Blocks-World Ontology

A Working Draft

Preliminary Remarks

1. In philosophy, "ontology" is the study of the nature of existence and the kinds of things that exist.

2. In AI, "an ontology" is a theory(?) specifying the things that there are in some domain, together with their properties and relationships.

3. In my view, an ontology is the semantic domain that some syntactic domain "talks about" or represents.

4. What follows is an ontology for a blocks world inspired by:
   • Winograd's blocks world in his Understanding Natural Language (1972)
   • the classic blocks world of AI planning
   • Barwise & Etchemendy's domain as originally presented in their "Tarski's World" and most recently in their Language, Proof, and Logic.

The blocks world consists of the following objects:

• a table, upon which all else can rest.
  • Things can be "off" the table, as well as "on" it.

  • The table is divided into (say) a 10x10 checkerboard, and each other object, when on the table, is on one of the squares of this board.
    • Each row and column is identified by a positive integer (1..10), and each square by the ordered pair of its (column,row)--or is this syntax, not ontology?

• 3-dimensional geometric solids, each of which is a block:
  • (minimal version):
    • cubes
    • dodecahedrons
    • tetrahedrons

  • (maximal, or Platonic-solids, version):
    • cube
    • dodecahedron
    • icosahedron
    • octahedron
    • tetrahedron

Each object (including the table?) has the following properties:

• color
  • red, blue, green (others?)

• label
  • A..Z, possibly with subscripts?

• size
  • big, small, medium(?)

and can stand in the following relations:

• smaller, larger, left-of, right-of, back-of, front-of, adjacent, next-to, on, under, above, below

• between

There can be functions:

• color-of, label-of, size-of