Remarks on ACCAT
(Applied and Computational Category Theory)

ACCAT was the name of a working group established during my time at RISC-Linz, Univ. Linz (1990 - 1996). The origins were two courses, given in the frame of the RISC-Linz curriculum: "Categories, Fiberings, Sheaves, and Topoi" ; "Computational Category Theory (with ML)".
CAT abbreviates Category Theory and since I was always interested in applications and in computational aspects I introduced the title Applied and Computational Category Theory (ACCAT), this reflects what I am finally interested in.
For more information on the Origins of ACCAT we refer to ACCAT Origins.

In 2006, I organized the First ACCAT Workshop jointly with Hartmut Ehrig and his group (TU Berlin) as a Satellite Event at the European Joint Conferences on Theory and Practice of Software, ETAPS-2006, March 25 - April 2, 2006, Vienna, Austria.
It can be considered as an successful event and was the starting point of a series of ACCAT Workshops.
Actually, it was Hartmut Ehrig who proposed to organize such workshops in the framework of ETAPS conferences.
2nd ACCAT Workshop at ETAPS-2007, March 24 - April 1, 2007, Braga, Portugal.
3rd ACCAT Workshop at ETAPS-2008, March 29 - April 6, 2008, Budapest, Hungary.
4th ACCAT Workshop at ETAPS-2009, March 22-29, 2009, in York, England.
The 5th ACCAT Workshop is already scheduled, cf. 5th ACCAT Workshop at ETAPS-2010.
(There one can read the aim and motivation of our joint workshop since its beginning).

ACCAT Tutorial: It is available as .pdf file - ACCAT-Tutorial.pdf
and is under continuous development (from time to time a new version will be available).

At request of a working group of Professor Wilfried Brauer (Informatik, TU Munich), in September 1997, I held an ACCAT Tutorial for the first time.
In the year 2004, I had the opportunity to present a new and updated version of an ACCAT Tutorial at an own Workshop (WS12) at 27th German Conference on Artificial Intelligence (KI-2004), September 24, 2004, University of Ulm, cf. ACCAT-KI-2004.

My colleague Hartmut Ehrig, TU Berlin, read the tutorial and made the proposal to organize a joint ACCAT Workshop as a Satellite Event at ETAPS-2006. This was accepted by ETAPS.
As it turned out at the end of that workshop there was enough interest to continue to organize ACCAT Workshops, as previously mentioned.

Prof.Hartmut Ehrig and his Group work on very interesting topics using notions and methods from CAT, among others, dealing with Software Science and Development.
From his extensive literature list I am pointing here to the very interesting foundational book
H.Ehrig,K.Ehrig,U.Prange,G.Taentzer: "Fundamentals of Algebraic Graph Transformation",
Springer-Verlag Berlin Heidelberg, 2006.

In my basic undergraduate course "Formale Systeme", offered every year here at the Department of Computer Sciences, University of Salzburg (cf. Formale Systeme Course), the first chapter deals with the basic notation and notions of mappings on sets, leading to the category SET. In this way it is possible to explain very smoothly to undergraduate students the elementary axioms of the notion of a category (Cat). In the past, some students showed their interest in hearing about CATs, this was the motivation for offering a two semesters course entitled ACCAT here, for the first time in 2000/2001. More details follow below.

Remarks on ACCAT and Network Structure Modeling and Theoretical Neurobiology

In December 2002, I obtained an invitation to give a plenary lecture at "International Conference on Theoretical Neurobiology", February 24 - 26, New Delhi, India.
Organized by National Brain Research Centre, India.
The talk I intended to present there had the title "Modeling Connectionist networks: Categorical, Geometric Aspects (towards 'Homomorphic Learning')".
I could not attend this conference, but I was invited to give a talk on this topic (same title) at the International Conference on Computing Anticipatory Systems CASYS'2003, Liège, Belgium, August 11-16, 2003. This contribution received a Best Paper Award, cf. ACCAT and Neural Networks.
Cf. also the abstract of a talk given at our 2nd ACCAT Workshop at ETAPS-2007:
ACCAT and Theoretical Neurobiology.

Further information about the New Delhi Conference on Theoretical Neurobiology follows.
Scope of the Conference:
Algebra, Geometry, and Logic of Cognition. Artificial and Natural Intelligence. Cognitive Neuroscience. Computational Neuroscience. Dynamical Systems Theory. Functional Imaging of Brain. Neural Correlates of Consciousness. Neural Networks. Neuroinformatics. Neuropsychiatric Disorders.
Aims of the Conference:
The main aim of the conference is to facilitate development of theoretical tools and methodology required to further our understanding of the brain. Towards this end, the organizers invite papers discussing experimental results that pose a challenge to current conceptualisations of brain function or call for better theoretical frameworks as well as critical analyses of present-day modelling strategies highlighting their limitations, in-depth examination of outstanding problems, and introduction of novel mathematical methods to elucidate the workings of the brain. One of the main goals of the conference is to provide a platform for experimental and computational neuroscientists to closely interact and exchange ideas with mathematicians working in the areas of category theory and higher dimensional algebra and explore the potential of these sophisticated mathematical methods, in view of their success in solving problems hitherto intractable within the point set theoretic framework, to meet the demands of cognitive neuroscience data. These interactions will also inspire mathematicians to develop new formal tools and techniques tailor-made to suit the unique nature of the brain and thereby accelerate the development of a comprehensive theory of brain function that provides a scientific account of not only photons and action potentials but also of percept, thoughts, emotions, intention, and action.

Remarks on Mathematical Modeling of Multiagent Systems (MAS)

A few years ago, I started some work on mathematical modeling in the wide area of Multiagent Systems (MAS). As a first step I introduced a general (generic) mathematical model of a MAS using Category Theory (CAT)as a unifying mathematical modeling language. This work belongs to ACCAT topics, cf. our ACCAT activities in own ACCAT Workshops at ETAPS Conferences ACCAT Workshop, ETAPS-2009.
First steps on CAT modeling in MAS and a logical modeling approach using Logical Fiberings (LogFib) are briefly presented in CAT and LogFib modeling in MAS.

In more recent work, I introduced the notion of a Base Diagram of a MAS, it represents the General Communication Structure of a MAS in terms of an associated arrow diagram. We note that every arrow diagram can itself be interpreted as a category.
For more details cf. Base Diagram of a MAS.

Further remarks and comments can be found in MAS and ROBOTICS .

Concluding this section, we refer to On General Mathematical Modeling Aspects.