ICGNS 2002

W. McCune
Argonne National Laboratory, USA
mccune@mcs.anl.gov

Architecture

ICGNS 2002 [McC02] searches for finite models of first-order (unsorted, with equality) statements. Given input clauses, it generates ground instances over a finite domain, then uses a decision procedure try to determine satisfiability. If there is no model of that size, it increments the domain size and tries again.

The ICGNS method is SEM-like [ZZ95] rather than MACE-like [McC01]; that is, the ground problem is propositional/equality rather than flattened and purely propositional. The two main parts of the ICGNS method are (1) selecting the next empty cell in the tables of functions being constructed and deciding which values need to be considered for that cell, and (2) propagating assignments. ICGNS uses the basic least number heuristic (LNH) to reduce isomorphism. The LNH was introduced in Falcon [Zha96] and is also used in SEM. Effective use of the LNH requires careful cell selection. Propagation is by ground rewriting and inference rules to derive negated equalities.

Implementation

ICGNS 2002 is a new program, started in the winter of 2002. It uses some pre-existing code from various sources for some of the low level operations such as parsing and term structure. ICGNS is coded in ANSI C and should be easily portable to recent variants of UNIX. The source code and test problems are available at the following location.

http://www.mcs.anl.gov/home/mccune/icgns/

Strategies

Several strategies are available for cell selection and for applying the negative inference rules. A single strategy is used for CASC-18: (1) the LNH, selecting cells with the fewest number of possible values, and (2) applying all negative propagation inference rules. The strategy was derived by experimenting on problems that arose in mathematics practice, mostly in abstract algebra. No tuning to the TPTP set has been done.

Expected Competition Performance

ICGNS seems to do well on equational problems, especially if the input set contains some simple equations. Satisfiable problems without reasonably sized finite models (including problems without finite models) are out of reach of ICGNS. Some of those problems can be done by satisfiability methods that work by saturation with a complete inference system. It is doubtful that ICGNS will do as well, overall, as programs that try various methods and various strategies.

Thanks

Olga Shumsky Matlin and Michael Rose assisted in the development of ICNGS 2002.

References

McC01: McCune W. (2001), MACE 2.0 Reference Manual and Guide, Tech. Memo ANL/MCS-TM-249, Argonne National Laboratory.
McC02: McCune W. (2002), ICGNS, http://www.mcs.anl.gov/~mccune/icgns, Argonne National Laboratory.
Zha96: Zhang J. (1996), Constructing Finite Algebras with FALCON, Journal of Automate Reasoning 17(1), pp.1-22.
ZZ95: Zhang J., Zhang, H. (1995), SEM: A System for Enumerating Models, IJCAI-95, pp.298-303, Morgan Kaufmann.