Interactive program verification using virtual programs

This thesis is concerned with ways of proving the correctness of computer programs. The first part of the thesis presents a new method for doing this. The method, called continuation induction, is based on the ideas of symbolic execution, the description of a given program by a virtual program, and the demonstration that these two programs are equivalent whenever the given program terminates. The main advantage of continuation induction over other methods is that it enables programs using a wide variety of programming constructs such as recursion, iteration, non-determinism, procedures with side-effects and jumps out of blocks to be handled in a natural and uniform way. In the second part of the thesis a program verifier which uses both this method and Floyd's inductive assertion method is described. The significance of this verifier is that it is designed to be extensible, and to this end the user can declare new functions and predicates to be used in giving a natural description of the program's intention. Rules describing these new functions can then be used when verifying the program. To actually prove the verification conditions, the system employs automatic simplification, a relatively clever matcher, a simple natural deduction system and, most importantly, the user's advice. A large number of commands are provided for the user in guiding the system to a proof of the program's correctness. The system has been used to verify various programs including two sorting programs and a program to invert a permutation 'in place' the proofs of the sorting programs included a proof of the fact that the final array was a permutation of the original one. Finally, some observations and suggestions are made concerning the continued development of such interactive verification systems

Concept and Role Forgetting in ALC Ontologies

Forgetting is an important tool for reducing ontologies by eliminating some concepts and roles while preserving sound and complete reasoning. Attempts have previously been made to address the problem of forgetting in relatively simple description logics (DLs) such as DL-Lite and extended . The ontologies used in these attempts were mostly restricted to TBoxes rather than general knowledge bases (KBs). However, the issue of forgetting for general KBs in more expressive description logics, such as and OWL DL, is largely unexplored. In particular, the problem of characterizing and computing forgetting for such logics is still open. In this paper, we first define semantic forgetting about concepts and roles in ontologies and state several important properties of forgetting in this setting. We then define the result of forgetting for concept descriptions in , state the properties of forgetting for concept descriptions, and present algorithms for computing the result of forgetting for concept descriptions. Unlike the case of DL-Lite, the result of forgetting for an ontology does not exist in general, even for the special case of concept forgetting. This makes the problem of how to compute forgetting in more challenging. We address this problem by defining a series of approximations to the result of forgetting for ontologies and studying their properties and their application to reasoning tasks. We use the algorithms for computing forgetting for concept descriptions to compute these approximations. Our algorithms for computing approximations can be embedded into an ontology editor to enhance its ability to manage and reason in (large) ontologies