Teaching Modal Logic from the Linear Algebraic Viewpoint.

This paper proposes a linear algebraic approach to teach modal logic to stu- dents who might not be familiar with first-order logic. Our approach is based on Fitting’s linear algebraic reformulation of Kripke semantics of modal logic. A key idea of his reformulation is to represent an accessibility relation R by a square matrix and a valuation V (p) of an atomic variable p by a column vector. Then, we may calculate the truth set of 3p as the multiplication of the square matrix R for the accessibility relation and the column vector for p. Hence, we can regard such matrix calculation as an extended version of truth table calcu- lation. We discuss how our reformulation is useful to teach modal logic to our target students before teaching first-order logic. In addition, we present our supporting software to avoid involved calculations on matrices and explain how we can use it for educational purposes.

Authors

• Ryo Hatano
• Katsuhiko Sano
• Satoshi Tojo

Keywords

• Modal logic
• Linear Algebra
• Quantification
• First-order logic