Inference systems Τ and search strategies E for T are distinguished from proof procedures β = (T,E) The completeness of procedures is studied by studying separately the completeness of inference systems and of search strategies. Completeness proofs for resolution systems are obtained by the construction of semantic trees. These systems include minimal α-restricted binary resolution, minimal α-restricted M-clash resolution and maximal pseudo-clash resolution. Certain refinements of hyper-resolution systems with equality axioms are shown to be complete and equivalent to refinements of the pararmodulation method for dealing with equality. The completeness and efficiency of search strategies for theorem-proving problems is studied in sufficient generality to include the case of search strategies for path-search problems in graphs. The notion of theorem-proving problem is defined abstractly so as to be dual to that of and" or tree. Special attention is given to resolution problems and to search strategies which generate simpler before more complex proofs. For efficiency, a proof procedure (T,E) requires an efficient search strategy E as well as an inference system T which admits both simple proofs and relatively few redundant and irrelevant derivations. The theory of efficient proof procedures outlined here is applied to proving the increased efficiency of the usual method for deleting tautologies and subsumed clauses. Counter-examples are exhibited for both the completeness and efficiency of alternative methods for deleting subsumed clauses. The efficiency of resolution procedures is improved by replacing the single operation of resolving a clash by the two operations of generating factors of clauses and of resolving a clash of factors. Several factoring methods are investigated for completeness. Of these the m-factoring method is shown to be always more efficient than the Wos-Robinson method.

This thesis describes the design and implementation of the IPE, an interactive proof editor for first-order intuitionistic predicate calculus, developed at the University of Edinburgh during 1983-1986, by the author together with John Cartmell and Tatsuya Hagino. The IPE uses an attribute grammar to maintain the state of its proof tree as a context-sensitive structure. The interface allows free movement through the proof structure, and encourages a "proof-byexperimentation" approach, since no proof step is irrevocable. We describe how the IPE's proof rules can be derived from natural deduction rules for first-order intuitionistic logic, how these proof rules are encoded as an attribute grammar, and how the interface is constructed on top of the grammar. Further facilities for the manipulation of the IPE's proof structures are presented, including a notion of IPE-tactic for their automatic construction. We also describe an extension of the IPE to enable the construction and use of simply-structured collections of axioms and results, the main provision here being an interactive "theory browser" which looks for facts which match a selected problem.

This thesis proposes improved methods for the automatic generation of proofs by structural induction in a formal system. The main application considered is proving properties of programs. The theorem-proving problem divides into two parts: (1) a formal system, and (2) proof generating methods. A formal system is presented which allows for a typed language; thus, abstract data types can be naturally defined in it. Its main feature is a general structural induction rule using a lexicographic ordering based on the substructure ordering induced by type definitions. The proof generating system is carefully introduced in order to convince of its consistency. It is meant to bring solutions to three problems. Firstly, it offers a method for generalizing only certain occurrences of a term in a theorem; this is achieved by associating generalization with the selection of induction variables. Secondly, it treats another generalization problem: that of terms occurring in the positions of arguments which vary within function definitions, besides recursion controlling arguments. The method is called indirect generalization, since it uses specialization as a means of attaining generalization. Thirdly, it presents a sound strategy for using the general induction rule which takes into account all induction subgoals, and for each of them, all induction hypotheses. Only then are the hypotheses retained and instantiated, or rejected altogether, according to their potential usefulness. The system also includes a search mechanism for counter-examples to conjectures, and a fast simplification algorithm.

The goal of this thesis is to find provably correct methods for detecting conflicts between XACML rules. A conflict occurs when one rule permits a request and another denies that same request. As XACML deals with access control, we can help prevent unwanted access by verifying that it contains rules that do not have unintended conflicts. In order to help with this, we propose an algorithm to find these conflicts then use the Coq Proof Assistant to prove correctness of this algorithm. The algorithm takes a rule set specified in XACML and returns a list of pairs of indices denoting which rules conflict. It is then up to the policy writer to see if the conflicts are intended, or if they need modifying. Since we will prove that this algorithm is sound and complete, we can be assured that the list we obtain is complete and only contains true conflicts.

Thesis (doctoral)--Université de Toulouse. Faculté de droit et des sciences ećonomiques, 1980. / At head of title: Universite de Toulouse. Includes bibliographical references.

Thesis (Ph.D.) - University of St Andrews, April 2007.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Habilitationsschrift--Bonn. / Includes bibliographical references (p. 93).

Habilitationsschrift--Bonn. / Includes bibliographical references (p. 93).

Thesis (M. Ed.)--University of Hong Kong, 1995. / Includes bibliographical references (leaf 90-99).