A Semantic Web-based Representation of Human-logical Inference for Solving Bongard Problems

Abstract

Bongard Problems (BPs) are a set of 100 visual puzzles introduced by M. M. Bongard in the mid-1960s. BPs have been established as benchmark puzzles for understanding the human context-based learning abilities to solve ill- posed problems. The puzzle requires the logical explanation as the answer to distinct two classes of figures from redundant options, which can be obtained by a thinking process to alternatively change the target frame (hierarchical level of analogy) of thinking from a wide range concept networks as D. R. Hofstadter suggested. Some minor research results to solve a limited set of BPs have reported based a single architecture accompanied with probabilistic approaches; however the central problem on BP's difficulties is the requirement of flexible changes of the target frame, therefore non-hierarchical cluster analyses does not provide the essential solution and hierarchical probabilistic models needs to include unnecessary levels for learning from the beginning to prevent a prompt decision making. We hypothesized that logical reasoning process with limited numbers of meta-data descriptions realizes the sophisticated and prompt decision-making and the performance is validated by using BPs. In this study, a semantic web-based hierarchical model to solve BPs was proposed as the minimum and transparent system to mimic human-logical inference process in solving of BPs by using the Description Logic (DL) with assertions on concepts (TBox) and individuals (ABox). Our results demonstrated that the proposed model not only provided individual solutions as a BP solver, but also proved the correctness of Hofstadter's idea as the flexible frame with concept networks for BPs in our actual implementation, which no one has ever achieved. This fact will open the new horizon for theories for designing of logical reasoning systems especially for critical judgments and serious decision-making as expert humans do in a transparent and descriptive way of why they judged in that manner.

Keywords

• Bongard problem (BPs)
• meta-data ontology
• resourc