You should now Launch Deriver and do the 3 exercises of Predicate Exercise 4 (Predex4).
In the Interpretation Panel...
Individuals are circles, properties are rectangles which may or may not surround a particular individual, and, later, we will come to relations which are lines which connect individuals.
If an individual is within a property rectangle; it is considered to have that property. If it is not, it does not. So if you have an individual 'a', and no property 'P' , then a is taken to lack P and so the formula Pa is false.
Formulas written in the Journal Panel are taken to be about the Interpretation Panel.
Try doing some drawing. Click on the circle in the palette, click on the point you want it in the window, move it slightly (to show your clicks are really intended), then release. This will leave you a little circle, probably with four blobs on it. The blobs mean that the individual is still selected. Selected items are not considered to be genuine parts of the drawing. Click down somewhere else in the drawing. This will stop the circle being selected, and thus add it. Up in the top left corner is a description of the drawing. You should see that the new entity is now part of the Universe.
If you wish to choose a name for the an entity that you add just type the constant term you want. Try this. Click on the circle in the palette, type lower case 'd', draw your circle. This will add 'd' to the Universe. If you do not wish to choose, the program will automatically choose names for the entities.
Try drawing some properties. Again if you want to give one a name just type the Predicate you want. Try this. Click on the square in the palette, type upper case 'K', draw a square around an existing circle. The drawing is constrained to be well presented.
An individual may or may not have a property. So you can draw (or move) individuals almost anywhere. But properties must apply to at least one individual-- you can draw a property around an individual, but not in empty space.
You can colour or shade your properties as you wish.
Produce drawings in which each of the following formulas are true. (To rid yourself of an earlier drawing merely Select All and Cut under the Drawing Edit Menu). If you are having trouble, select the formula and click Satisfiable?
a) Fa
b) Gb
c) ~Fb
d) ~Fa⊃~Gb
e) (~Fa∨~Gb)∨Hc
f) Fa≡Gb
g) ~Fc∨(Fa∧Gb)
Produce a drawing in which each separate formula in the following list of formulas are true. If you are having trouble, select the list and click Satisfiable?
Fa,
Gb,
~Fb,
~Fa⊃~Gb,
(~Fa∨~Gb)∨Hc,
Fa≡Gb,
~Fc∨(Fa∧ Gb)
Produce a drawing which proves the following argument to be invalid (i.e. in which all the premises are true and the conclusion false). If you are having trouble, select the test list and click Satisfiable?
Fa,
Gb,
∴
(Fa≡Gb)⊃Ha
{Test list
Fa,Gb,~((Fa≡Gb)⊃Ha)
}