Logical System
5/17/26
Reading
Rod Girle [2000] Modal Logics and Philosophy Chapter 3
ModalTruth Table Widget [Single Line]
The next step is to relativize necessity and possibility to Access. You can experiment with this...
Roll your own [choose S5 or K]
Girle's Chapter 3 has a number of exercises. You can do them here (be sure to use the following logical symbols)
∼ & ∨ ⊃ ≡ ∀ ∃ ∴ □ ◊
[There are many other logics in Girle Chapter 3, send us an email if you would like them.]
- 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, the quantifiers have brackets around them so a quantified formula might look like (∀x)(Ax→Bxy). Notice that the 'arguments' to a predicate do not have brackets around them. You can use proper subscripts (shown above) on variables (or constants or predicates). For example, (∀x₁)(Ax₁→Bx₁y₁).
- 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)).