LGPSolver - Solving Logic Grid Puzzles Automatically

Findings of the Association for Computational Linguistics: EMNLP 2020, pages 1118–1123 November 16 - 20, 2020. c⃝2020 Association for Computational Linguistics 1118 LGPSolver - Solving Logic Grid Puzzles Automatically Elgun Jabrayilzade Department of Computer Engineering Izmir Institute of Technology elgun1999@gmail.com Selma Tekir Department of Computer Engineering Izmir Institute of Technology selmatekir@iyte.edu.tr Abstract Logic grid puzzle (LGP) is a type of word problem where the task is to solve a problem in logic. Constraints for the problem are given in the form of textual clues. Once these clues are transformed into formal logic, a deductive reasoning process provides the solution. Solving logic grid puzzles in a fully automatic manner has been a challenge since a precise understanding of clues is necessary to develop the corresponding formal logic representation. To meet this challenge, we propose a solution that uses a DistilBERT-based classifier to clas- sify a clue into one of the predefined predi- cate types for logic grid puzzles. Another nov- elty of the proposed solution is the recognition of comparison structures in clues. By collect- ing comparative adjectives from existing dic- tionaries and utilizing a semantic framework to catch comparative quantifiers, the semantics of clues concerning comparison structures are better understood, ensuring conversion to cor- rect logic representation. Our approach solves logic grid puzzles in a fully automated man- ner with 100% accuracy on the given puzzle datasets and outperforms state-of-the-art solu- tions by a large margin. 1 Introduction Logic grid puzzle (LGP) is a type of word problem where the task is to solve a problem in logic. LGP can be on any domain. Constraints for an LGP are provided as textual clues. The precise understand- ing of these clues is crucial to correctly solve the puzzle because the representation of clues leads the logical reasoning process. Automatically solving any word problem paves the way for more equipped digital assistants that take textual commands. Both word algebra prob- lems and logic puzzles appear in admission tests such as the Graduate Record Exam (GRE). Thus, automation improves the understanding of these problems and can be used in the training of stu- dents. In the field of Natural Language Processing (NLP), semantic representations are improved day by day. State-of-the-art BERT (Devlin et al., 2019) representations have boosted performance in a wide variety of NLP tasks. The rising interest is on frameworks that combine neural network-driven representations with logic representations to rea- son about language and predict correct outputs for tasks such as natural language inference (NLI) (Li et al., 2019). Logic puzzle solving is a task that is considered in this direction, as well. LGPs are usually defined by a description and clues. The description part introduces categories and instances associated with each of them, and clues provide the definitions of constraints on the relationships between instances. The description can be represented by an N ×M matrix where N is the number of categories, and M is the number of instances of a category. The main rule of logic grid puzzles is …

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