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.