lazyCoP 0.1

Michael Rawson & Giles Reger
University of Manchester, UK

Architecture

lazyCoP 0.1 is a connection-tableaux system for first-order logic with equality. It implements the lazy paramodulation calculus described in [Pas08], with some additional inferences such as "shortcut" strict rules and equality lemmas. The system implements well-known refinements of the predicate connection calculus, such as tautology elimination and strong regularity, and these are lifted to equalities where appropriate. The resulting system appears to be complete, but we make no theoretical claim one way or another.

The system was originally conceived to efficiently accommodate a machine-learned heuristic guidance system: this system is not yet guided in this way, but learned heuristics are intended for a future version.

Strategies

The system explores a tableaux-level search space using the classic A* informed-search algorithm. The (admissible) heuristic function is the number of open branches. Typical connection systems explore via some kind of iterative deepening: A* search is a necessity for future learned guidance, and is not as catastrophic in memory consumption as might be expected. No form of strategy scheduling is yet implemented and the system will run for the entire time allowed on all available cores.

Implementation

A finite tree of inference rules forms a search space. To expand a selected leaf node, the system traverses from root to leaf, applying each rule to a new empty tableau. Possible inferences from the resulting tableau are added to the leaf and the resulting nodes are enqueued. The system does not yet include a custom clausification routine: a recent build of Vampire is employed for this purpose. lazyCoP is implemented entirely in the Rust programming language, allowing tight control over memory allocation and layout while avoiding some classes of memory- and thread- safety bugs. The source code (likely to be incomplete and/or buggy up to and including the competition!) is available at:

    https://github.com/MichaelRawson/lazycop

Expected Competition Performance

Performance on problems without equality is hoped to be comparable with other connection systems, if slightly slower. Problems requiring a modest amount of equational reasoning (or problems requiring no equational reasoning but containing extraneous equality axioms) are not expected to perform well, but should not cause catastrophic blowup either. Pure-equality problems (such as UEQ) are not the intended domain and do not perform well, but the first author remains hopeful for At Least One Problem.

References

Pas08: Paskevitch A. (2008), Connection tableaux with lazy paramodulation, Journal of Automated Reasoning 40(2-3), pp.179-194, Springer.