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An Ontology-Based Kinematics Problem Solver Using Qualitative and Quantitative Knowledge

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Abstract

One of the major tasks involved in the development of a knowledge-based problem solver is domain knowledge representation and reasoning. In this paper, we address this task for a knowledge-based kinematics word problem solver that solves problems from the domain of kinematics automatically, where solving each problem involves identifying the value of a specific unknown quantity referred to, within the problem. Knowledge about kinematics domain is captured at two levels: quantitative level and a more abstract qualitative level. We leverage OWL (Web Ontology Language) and RDF (Resource Description Framework) rules to represent both qualitative and quantitative knowledge of the domain in a single framework. We build an ontology, wherein we identify a fixed number of classes and properties that provide a vocabulary to formally represent a domain qualitatively and quantitatively. We then define the kinematics domain in terms of these classes and properties using RDF rules and OWL axioms. This is then used as a knowledge base (KB) to a kinematics problem solver. The input to this solver is represented as an RDF graph, called the problem scenario graph. Inference based on the OWL axioms and RDF rules in the KB adds knowledge, that is required to solve the problem, to the problem scenario graph. The knowledge enriched problem scenario graph is then used by an external reasoner to infer the value of the unknown quantity in the problem. We created a dataset of around 100 problems from the domain to provide a qualitative analysis of the solver by describing the various failure modes with examples.

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Notes

  1. These are axioms of the form: if the current value of a parameter is [0,0] and the value of the parameter is increasing, then its next possible value is (0, inf). Since the landmark values in a parameter’s quantity space are in ascending order, an increase (decrease) in the parameter will result in shifting right (left) from the current value in the quantity space.

  2. https://jena.apache.org/documentation/inference/#rules

  3. It may be noted that angle of projection being 0 always does not mean straight line motion—for example, a ball projected horizontally from a height has motion in vertical and horizontal dimensions.

  4. http://protege.stanford.edu/.

  5. http://www.solvephysics.com, http://www.physicsclassroom.com, http://www.real-world-physics-problems.com/.

  6. https://schools.aglasem.com/15578.

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  1. Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India

    Savitha Sam Abraham & Sowmya S. Sundaram

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  1. Savitha Sam Abraham
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  2. Sowmya S. Sundaram
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Correspondence to Savitha Sam Abraham.

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Abraham, S.S., Sundaram, S.S. An Ontology-Based Kinematics Problem Solver Using Qualitative and Quantitative Knowledge. New Gener. Comput. 37, 551–584 (2019). https://doi.org/10.1007/s00354-019-00067-x

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