9/6/2026
The game is going to use a drawing, or interpretation panel. You can find help with that at The Drawing Panel .
With the widget being used here, you can draw into the drawing panel and you can type text into the lower 'Journal'. Some of the exercises will be supplied with an existing drawing. Some will be supplied with text.
A Small Finite Universe and Named Individuals need to exist
As the Drawing Panel explains, the Universe consists of a small number of individuals (there are a limited number of lower case letters in the alphabet that is being used). Also a named individual needs to exist in the Universe. Consider, for example, the formula F(c). If there is no individual c in the Universe, i.e. in the drawing, the widget will refrain entirely from discussing the truth of F(c) (and similar matters).
The finite Universe is also of significance. A huge swath of logic and mathematics concerns infinite universes. What is being taught here omits those completely.
Complete and Incomplete Information
Game Theoretic Semantics (GTS), of which this is a very simple exposure, recognizes that there are formulas which are true, and known to be true, without knowledge or information about their components. For example, 'P or not-P' would usually be taken to be true, where P is a proposition. Yet, whether P is true, or not-P is true might not be known. An ordinary language instance of that might be 'Arsenal will score 3 goals tonight or Arsenal will not score 3 goals tonight'. Putting an example of that kind into our formalism, it might be the case that (F(c) v ~F(c)) is true without it being known whether F(c) is true or ~F(c) is true. Of course, these cases of incomplete information would completely blow apart our game because, for example, endorsing (F(c) v ~F(c)) requires the holder to either endorse F(c) or to endorse ~F(c) and that cannot be done rationally nor can a non-rational choice be assessed.
However, our simple game bi-passes this. Consider (F(c) v ~F(c)) ... the individual c has to be in the Universe or the widget will not even consider the formula; then either there is a rectangle F in the drawing which encloses c (in which case F(c) is true) or there is not a rectangle F in the drawing which encloses c (in which case ~F(c) is true); so, if Endorse or Deny are in order for (F(c) v ~F(c)), Endorse or Deny are going to be in order for that formula's components. Our simple game has complete information.
The Default Parser
The wider Deriver software can parse many different symbolization styles or conventions for logic. What has been chosen here is the 'Default' parser, and the main reason is that the default parser can parse 'quasi-English'. To give an example, for a sentence like 'b is a red circle', most of the other systems would adopt obvious conventions and symbolize that by a formula like 'Rb&Cb', but the default ca use and read a formula like 'Red(b)&Circle(b)' (and that is obviously better for teaching). What do the labels 'Bergmann', 'Default', 'Gentzen', 'Howson', etc. mean?
Introductory Video
Exercise
Try Endorsing or Denying the following formulas. (You could also try altering the diagram, typing or pasting your own formulas in, and Endorsing or Denying the results.)