Efficient Approximate Deduction and an Application to Computer Security

Abstract

of the Dissertation The use of logics and formal methods for speci cation and veri cation requires e ective deduction methods which can be e ciently implemented. To this aim, the rst part of this dissertation is devoted to the design and validation (both theoretical and experimental) of a number of e cient tableau inference systems, which constitute a signi cant advance with respect to other state of the art deductive systems. This parts starts by enhancing the classical propositional tableau calculus with an operation for constraints propagation (called simpli cation). This technique subsume a number of other approaches presented in the literature in a uniform framework. For instance, it is shown that Davis-Putnam and KSAT procedures are variant of tableau calculi with simpli cation. This framework is lifted to propositional multi modal logic by introducing the concept of pre xed tableau and incorporating the notion of modal constraints propagation. The extension to propositional dynamic logic with converse is carried forward by generalizing a combination of techniques used in modal theorem proving, model checking for temporal logics and automata theoretic approaches. This is the rst tableau for converse PDL, thus solving an open problem by Pratt. The computational characteristics of the various techniques are evaluated, either by extensive experimentation on relevant benchmarks (eg IFIP benchmark on hardware veri cation) or by careful complexity analysis. As modal and dynamic logic theorem proving is complex, we carefully analyze computational properties such as modularity, query combination, the design of decision procedures and the complexity of search strategies, possibly generalizing our results to other deduction methods such as those based on rst-order translations and resolution. E cient procedures are not enough and, to tame the complexity of logical inference, a second step is taken: the transformation of e cient exact deduction methods into anytime approximate deduction systems which can be interrupted at any time, and whose precision improves with time. A general theory, which capitalizes in essential ways on the deductive machinery designed in the rst part, is introduced for propositional and modal approximation. Only sound, only complete and multi-directional approximation of i ii the classical notion of proof are presented. These approximations are shown to converge to the classical notion of proof and we discuss the guarantees on the quality of the approximation provided by this anytime deduction mechanism. In the last part of the dissertation { to show the potentials of our approach { we show an example of the application of logic as speci cation and veri cation language to a problem of computer security (namely access control). Among the various possibilities we single out the logic for access control developed at the Digital System Research Center by Abadi, Lampson et al. and design a tableau based deduction method for the logic based on these techniques. The overall claim of this dissertation is that tableaux can be used as efcient, e ective and approximate tools for automated reasoning and formal veri cation in a wide range of practical cases without losing their natural ease of use.

Cite this paper

@inproceedings{Massacci1998EfficientAD, title={Efficient Approximate Deduction and an Application to Computer Security}, author={Fabio Massacci and Marco Schaerf and Dott.ssa Fiora Pirri}, year={1998} }