ACCAT   Workshop   at   KI-2004
27th German Conference on Artificial Intelligence


NOTA:   For recent developments wrt. ACCAT Workshops,   cf. the two Satellite Events at ETAPS-Conferences:

ACCAT Workshop ETAPS-2006,   ACCAT Workshop ETAPS-2007.



ACCAT   Workshop/Tutorial zur Konferenz KI-2004.
September 20 - 24 (2004),     Univ. Ulm, Germany.

TITLE:   WS 12     "Applied and Computational Category Theory"   (ACCAT)

        ORGANISER and Lecturer:     Jochen PFALZGRAF

DATE:       24   September,   2004

DEADLINE for Extended ABSTRACTS:       31 August,   2004     (send to Organiser)

REGISTRATION:     online registration.     Reduced price   (Frühbuchrabatt)   until August   20.


                                ****** PLEASE,   everybody who wants to attend,   CONTACT ME ! ******


IMPORTANT   NOTE:     Lecture notes of an ACCAT-Tutorial will be distributed at the workshop.
An Introductory Tutorial will be offered anyway by the organiser (J.Pfalzgraf),   its duration will depend on the number of active workshop contributions on Friday,   24 September.


SCHEDULE   -   ZEITPLAN   (Friday,   Sept. 24):
    10.00h                     Opening and Coffee
    11.00 - 12.30h       ACCAT - Tutorial
                    Lunch Break
    14.00h       ACCAT - Workshop/Tutorial       (15.30 - 16.00h     Coffee Break)
    END         ~ 17.30h



REMARKS   on the   WORKSHOP


Note:   CAT abbreviates category (theory)

Nachfolgend ist die geplante Veranstaltung beschrieben in Form eines Tutorials. Die einzelnen Punkte sind zur thematischen Orientierung des Workshops gedacht, aber nicht bindend. Der Workshop soll offen sein.   Der Umfang des Tutorials wird den lokalen Gegebenheiten flexibel angepasst.
    ACCAT-Tutorial Scriptum   as .pdf File:     ACCAT-Tutorial.pdf.


OBJECTIVE:
To offer a compact introduction to elementary notions in category theory. CAT is a powerful mathematical modeling language (containing universal construction principles) with a wide area of potential applications, especially in computer science and AI. The workshop will discuss aspects from theory and practice (applications).
Depending on participants and submissions, the meeting can offer a brief tutorial on ACCAT by the organiser.


MOTIVATION:
Introductory and motivating remarks: CAT provides a unifying formal (mathematical) language with constructive elements, of increasing importance in computer science and AI. The concept of a CAT, by its very nature, contains OO aspects. There are obvious trends in interdisciplinary modeling with CAT, algebra, geometry, topology, logic, as can be observed in activities and events, taking place in large areas like Neurobiology, Cognitive Sciences, Brain Research, Topological Psychology, Music Theory.
(Further motivating remarks and information:   Remarks on ACCAT ).


CONTENTS (of an extended tutorial   -   a guideline):
- Introduction to basic notions and notation of category theory, examples.
- Implementational aspects (in ML syntax). Categorical description of LIST handling.
- Categorical modeling of general relational structures (with many examples); towards a general semantics for relations. Arrow diagrams interpreted categorically; in particular, this aspect applies to UML diagrams.
- Example: Categorical treatment of forming the greatest common divisor and least common multiple as (co-)limit constructions (the universal property).
- Remarks on the textbook Bird/de Moor: Algebra of Programming (published by Prentice Hall, 1997).
- Towards a generic CAT based model for multiagent systems (MAS).
- Report on two doctoral theses dealing with CATs to solve open problems of relevance in computer science (former PhD students in my ACCAT group at RISC-Linz).
- Petri Nets in a CAT environment: Morphisms, Reductions, and Simulation   [cf. Girault/Valk: "Petri Nets for Systems Engineering"].
- Remarks on a CAT based structure modeling in connectionist networks and towards a therory of "homomorphic learning". An industrially relevant application of CAT based modeling in simulation of neural networks (hints to the Salzburg "FlexSimTool").
- New trends in interdisciplinary modeling with   CAT, Algebra, Geometry, Topology, Logic   (cf. On General Mathematical Modeling Aspects),     e.g. in   Neurobiology, Cognition, Brain Research, Topological Psychology (cf. Topology), Music Theory (cf. EncycloSpace).


Some LITERATURE Hints:
Renowned classical textbook by one of the inventors of CAT theory:
- Saunders Mac Lane: Categories for the Working Mathematician (2nd ed.). (Springer Graduate Texts in Mathematics, Vol.5, 1998)
- Lawvere/Schanuel: Conceptual Mathematics. A first introduction to categories. (Cambridge University Press, 2000)
- Rydeheard/Burstall: Computational Category Theory. (Prentice Hall, 1988)
- Adamek/Herrlich/Strecker: Abstract and Concrete Categories. (J.Wiley Interscience, 1990)
- Goldblatt: TOPOI. The categorical analysis of logic. (North-Holland, 1986)
- Pierce: Basic Category Theory for Computer Scientists. (The MIT Press, 1991)
- Mazzola: The Topos of Music. (Birkhäuser Verlag, 2002)
- Pfalzgraf: ACCAT Tutorial, held at TU Munich, Sept. 3-5, 1997.
ACCAT lecture notes, worked out with details, exist as material for a two semester course.
- Pfalzgraf: Modeling connectionist network structures: some geometric and categorical aspects. (Annals of Math. and AI, 36 (2002),pp.279-301)
- Pfalzgraf: Modeling Connectionist Networks: Categorical, Geometric Aspects (Towards "Homomorphic Learning").
Presentation at CASYS'2003, Li`ege, Belgium, Aug.2003.   Received a Best Paper Award.
In:   CASYS'2003, AIP Proceedings,   Vol. 718 (2004), D.M.Dubois (Ed.),   American Institute of Physics, 2004.


NOTE:     Further information of relevance, cf.   Remarks on ACCAT (applied and computational category theory)
On General Mathematical Modeling Aspects. Mathematical Informatics.