Loughborough University
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Goal driven theorem proving using conceptual graphs and Peirce logic

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posted on 2011-01-12, 09:17 authored by John E. Heaton
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.



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© John Edward Heaton

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A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.

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