# IEEE Systems, Man and Cybernetics Magazine - July 2018 - 22

```where Connection consists of the following conditions:
OnLeft (Left, Central)
OnLeft (Central, Right)
Below (Central, Top)
Below (Bottom, Central)

OnLeft (Corners.c ul, Top)
OnLeft (Top, Corners.c ur)
OnLeft (Bottom, Corners.c lr)
OnLeft (Corners.c ll, Bottom).

Algebra of Pattern Operators
The operators on patterns obey a set of algebraic laws,
which can be proven from the definitions of the operators. Figure 4 shows some of the complete set of laws in
[8]. Using laws like this, we can simplify pattern expressions to prove that two patterns are equivalent or that
one is a subpattern of another. One example is that for all
patterns P that contain variable X of power set type
P (T) , we have
P ^ X 0 x h = P 6| X | = 1@ .
Such reasoning about patterns has been proven to be
very useful for software design [8], [9]. For example, we
can define VL patterns as a lift of vertical two, similar to
the way an HL pattern is defined, and then prove that
this definition is equivalent to how we have defined VL
in the previous subsection. In general, any pattern expression can be transformed into a unique normal form
using the complete set of algebraic laws given in [8].
Therefore, the equivalence between two pattern expressions can be deduced by logic inferences of the equivalence of their normal forms using the axioms of the
subject domain with a logic inference engine like SPASS,
as shown in [8] and [9].

offers such a platform for thousands of computer scientists
to contribute to the construction of knowledge about
cyberspace, an activity we have only just started. The first
step toward this will be a common pattern-specification
language that is suitable for all subject domains. This is
what we are working on at the moment.
Hong Zhu (hzhu@brookes.ac.uk) earned his B.Sc., M.Sc.,
and Ph.D. degrees in computer science from Nanjing University, China, in 1982, 1984, and 1987, respectively. He is
a professor of computer science at the Oxford Brookes
University, United Kingdom, where he chairs the Applied
Formal Methods Research Group. He is a Senior Member of
the IEEE, British Computer Society, and Association for
Computing Machinery.
Ian Bayley (ibayley@brookes.ac.uk) earned his M.Eng.
degree in computing from Imperial College, London, United
Kingdom, in 1997 and his D.Phil. degree in computing from
the University of Oxford, United Kingdom, in 2002. He was a
lecturer at Bournemouth University, United Kingdom, from
2002 and has been a lecturer at Oxford Brookes University,
United Kingdom, since 2005.
References
[1] L. G. Valiant, "Knowledge infusion: In pursuit of robustness in artificial intelligence," in Foundations of Software Technology and Theoretical Computer Science, R.
Hariharan, M. Mukund, and V. Vinay, Eds. Dagstuhl, Germany: Schloss Dagstuhl-Leibniz Center for Computer Science, 2008, pp. 415-422.
[2] Y. Shoham, "Why knowledge representation matters," Commun. ACM, vol. 59, no.
1, pp. 47-49, 2016.
[3] A. dAvila Garcez, T. R. Besold, L. de Raedt, P. Földiak, P. Hitzler, T. Icard,
K.-U. Kühnberger, L. C. Lamb, R. Miikkulainen, and D. L. Silver, "Neural-

Conclusion
Nobel laureate Ernest Rutherford once pointed out that
"all science is either physics or stamp collecting." By
physics, he meant clean, succinct principles that apply
to diverse phenomena. By stamp collecting, he was
referring to the act of cataloging and organizing large
sets of observations. Since patterns are reusable knowledge about recurring phenomena, we believe they form
a bridge from, as it were, stamp collecting to physics.
This is because pattern-oriented research methods not
only recognize, catalog, and organize observations but
also discover regularities, interrelationships, and interactions. Such knowledge is the mother of clean, succinct principles.
Rutherford also pointed out that "scientists are not
dependent on the ideas of a single man, but on the combined wisdom of thousands of men, all thinking of the
same problem, and each doing his little bit to add to the
great structure of knowledge which is gradually being
erected." The pattern-oriented research methodology

22

IEEE SyStEmS, man, & CybErnEtICS magazInE July 2 0 1 8

symbolic learning and reasoning: Contributions and challenges," in Proc. Workshop
Knowledge Representation and Reasoning: Integrating Symbolic and Neural
Approaches, 2015 Association for the Advancement of Artificial Intelligence Spring
Symp., 2015, pp. 18-21.
[4] L. Cao, "Data science: Challenges and directions," Commun. ACM, vol. 60, no. 8,
pp. 59-68, 2017.
[5] E. Gamma, R. Helm, R. Johnson, and J. Vlissides, Design Patterns: Elements of
[6] C. Blackwell and H. Zhu, Eds., CyberPatterns: Unifying Design Patterns
with Security Patterns and Attack Patterns. Cham, Switzerland: SpringerVerlag, 2014.
[7] C. Blackwell and H. Zhu, Eds., "Proceedings of the Third International Workshop
on Cyberpatterns: From big data to reusable knowledge," in Proc. IEEE 8th Int. Symp.
Service Oriented System Engineering, Apr. 2014, pp. 384-429.
[8] H. Zhu and I. Bayley, "An algebra of design patterns," ACM Trans. Software Eng.
Methodol., vol. 22, no. 3, 2013. doi: 10.1145/2491509.2491517.
[9] H. Zhu and I. Bayley, "On the composibility of design patterns," IEEE Trans. Softw.
Eng., vol. 41, no. 11, pp. 1138-1152, 2015.

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# Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - July 2018

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