VL1(ID:7327/vl1001)

Picture representation by variable vlaued logic 

for Variable-valued Logic One (written VL1)

Picture representation system by Michalski, 1972 Warsaw and then Illinois


A variable-valued logic system (a VL system) is an ordered quintuple:
     (X,H,S,Rf,RI)
where:
  • X is a finite non-empty (f.n.) set of input variables, whose domains are any f. n. sets, called input name sets
  • H is a f.n. set, called output name set,
  • S is a f.n. set of improper symbols,
  • RF is a f.n. set of formation rules which define well-formed formulas (wffs) in the VL System (or VL formulas). A string of elements from X, H, or S is a wff if and only if it can be derived from a finite number of applications of the formation rules.
  • RI is a f.n. set of interpretation rule which give an interpretation to the VL formulas.


VL1 is a VL system with improper symbols that represent graphical subcomponent relations
References:
  • Michalski, Ryszard S. "A variable-valued logic system as applied to picture description and recognition and recognition" view details Abstract: Abstract: The paper introduces a concept of a variable-valued logic system, defines  a particular system VLl and demonstrates, by examples, its application as a language for describing complex graphical objects and also as a tool for making inferences about significant properties of the objects or classes of objects. (Included examples show how to use the system to describe a picture
    treated as a structure of interrelated components, to deduce a simple rule characterizing one class of patterns as opposed to another and to synthesize a minimal set of filters for the discrimination of a collection of textures.) A brief summary of the computer implementations of the developed concepts is also included
          in Nake, F. and Rosenfeld, A. "Graphic Languages" Amsterdam: North-Holland Publishing Company 1972. view details