Chair for Automata Theory of the Institute for Theoretical Computer Science, Faculty of Computer Science at TU Dresden


GF1- is a description logic which is defined as a restriction of the "First Guarded Fragment". The language itself, its complexity (PSPACE) and a satisfiability algorithm are described in [LutzSattlerTobies99]  (BibTeX).

Gost ("GF One Minus Satisfiability Tester") is a Lisp implementation of this algorithm. The implementation and some empirical results are presented in  [Hladik00]  (BibTeX).


The system consists of several files:

gost.lisp contains the tableau algorithm for testing satisfiability of a GF1- formula. gost-simplify.lisp contains auxiliary functions for syntactic preprocessing of a formula. Both files are contained in gost.tar.gz.

To run the "LWB" benchmark, you need the files contained in the file gost-lwb.tar.gz. The benchmark formulae themselves are slightly modified in order to make parsing and translation easier.

To run the "TANCS-QBF" benchmark, you need the file gost-tancs.tar.gz. Again, the syntax of the formulae is slightly modified.


If you want to run one of the benchmarks, download the appropriate tarfile, unpack it and load the corresponding benchmark file, gost-bench-lwb.lisp or gost-bench-tancs.lisp. Call (recomp) to compile the source files, then (bench) or (tbench) to run the benchmark. For LWB, the results are printed, for TANCS, they are written to the *outfile* specified in gost-bench-tancs.lisp.

If you want to test your own formulae, you need to compile and load gost.lisp and gost-simplify.lisp. After that, you can test a formula with (solve <formula>). If there is a model, a (list of) models is returned, otherwise NIL. The syntax of <formula> is described below. For formulae including quantifiers, there are several restrictions to obey, in particular the formulae have to be guarded, and there has to be a fixed grouping of the variables appearing in the guard, as described in the papers mentioned above.

Please make sure that you strictly follow the GF1- syntax, since Gost does not perform syntax checking, and using non-GF1- formulae may lead to strange results.


Formula PL syntax Gost syntax
Variables x_i  (? i)
Predicates P(x_i, x_j)  (P (? i) (? j))
Negation NOT phi  (:NOT <phi>)
Conjuncions phi AND psi  (:AND <phi> <psi>)
Disjunctions phi OR psi  (:OR <phi> <psi>)
Universal Quantification FORALL (x_i, ... , x_n, ) 
(G(x_i, ... ,  x_n, y_j, ... , y_m) -> phi (x_i, ... , x_n))
(:ALL ((? i) ... (? n)) 
(G (? i) ... (? j_n) (? j) ... (? m)) <phi>)
Existential Quantification SOME (x_i, ... , x_n) 
(G(x_i, ... , x_n, y_j, ... , y_m) AND phi (x_j, ... , x_n))
(:EX ((? i) ... (? n)) 
(G (? i) ... (? n) (? j) ... (? m)) <phi>)
"True" e.g. (phi OR (NOT phi)) (:TOP)

i, j, k etc are natural numbers.
phi and psi GF1- formulae, phi (x_i, ... x_n) is a formula with free variables x_i, ..., x_n.
G(...) is the guard predicate.


Copyright (C) 2000 by Lehr- und Forschunggebiet Theoretische Informatik
RWTH Aachen, 52056 Aachen, Germany
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