Counterexample Guided Abstraction Refinement Algorithm for Propositional Circumscription

Circumscription is a representative example of a nonmonotonic reasoning inference technique. Circumscription has often been studied for first order theories, but its propositional version has also been the subject of extensive research, having been shown equivalent to extended closed world assumption (ECWA). Moreover, entailment in propositional circumscription is a well-known example of a decision problem in the second level of the polynomial hierarchy. This paper proposes a new Boolean Satisfiability (SAT)-based algorithm for entailment in propositional circumscription that explores the relationship of propositional circumscription to minimal models. The new algorithm is inspired by ideas commonly used in SAT-based model checking, namely counterexample guided abstraction refinement. In addition, the new algorithm is refined to compute the theory closure for generalized close world assumption (GCWA). Experimental results show that the new algorithm can solve problem instances that other solutions are unable to solve

DRUM-II : efficient model based diagnosis of technical systems

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The complexity of theorem proving in circumscription and minimal entailment

We provide the first comprehensive proof-complexity analysis of different proof systems for propositional circumscription. In particular, we investigate two sequent-style calculi: MLK defined by Olivetti [28] and CIRC introduced by Bonatti and Olivetti [8], and the tableaux calculus NTAB suggested by Niemelä [26]. In our analysis we obtain exponential lower bounds for the proof size in NTAB and CIRC and show a polynomial simulation of CIRC by MLK. This yields a chain NTAB < CIRC < MLK of proof systems for circumscription of strictly increasing strength with respect to lengths of proofs

New Models for Expert System Design

This thesis presents new work on the analysis of human lung sound. Experimental studies investigated the relationship between the condition of the lungs and the power spectrum of lung sound detected at the chest wall. The conclusion drawn from two clinical studies was that the median frequency of the lung sound power spectrum increases with a decrease in airway calibre. The technique for the analysis of lung sound presented in this thesis is a non-invasive method which may be capable of assessing differences in airway calibre between different lobes of the lung. An expert system for the analysis of lung sound data and pulmonary function data was designed. The expert knowledge was expressed in a belief logic, a system of logic which is more expressive than first order logic. New automated theorem proving methods were developed for the belief logic. The new methods were implemented to form the 'inference engine' of the expert system. The new expert system compared favourably with systems which perform a similar task. The use of belief logic allows introspective reasoning to be carried out. Plausible reasoning, a type of introspective reasoning which allows conclusions to be drawn when the database is incomplete, was proposed and tested. The author concludes that the use of a belief logic in expert system design has significant advantages over conventional approaches. The experimental results of the lung sound research were incorporated into the expert system rule base: the medical and expert system research were complementary