- Retrieve Information About Concepts --- p.30Chapter 5.4.1.3 --- Find a Path Between Two Concepts --- p.31Chapter 5.4.2 --- Occurrence Manipulation Language --- p.32Chapter 5.5 --- Examples --- p.35Chapter 6 --- RESULTS AND DISCUSSIONS --- p.41Chapter 6.1 --- Allow Non-Homogeneity of Facts about Entities --- p.41Chapter 6.2 --- Field Name is Information --- p.42Chapter 6.3 --- Description of Group of Information --- p.43Chapter 6.4 --- Explicitly Description of Interaction --- p.43Chapter 6.5 --- Information about Entities --- p.44Chapter 6.6 --- Automatically Joining Tables --- p.45Chapter 6.7 --- Automatically Union Tables --- p.45Chapter 6.8 --- Automatically Select Tables --- p.46Chapter 6.9 --- Ambiguity --- p.47Chapter 6.10 --- Normalization --- p.47Chapter 6.11 --- Update --- p.50PART IIIChapter 7 --- SCHEMA VERIFICATION --- p.55Chapter 7.1 --- Introduction --- p.55Chapter 7.2 --- Need of Schema Verification --- p.57Chapter 7.3 --- Integrity Constraint Handling Vs Schema Verification --- p.58Chapter 8 --- AUTOMATIC THEOREM PROVING --- p.60Chapter 8.1 --- Overview --- p.60Chapter 8.2 --- A Discussion on Some Automatic Theorem Proving Methods --- p.61Chapter 8.2.1 --- Resolution --- p.61Chapter 8.2.2 --- Natural Deduction --- p.63Chapter 8.2.3 --- Tableau Proof Methods --- p.65Chapter 8.2.4 --- Connection Method --- p.67Chapter 8.3 --- Comparison of Automatic Theorem Proving Methods --- p.70Chapter 8.3.1 --- Proof Procedure --- p.70Chapter 8.3.2 --- Overhead --- p.70Chapter 8.3.3 --- Unification --- p.71Chapter 8.3.4 --- Heuristics --- p.72Chapter 8.3.5 --- Getting Lost --- p.73Chapter 8.4 --- The Choice of Tool for Schema Verification --- p.73Chapter 9 --- IMPROVEMENT OF CONNECTION METHOD --- p.77Chapter 9.1 --- Motivation of Improving Connection Method --- p.77Chapter 9.2 --- Redundancy Handled by the Original Algorithm --- p.78Chapter 9.3 --- Design Philosophy of the Improved Version --- p.82Chapter 9.4 --- Primary Connection Method Algorithm --- p.83Chapter 9.5 --- AND/OR Connection Graph --- p.89Chapter 9.6 --- Graph Traversal Procedure --- p.91Chapter 9.7 --- Elimination Redundancy Using AND/OR Connection Graph --- p.94Chapter 9.8 --- Further Improvement on Graph Traversal --- p.96Chapter 9.9 --- Comparison with Original Connection Method Algorithm --- p.97Chapter 9.10 --- Application of Connection Method to Schema Verification --- p.98Chapter 9.10.1 --- Express Constraint in Well Formed Formula --- p.98Chapter 9.10.2 --- Convert Formula into Negation Normal Form --- p.101Chapter 9.10.3 --- Verification --- p.101PART IVChapter 10 --- FURTHER DEVELOPMENT --- p.103Chapter 10.1 --- Intelligent Front-End --- p.103Chapter 10.2 --- On Connection Method --- p.104Chapter 10.3 --- Many-Sorted Calculus --- p.104Chapter 11 --- CONCLUSION --- p.107APPENDICESChapter A --- COMPARISON OF SEMANTIC DATA MODELS --- p.110Chapter B --- CONSTRUCTION OP OCCURRENCES --- p.111Chapter C --- SYNTAX OF DDL FOR THE SCHEMA --- p.113Chapter D --- SYNTAX OF SEMANTIC MANIPULATION LANGUAGE --- p.116Chapter E --- TESTING SCHEMA FOR FUND INVESTMENT DBMS --- p.118Chapter F --- TESTING SCHEMA FOR STOCK INVESTMENT DBMS --- p.121Chapter G --- CONNECTION METHOD --- p.124Chapter H --- COMPARISON BETWEEN RESOLUTION AND CONNECTION METHOD --- p.128REFERENCES --- p.13