[en] 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.
Disciplines :
Computer science
Author, co-author :
Laufer, Azriel
Gabbay, Dov M. ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
External co-authors :
yes
Language :
English
Title :
Topological Aspects of Matrix Abduction 1
Publication date :
2015
Main work title :
The Road to Universal Logic: Festschrift for the 50th Birthday of Jean-Yves Béziau Volume II
Editor :
Koslow, Arnold
Buchsbaum, Arthur
Publisher :
Springer International Publishing, Cham, Unknown/unspecified
Abraham, M., Gabbay, D., Schild, U.: Analysis of the Talmudic argumentum a fortiori inference rule (Kal Vachomer) using matrix abduction. Stud. Log. 92(3), 281–364 (2009)
Anderson, I.: Combinatorics of Finite Sets. Clarendon Press, Oxford University Press, Oxford (1987)
Ben-Adar Bessos, M.: Improving the practical ability to perform matrix abduction. Research proposal for Master degree. Department of Computer Science, Bar Ilan University (2013)
