MEREOLOGY
Mereology, i.e. ‘theory of parts’ is a substantial
element of every design
process, but the standard mathematics lacks the strong formal concept of being a
“part of”. Classical mereologies of (Leśniewski 1916-37) or (Leonard-Goodman
1930-50) work nicely in philosophy and cognitive sciences but they are difficult
to fit to applications in science and engineering. Leśniewski’s systems are
different from the standard set theory, Leonard and Goodman's
model is too rigid
for most of
the
potential science and engineering applications.
This topic is currently dormant, but it can awaken anytime, especially is
potential grad students would be interested in. There is a lot of potential
applications in software engineering were ‘building a whole from parts’ is a
fundamental paradigm
which still lacks solid theoretical foundations.
LIST OF PUBLICATIONS - MEREOLOGY
2008
D.T.M. Le,
R. Janicki, A Categorical Approach to Mereology and Its Application to
Modelling Software Components,
Transactions on Rough Sets 8 (2008), 146-174.
2007
R. Janicki, D.T.M. Le, Towards a Pragmatic Mereology,
Fundamenta Informaticae
75, 1– 4 (2007), 295-314.
2006
D.T.M. Le, R. Janicki, On a Parthood
Specification Method for Component Software, Proc. of RSCTC’2006
(Rough Sets and Current Trends in Computing), Lecture Notes in Artificial
Intelligence 4259, Springer 2006, 537-546
2004
R. Janicki, Y. Zhai, On Properties of “Part of” Relations, Proc. of SERP’2004 (Software Engineering Research and Practice), Las Vegas, USA, 2004, 1pp. 393-399.
2002
R. Janicki, Remarks on Mereology of Direct Product and Relations,
In J. Desharnais, M. Frappier, W. MacCaull (eds.)
Relational Methods in Computer Science, Methodos Publ. 2002, pp.
65-84.
2000
R. Janicki, R. Khédri, On Mereology of Relation Algebras, Proc. of
RelMiCS'2000 (Relational Methods
in Computer Science), Quebec City, Canada, 2000, pp. 133-140.