Predicate Trees: Roll your own

Logical System
howson

8/16/2026

Reading

Colin Howson, [1997] Logic with trees Chapter 2

Exercises

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.
  • Lightweight Input. Just type, cut and paste, or drag and drop, whatever you wish, into the lower text box (the 'Journal'). Then make a selection and hit the Start button.
  • Lightweight Output. You can write a tree out to the Journal (then copy it and paste it into WORD (for example)).
  • The iPad, and similar, keyboards have a little trick that might catch you out. If you type a single letter, say 'a', they will automatically put it in upper case to 'A' because they assume you are starting a sentence. But, actually, if you are instantiating a quantifier you have to use lower case.

 

Exercise: Roll your own

Should you wish to use the application, you might want to glance at Deriver in a web page Then you can launch Deriver from here Deriver20 [Howson Parser].  Then either copy and paste, or type, into the Journal or use the Deriver File Menu to Open from URL... with this address

https://softoption.us/test/treesStandAlone/howson/CombinedTutorialsHowson.html

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 default. The title bar of the Deriver window will show you what system you are running e.g. 'DeriverDefault', 'DeriverGentzen', etc.]