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MTH110

Additional Tilomino Notation for Assignments

Ryerson University
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Table of Contents

Introduction and Page Guide

MTH110 assignments are based on Tilomino, a universe consisting of tiles of various sizes, shapes and colors, about which logical questions can be asked. Tilomino can be accessed by any Java enabled browser on any modern operating system.

Note that you will be expected to be able to answer questions on Tilomino in the midterm and final exams.

The sections on this page are in order. This means that in order to understand a specific section, you will need to read the sections that precede it.

Tilomino Notation

In some of the assignment questions you will be asked to translate statements to or from "Tilomino". By this, we mean that you may use any of the functions, logical connectives, and quantifiers defined in Tilomino. Alternatively you may use the standard logical symbols for connectives and quantifiers if you wish. However, if you wish to input a statement into Tilomino you must use the syntax of the Tilomino program.

Additional Tile Notation

Here is some additional notation for tiles that you will need for your assignments. This notation will not work on the version of Tilomino.

  1. Simple Notation for Unnamed Tiles
  2. If, in your assignments, you need to refer to a tile which does not have a name, you may reference it by (row, column), starting from (1,1) in the top left corner. For example, if you need to discuss the unnamed circle in the The World is Round world you can refer to it as (6,8).

    Remember: this notation is only for your assignment description and writeup. It will not work in Tilomino.

  3. Generalized Tile Notation
  4. In many of the assignment questions, you will only work on one world at a time, so simple tile notation (e.g. a, b, c, (6,8)) will be enough.

    However, in some of the questions we will need to discuss tiles in more than one world. This will be problematic because the same tile names (e.g. a, b, c) are used from one world to another even though tiles of the same name in different worlds are not the same. For example even though the All Here world has a large square called a in position (8,8) and the All Here Revisited world also has a large square called a in that same position, these two tiles are not the same, simply because they are in different worlds.

    Therefore, if we want to discuss a collection of tiles from different worlds, we need a more precise naming mechanism for tiles that not only names the tile that is being discussed but also the world containing this tile.

    The notation used is:

      [world:tile] which refers to a specific tile in a specific world.

    For example:

    For the earlier example above, [A:a] refers to tile a in the All Here world, whereas [H:a] refers to tile a in the All Here Revisited world.

    Remember: this notation is only for your assignment description and writeup. It will not work in Tilomino.

Set Notation and Sets

Set theory notation will be used throughout the assignments. The following notation will be used in the description of the assignments. You can (and should) use this notation in your assignment writeups, but you will not be able to use it with Tilomino.

For a general introduction to the set theory concepts needed to understand this section, please read section 5.1 of the Epp textbook pages 255 to 262.

  1. Set Notation for Tilomino Worlds
  2. A Tilomino world is really a set of tiles. Therefore we will use the name of a world to refer to the set of tiles in that world.
    For example, 2 = Two By Two = {a, b, c, (8,4)}

    Of course, worlds can also be defined using the generalized tile notation: For example, 2 = Two By Two = { [2:a], [2:b], [2:c], [2:(8,4)] }

    Remember: this notation is only for your assignment description and writeup. It will not work in Tilomino.

  3. Other Tilomino Sets
  4. In addition to the Tilomino worlds just described, some of the assignment questions will refer to the following sets:

    Remember: this notation is only for your assignment description and writeup. It will not work in Tilomino.

Functions and Relations

  1. Additional Functions
  2. The assignments may also refer to the following functions.

    Given any tile x and any w TILOMINOUNIVERSE, define

    For example: ROWOF(e,B)=7 and COLOF(e,B)=3 but ROWOF(e,2)=0 and COLOF(e,2)=0 because there is no e tile in world 2.

    Remember: this notation is only for your assignment description and writeup. It will not work in Tilomino.

  3. Additional Relations
  4. The assignments may also refer to the following relations:

    Remember: this notation is only for your assignment description and writeup. It will not work in Tilomino.


Maintained by Peter Danziger.
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Last modified Friday, 07-Oct-2005 09:51:47 EDT