Tree Predicate Exercises: Roll your own

Logical System



Colin Howson, [1997] Logic with trees Chapter 2


Howson [1997] has a number of exercises. Many of them you will be able to do in the Widget below.

Here are a few hints

  • You have to use the right (unicode/html) logical symbols. Check Writing symbols
  • The symbols in use here are ¬ ∧ ∨ → ↔ ∀ ∃ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ (so copy and paste or drag and drop these). The Howson syntax is that the quantifers do not have brackets around them so a quantified formula might look like ∀x(A(x)→B(x,x)). Notice that the 'arguments' to a predicate have brackets around them, and if the arguments are a list they will be separated by commas. You can use proper subscripts (shown above) on variables (or constants or predicates). For example, ∀x₁(A(x₁)→B(x₁,x₁)).
  • When entering from a selection, the software will take a single formula (say, A) or a comma separated list of formulas (say, A,B,C) or a possibly empty comma separated list of formulas followed by ∴ and another formula (say, A,B,C ∴ D). In the last case it will load the negation of the conclusion.
  • Just type, cut and paste, or drag and drop, whatever you wish, into the lower text box. Then make a selection and hit the Start button.


Exercise: Roll your own

If you decide to use the web application you can launch it from here Deriver [Howson] — username 'logic' password 'logic'. Then type your material into the Journal. Then select the desired formula(s) and Start Tree off the Actions Menu. [If you find you need to set the Preferences (because you, or someone else, has been doing something totally different with Deriver on the computer in use), set the parser to Howson. ]