Automated Inference of Finite Unsatisfiability
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We present Infinox, an automated tool for analyzing first-order logic problems, aimed at showing finite unsatisfiability, i.e., the absence of models with finite domains. Finite satisfiability is not a decidable problem (only semi-decidable), which means that such a tool can never be complete. Nonetheless, our hope is that Infinox be a useful complement to finite model finders in practice. Infinox uses several different proof techniques for showing infinity of a set, each of which requires the identification of a function or a relation with particular properties. Infinox enumerates candidates to such functions and relations, and subsequently uses an automated theorem prover as a sub-procedure to try to prove the resulting proof obligations. We have evaluated Infinox on the relevant problems from the TPTP benchmark suite, and we are able to automatically show finite unsatisfiability for over 25% of these problems.
KeywordsFinite unsatisfiability Automated theorem proving Automated reasoning
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- 1.Benzmüller, C., Theiss, F., Paulson, L., Fietzke, A.: LEO-II—a cooperative automatic theorem prover for higher-order logic. In: Automated Reasoning, 4th International Joint Conference, IJCAR 2008, Sydney, Australia, 12–15 August, 2008, Proceedings. LNCS, vol. 5195, pp. 162–170. Springer (2008)Google Scholar
- 2.Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Universitext. Springer (2001)Google Scholar
- 4.Claessen, K., Sörensson, N.: New techniques that improve MACE-style model finding. In: Proc. of Workshop on Model Computation (MODEL) (2003)Google Scholar
- 5.Curry, H.B.: Foundations of Mathematical Logic. Courier Dover Publications (1977)Google Scholar
- 7.McCune, W.: Mace4 reference manual and guide. CoRR, cs.SC/0310055 (2003)Google Scholar
- 8.Roederer, A., Puzis, Y., Sutcliffe, G.: Divvy: an ATP meta-system based on axiom relevance ordering. In: CADE, pp. 157–162 (2009)Google Scholar
- 10.Sutcliffe, G.: The SZS ontologies for automated reasoning software. In: Rudnicki, P., Sutcliffe, G., Konev, B., Schmidt, R.A., Schulz, S. (eds.) LPAR Workshops. CEUR Workshop Proceedings, vol. 418. CEUR-WS.org (2008)
- 13.Vännännen, J.: A Short Course on Finite Model Theory. Department of Mathematics, University of Helsinki (2006)Google Scholar
- 14.Weidenbach, C., Brahm, U., Hillenbrand, T., Keen, E., Theobalt, C., Topić, D.: SPASS version 2.0. In: Voronkov, A. (ed.) Automated Deduction, CADE-18: 18th International Conference on Automated Deduction. Lecture Notes in Artificial Intelligence, vol. 2392, pp. 275–279. Springer, Copenhagen, Denmark (2002)Google Scholar