Topological Aspects of Matrix Abduction 1

A new method of abduction, matrix abduction, has been introduced in Abraham, M., Gabbay, D., Schild, U.: Talmudic argumentum a fortiori inference rule (Kal Vachomer) using matrix abduction. Studia Logica 92(3), 281–364 (2009). This method describes the Kal Vachomer and the Binyan Abh rules by using microscopic parameters which exist in the inputs of these rules. In order to find these parameters the method needs to calculate the minimal number of parameters that will describe the logical rule. In the current chapter, the matrix abduction method is formulated by Partially Orderd Sets (Posets). Consequently it is shown that the minimal number of parameters similarly defined to the dimension and k-dimension of Posets and a new poset dimension is defined which is the Kal Vachomer Dimension. In addition, several theorems and bounds of this dimension are shown.