Goal driven theorem proving using conceptual graphs and Peirce logic

The thesis describes a rational reconstruction of Sowa's theory of Conceptual Graphs. The reconstruction produces a theory with a firmer logical foundation than was previously the case and which is suitable for computation whilst retaining the expressiveness of the original theory. Also, several areas of incompleteness are addressed. These mainly concern the scope of operations on conceptual graphs of different types but include extensions for logics of higher orders than first order. An important innovation is the placing of negation onto a sound representational basis. A comparison of theorem proving techniques is made from which the principles of theorem proving in Peirce logic are identified. As a result, a set of derived inference rules, suitable for a goal driven approach to theorem proving, is developed from Peirce's beta rules. These derived rules, the first of their kind for Peirce logic and conceptual graphs, allow the development of a novel theorem proving approach which has some similarities to a combined semantic tableau and resolution methodology. With this methodology it is shown that a logically complete yet tractable system is possible. An important result is the identification of domain independent heuristics which follow directly from the methodology. In addition to the theorem prover, an efficient system for the detection of selectional constraint violations is developed. The proof techniques are used to build a working knowledge base system in Prolog which can accept arbitrary statements represented by conceptual graphs and test their semantic and logical consistency against a dynamic knowledge base. The same proof techniques are used to find solutions to arbitrary queries. Since the system is logically complete it can maintain the integrity of its knowledge base and answer queries in a fully automated manner. Thus the system is completely declarative and does not require any programming whatever by a user with the result that all interaction with a user is conversational. Finally, the system is compared with other theorem proving systems which are based upon Conceptual Graphs and conclusions about the effectiveness of the methodology are drawn

Reason Maintenance - Conceptual Framework

This paper describes the conceptual framework for reason maintenance developed as part of WP2

CGs to FCA Including Peirce's Cuts

Previous work has demonstrated a straightforward mapping from Conceptual Graphs (CGs) to Formal Concept Analysis (FCA), and the combined benefits these types of Conceptual Structures bring in capturing and reasoning about the semantics in system design. As in that work, a CGs Transaction Model (or `Transaction Graph') exemplar is used, but in the form of a richer Financial Trading (FT) case study that has its business rules visualised in Peirce's cuts. The FT case study highlights that cuts can meaningfully be included in the CGs to FCA mapping. Accordingly, the case study's CGs Transaction Graph with its cuts is translated into a form suitable for the CGtoFCA algorithm described in that previous work. The process is tested through the CG-FCA software that implements the CGtoFCA algorithm. The algorithm describes how a Conceptual Graph (CG), represented by triples of the form source-concept, relation, target-concept can be transformed into a set of binary relations of the form target-concept, source-conceptnrelation thus creating a formal context in FCA. Cuts though can now be included in the same formal, rigorous, reproducible and general way. The mapping develops the Transaction Graph into a Transaction Concept, capturing and unifying the features of Conceptual Structures that CGs and FCA collectively embody

Using conceptual graphs for clinical guidelines representation and knowledge visualization

The intrinsic complexity of the medical domain requires the building of some tools to assist the clinician and improve the patient’s health care. Clinical practice guidelines and protocols (CGPs) are documents with the aim of guiding decisions and criteria in specific areas of healthcare and they have been represented using several languages, but these are difficult to understand without a formal background. This paper uses conceptual graph formalism to represent CGPs. The originality here is the use of a graph-based approach in which reasoning is based on graph-theory operations to support sound logical reasoning in a visual manner. It allows users to have a maximal understanding and control over each step of the knowledge reasoning process in the CGPs exploitation. The application example concentrates on a protocol for the management of adult patients with hyperosmolar hyperglycemic state in the Intensive Care Unit

Security Policy Specification Using a Graphical Approach

A security policy states the acceptable actions of an information system, as the actions bear on security. There is a pressing need for organizations to declare their security policies, even informal statements would be better than the current practice. But, formal policy statements are preferable to support (1) reasoning about policies, e.g., for consistency and completeness, (2) automated enforcement of the policy, e.g., using wrappers around legacy systems or after the fact with an intrusion detection system, and (3) other formal manipulation of policies, e.g., the composition of policies. We present LaSCO, the Language for Security Constraints on Objects, in which a policy consists of two parts: the domain (assumptions about the system) and the requirement (what is allowed assuming the domain is satisfied). Thus policies defined in LaSCO have the appearance of conditional access control statements. LaSCO policies are specified as expressions in logic and as directed graphs, giving a visual view of policy. LaSCO has a simple semantics in first order logic (which we provide), thus permitting policies we write, even for complex policies, to be very perspicuous. LaSCO has syntax to express many of the situations we have found to be useful on policies or, more interesting, the composition of policies. LaSCO has an object-oriented structure, permitting it to be useful to describe policies on the objects and methods of an application written in an object-oriented language, in addition to the traditional policies on operating system objects. A LaSCO specification can be automatically translated into executable code that checks an invocation of a program with respect to a policy. The implementation of LaSCO is in Java, and generates wrappers to check Java programs with respect to a policy.Comment: 28 pages, 22 figures, in color (but color is not essential for viewing); UC Davis CS department technical report (July 22, 1998

An introduction to Graph Data Management

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type constructors. In this article we present the basic notions of graph databases, give an historical overview of its main development, and study the main current systems that implement them