From approximate clausal reasoning to problem hardness

Authors:
David Rajaratnam;Maurice Pagnucco
Affiliations:
ARC Centre of Excellence for Autonomous Systems, School of Computer Science and Engineering, The University of New South Wales, Sydney, Australia;ARC Centre of Excellence for Autonomous Systems, School of Computer Science and Engineering, The University of New South Wales, Sydney, Australia
Venue:
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
Year:
2011

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Abstract

Approximate propositional logics provide a response to the intractability of classical inference for the modelling and construction of resource-bounded agents. They allow the degree of logical soundness (or completeness) to be balanced against the agent's resource limitations. We develop a logical semantics, based on a restriction to Finger's logics of limited bivalence [5], and establish the adequacy of a clausal tableau based proof theory with respect to this semantics. This system is shown to characterise DPLL with restricted branching, providing a clear path for the adaptation of DPLL-based satisfiability solvers to approximate reasoning. Furthermore it provides insights into the traditional notion of problem hardness, as we show that the parameter set of these logics correspond to the strong backdoor for an unsatisfiable problem.