Modal Trees: Roll Your Own

Logical System
howson
8/15/26

Roll your own

  • 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). In the syntax we prefer 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.

 

 

Should you wish to use the Deriver application you might want to glance at Deriver in a web page Then you can launch Deriver from here Deriver20 [Howson Parser].

Good advice is: start these tutorials without it, but if you get to the point of wishing to save some work, then switch to the Deriver Web Application.

Then either copy and paste formulas into the Journal or use the Deriver File Menu to Open from URL... with this address https://softoption.us/test/treesStandAlone/CombinedTutorialsDefault.html . Then select the desired formula(s) and Start Tree off the Actions Menu.

Preferences

You will need to set some Preferences for this.

  • set identity to true (and that will give you the identity rules)
  • set modal to true (to get modal)
  • and  you can check that the parser is set to howson