10/15/14 under construction
[Deriver works in the form either of javascript widgets, which appear directly in a web page viewed through a web browser, or as a downloadable java application, which runs like any other application (usually off the desktop on your computer).]
With the widgets in web pages, it should be fairly clear what the possibilities are. The downloaded application offers more, but at the cost of being more complex.)
2013
You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'. [Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]
You will need to use the correct logical symbols. Here they are
F ∴ F & G ∼ & ∨ ⊃ ≡ ∀ ∃ ∴ (or use the palette to produce them)
4/24/06
4/24/06
4/24/06
4/24/06
To understand how the various restrictions on the quantificational rules work to exclude certain kinds of invalid inferences
Bergmann[2004] The Logic Book Section 10.1
If a derivation contains a line of the form
n (∀<variable>)<scope> <any justification>
then a line of the form
<<scope>[<constant>/<variable>]> 'n ∀E'
The semantics of relations proceeds in much the way one would expect-- the new item that has to be taken account of is the order of the terms (because, for example, Tab is not at all the same thing as Tba -- Arthur being taller than Beryl is not the same as Beryl being taller than Arthur).
Let us start with an Interpretation
Interpretation 1
Universe= {a,b}
F={a}
2013
Thus far we have considered only 'monadic' predicates-- our atomic formulas consist of a predicate followed by only one term-- for example, Fx. But in English we regularly encounter dyadic predicates or relations. For example, 'Arthur is taller than Bert' cannot be symbolized with the tools we have used so far; what is needed is a relation to represent '...is taller than ...' Txy, say, and then the proposition would be symbolized Tab.