Abstract
This work extends the existing MACE-style finite model finding approach to multi-sorted first-order logic. This existing approach iteratively assumes increasing domain sizes and encodes the related ground problem as a SAT problem. When moving to the multi-sorted setting each sort may have a different domain size, leading to an explosion in the search space. This paper focusses on methods to tame that search space. The key approach adds additional information to the SAT encoding to suggest which domains should be grown. Evaluation of an implementation of techniques in the Vampire theorem prover shows that they dramatically reduce the search space and that this is an effective approach to find finite models in multi-sorted first-order logic.
This work was supported by EPSRC grant EP/K032674/1. Martin Suda and Andrei Voronkov were partially supported by ERC Starting Grant 2014 SYMCAR 639270. Andrei Voronkov was also partially supported by the Wallenberg Academy Fellowship 2014 - TheProSE.
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References
Barrett, C., Stump, A., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB) (2010). http://www.SMT-LIB.org
Blanchette, J.C., Böhme, S., Popescu, A., Smallbone, N.: Encoding monomorphic and polymorphic types. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013 (ETAPS 2013). LNCS, vol. 7795, pp. 493–507. Springer, Heidelberg (2013)
Claessen, K., Lillieström, A.: Automated inference of finite unsatisfiability. J. Autom. Reasoning 47(2), 111–132 (2011)
Claessen, K., Lillieström, A., Smallbone, N.: Sort it out with monotonicity. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 207–221. Springer, Heidelberg (2011)
Claessen, K., Sörensson, N.: New techniques that improve MACE-style model finding. In: CADE-19 Workshop: Model Computation - Principles, Algorithms and Applications (2003)
Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005)
Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)
Hoder, K., Kovács, L., Voronkov, A.: Case studies on invariant generation using a saturation theorem prover. In: Batyrshin, I., Sidorov, G. (eds.) MICAI 2011, Part I. LNCS, vol. 7094, pp. 1–15. Springer, Heidelberg (2011)
Korovin, K.: iProver – an instantiation-based theorem prover for first-order logic (System Description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 292–298. Springer, Heidelberg (2008)
Kovács, L., Voronkov, A.: First-order theorem proving and vampire. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 1–35. Springer, Heidelberg (2013)
Mccune, W.: A Davis-Putnam Program and its Application to Finite First-Order Model Search: Quasigroup Existence Problems. Technical report, Argonne National Laboratory (1994)
Reynolds, A., Tinelli, C., Goel, A., Krstić, S.: Finite model finding in SMT. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 640–655. Springer, Heidelberg (2013)
Schulz, S.: A comparison of different techniques for grounding near-propositional CNF formulae. In: Proceedings of the Fifteenth International Florida Artificial Intelligence Research Society Conference, May 14–16, 2002, Pensacola Beach, Florida, USA, pp. 72–76 (2002)
Stump, A., Sutcliffe, G., Tinelli, C.: StarExec, a cross community logic solving service (2012). https://www.starexec.org
Sutcliffe, G.: The TPTP problem library and associated infrastructure. J. Autom. Reasoning 43(4), 337–362 (2009)
Tammet, T.: Reasoning. Gandalf. J. Autom 18(2), 199–204 (1997)
Zhang, J., Zhang, H.: SEM: a system for enumerating models. In: Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence, IJCAI 95, Montréal Québec, Canada, August 20–25 1995, vol. 2s, pp. 298–303 (1995)
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Reger, G., Suda, M., Voronkov, A. (2016). Finding Finite Models in Multi-sorted First-Order Logic. In: Creignou, N., Le Berre, D. (eds) Theory and Applications of Satisfiability Testing – SAT 2016. SAT 2016. Lecture Notes in Computer Science(), vol 9710. Springer, Cham. https://doi.org/10.1007/978-3-319-40970-2_20
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