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Paraconsistency and word puzzles

  • TIANTIAN GAO (a1), PAUL FODOR (a1) and MICHAEL KIFER (a1)

Abstract

Word puzzles and the problem of their representations in logic languages have received considerable attention in the last decade (Ponnuru et al. 2004; Shapiro 2011; Baral and Dzifcak 2012; Schwitter 2013). Of special interest is the problem of generating such representations directly from natural language (NL) or controlled natural language (CNL). An interesting variation of this problem, and to the best of our knowledge, scarcely explored variation in this context, is when the input information is inconsistent. In such situations, the existing encodings of word puzzles produce inconsistent representations and break down. In this paper, we bring the well-known type of paraconsistent logics, called Annotated Predicate Calculus (APC) (Kifer and Lozinskii 1992), to bear on the problem. We introduce a new kind of non-monotonic semantics for APC, called consistency preferred stable models and argue that it makes APC into a suitable platform for dealing with inconsistency in word puzzles and, more generally, in NL sentences. We also devise a number of general principles to help the user choose among the different representations of NL sentences, which might seem equivalent but, in fact, behave differently when inconsistent information is taken into account. These principles can be incorporated into existing CNL translators, such as Attempto Controlled English (ACE) (Fuchs et al. 2008) and PENG Light (White and Schwitter 2009). Finally, we show that APC with the consistency preferred stable model semantics can be equivalently embedded in ASP with preferences over stable models, and we use this embedding to implement this version of APC in Clingo (Gebser et al. 2011) and its Asprin add-on (Brewka et al. 2015).

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Baral, C. and Dzifcak, J. 2012. Solving puzzles described in English by automated translation to answer set programming and learning how to do that translation. In Principles of Knowledge Representation and Reasoning: Proceedings of the Thirteenth International Conference, KR 2012, Rome, Italy, June 10-14, 2012. AAAI Press, Rome, Italy.
Belnap, N. D. Jr 1977. A useful four-valued logic. In Modern uses of multiple-valued logic. Springer, Volume 2, 537.
Blair, H. and Subrahmanian, V. 1989. Paraconsistent logic programming. Theoretical Computer Science 68, 135154.
Brewka, G., Delgrande, J. P., Romero, J. and Schaub, T. 2015. asprin: Customizing answer set preferences without a headache. In Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, January 25-30, 2015, Austin, Texas, USA. AAAI Press, Austin, Texas, 14671474.
C. Guéret, C. P. and Sevaux, M. 2000. Programmation linéaire - 65 problèmes d'optimisation modélisés et résolus avec Visual Xpress. Eyrolles, France. ISBN: 2-212-09202-4.
da Costa, N. 1974. On the theory of inconsistent formal systems. Notre Dame J. of Formal Logic 15, 4 (October), 497510.
Finkel, R. A., Marek, V. W. and Truszczynski, M. 2004. Constraint lingo: towards high-level constraint programming. Softw., Pract. Exper. 34, 15, 14811504.
Fuchs, N. E., Kaljurand, K. and Kuhn, T. 2008. Attempto controlled English for knowledge representation. In Reasoning Web, 4th International Summer School 2008, Venice, Italy, September 7-11, 2008, Tutorial Lectures, Lecture Notes in Computer Science, vol. 5224. Springer, Venice, Italy, 104124.
Gao, T., Fodor, P. and Kifer, M. 2016. Paraconsistency and Word Puzzles. ArXiv e-prints http://arxiv.org/abs/1608.01338, 1–30.
Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T. and Schneider, M. 2011. Potassco: The Potsdam answer set solving collection. AI Communications 24, 2, 107124.
Beziau, J. Y., Carnielli, W., D. M. G. 2007. Handbook of Paraconsistency (Studies in Logic). College Publications, United States.
Kifer, M. and Lozinskii, E. L. 1992. A logic for reasoning with inconsistency. J. Autom. Reasoning 9, 2, 179215.
Kifer, M. and Subrahmanian, V. S. 1992. Theory of generalized annotated logic programming and its applications. J. Log. Program. 12, 3&4, 335367.
Ponnuru, H., Finkel, R. A., Marek, V. W. and Truszczynski, M. 2004. Automatic generation of English-language steps in puzzle solving. In Proceedings of the International Conference on Artificial Intelligence, IC-AI '04, June 21-24, 2004, Las Vegas, Nevada, USA, Volume 1. CSREA Press, Las Vegas, Nevada, USA, 437442.
Priest, G., Tanaka, K. and Weber, Z. 2015. Paraconsistent logic. In The Stanford Encyclopedia of Philosophy, Spring 2015 ed., Zalta, E. N., Ed. Stanford, USA.
Schwitter, R. 2013. The Jobs Puzzle: Taking on the challenge via controlled natural language processing. Theory and Practice of Logic Programming 13, 4–5, 487501.
Shapiro, S. C. 2000. An introduction to sneps 3. In Conceptual Structures: Logical, Linguistic, and Computational Issues, 8th International Conference on Conceptual Structures, ICCS 2000, Darmstadt, Germany, August 14-18, 2000, Proceedings. Springer, Darmstadt, Germany, 510524.
Shapiro, S. C. 2011. The jobs puzzle: A challenge for logical expressibility and automated reasoning. In Logical Formalizations of Commonsense Reasoning, Papers from the 2011 AAAI Spring Symposium, California, USA, March 21-23, 2011. AAAI, Stanford, California, USA.
Soininen, T., Niemelä, I., Tiihonen, J. and Sulonen, R. 2001. Representing configuration knowledge with weight constraint rules. In Answer Set Programming, Towards Efficient and Scalable Knowledge Representation and Reasoning, Proceedings of the 1st Intl. ASP'01 Workshop, Stanford, March 26-28, 2001. Springer, Stanford, California, USA.
Syrjänen, T. and Niemelä, I. 2001. The Smodels system. In Logic Programming and Nonmonotonic Reasoning, 6th International Conference, LPNMR 2001, Vienna, Austria, September 17-19, 2001, Proceedings. Springer, Vienna, Austria, 434438.
White, C. and Schwitter, R. 2009. An update on PENG Light. In Proceedings of ALTA. Vol. 7. Springer, Sydney, Australia, 8088.
Wos, L., Overbeck, R., Lusk, E. and Boyle, J. 1984. Automated reasoning: Introduction and applications. Prentice Hall Inc., Old Tappan, NJ, United States.

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Paraconsistency and word puzzles

  • TIANTIAN GAO (a1), PAUL FODOR (a1) and MICHAEL KIFER (a1)

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