[Solomonov Seminar] 53. Solomonov seminar

[Marko Grobelnik]

Vabim vas na 53. Solomonov seminar, ki bo
IZJEMOMA (!!!) v ponedeljek (24.9.2001) 
ob 11h v fizikalnem seminarju IJS (glavna stavba IJS, levo).
Seminarju bo sledila ob 14h dvourna delavnica, kjer bo
tematika predstavljena nekoliko obsirneje in podrobneje. 
Za udelezbo na delavnici bi prosil, da mi posljeto prijavo (email).

Na tokratnem seminarju bomo gostili prof. Luisa Pinedo
iz Mehike, ki se ukvarja s t.i. "sklepanjem z diagrami".
Diagramatic reasoning je sklepanje na osnovi diagramov,
dokaj novo, majhno in sveze podrocje v UI. Gre za to, da
npr. izrek dokazes vizualno, s sliko/risbo/diagramom,
namesto suhoparno z matematicnimi formulami. Najbolj
znani primeri so elegantni dokazi Evklidovega izreka
z diagramom, ko clovek takoj VIDI, da izrek drzi, namesto
dolgovezne formalne izpeljave. Taki diagramatski dokazi 
navadno ne veljajo kot matematicni dokazi in so koristni le kot
intuitivna ilustracija. Vcasih pa imajo celo veljavo v najstrozjem
matematicnem pomenu. Vprasanje je kdaj? Vprasanje je tudi, kako
to realizirati racunalnisko? S temi se ukvarja Pineda.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Abstraction, Visualization and Graphical Proof
                             Luis A. Pineda (National Univ. of Mexico)

In  this  workshop  we  explore the  representational  properties  and
inferential  processes  involved  in  diagrammatic  proofs  and  valid
graphical  reasoning  schemes. As  an  antecedent,  the properties  of
analogical  and  propositional  knowledge  representation schemes  are
reviewed, and a brief  introduction to the imagery debate of cognitive
psychology  and AI  is presented.  Then, the properties  of analogical
representations are  reviewed from the perspective  of standard Turing
Machines and, following the  architecture of the Whisper System (Funt,
1980), the  structure of a "Diagrammatic  Turing Machine" is proposed.
We  also review the  notion of  interpretation change in  ambiguous of
pictures.

Next, we explore whether diagrams can express abstract information. We
present  and  discuss  the  theory  of  the  Specificity  of  Graphics
(Stenning and Oberlander, 1995)  in which representational systems are
classified  as   MARS,  LARS  or  UARS,   according  to  the  kind  of
abstractions they are able to express (Minimal, Limited and Unlimited,
respectively). S&O argue that diagrams are LARS and can be interpreted
effectively with limited  computational resources. However, we observe
that diagrams need to be able to express full abstractions if theorems
and proofs  can be diagrammatical at all!  To address this concern, we
propose an  alternative for  S&O theory. We  introduce the notions  of
universal key  and  Diagrammatic Unlimited  Abstraction Representation
Systems  (DUARS).  Universal keys  are  general  statements about  the
notation of a representational  system and DUARS permit the expression
of  theorems to  diagrams. The  theory is  applied to  the study  of a
diagrammatic  proof of  the  theorem of  the sum  of the  first  n odd
numbers.

Finally,  we study  the relation  between the diagrammatic  proofs and
learning,  and we proposed  a reasoning  scheme in which  theorems are
induced out  of the  basic notation of a  representational systems and
the  properties of  the  representational medium.  We apply  the final
theory  to understand a  purely diagrammatic  proof of the  Theorem of
Pythagoras.