7/26/08 10 Software
R.C.Jeffrey, [1967] Formal Logic: Its Scope and Limits Chapter
Jeffrey [1967] has a number of exercises. Many of them you will be able to do in the Applet below.
Here are a few hints
Colin Howson, [1997] Logic with trees Chapter 2
A central use for Trees is to produce a counter example to an invalid argument. To do this, you construct a tree with a complete open branch. You will be able to do this for invalid arguments (but not valid ones). Then you run up that branch assigning all atomic formulas True and all negations of atomic formulas False.
This software will let you try a few.
2/10/08
[This is a Quicktime Movie, click the Play button to view it. The logical symbols you see in use may be different to the ones you are familiar with (sorry about that, but it is not practical to produce different movies for all the minor variations in symbols). Any differences will not affect the principles being explained here.]
This section of the tutorials and
Richard Jeffrey, [1967-2006] Formal Logic: its Scope and Limits
would work well together (and it is an excellent book).
You need to know some propositional logic to be able to understand the tutorials to come. In particular, you need to know about the symbols used in propositional logic, truth tables, satisfiability, consistency, and semantic invalidity (by counter example). You do not need to know propositional rules of inference and derivations.
2/40/20 20 Software
The logical symbols in here are ¬ ∧ ∨ → ↔ ∀ ∃ .
Determine whether these arguments are valid (ie try to produce closed trees for them)
a) ∀x(F(x)→G(x)), ∃x¬G(x) ∴ ∃x¬F(x)
b) ∀x(F(x)→∀yG(y)), F(a) ∴ ∀xG(x)
c) ∀x(A(x)→B(x)), ∀x(¬A(x)→C(x))∴ ∀x(¬B(x)→¬C(x))
d) ∃xF(x),∀x(¬G(x)→¬F(x)),∀xM(x) ∴ ∃xG(x)∧∃xM(x)
2013
To become familiar with the new rules for predicate logic trees with identity.
Colin Howson, [1997] Logic with trees Chapter 9
It is possible to use trees with formulas containing identity. Really there are two different ways to implement it: either there are two new rules, or there is one new rule and a new way of closing a branch from a single formula. Both will be described.
2/3/08 10 Software The Widget for this has yet to be written. 2013
Quiz 2 Applet
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9/16/08 10 Software
Richard Jeffrey, [1967-2006] Formal Logic: its Scope and Limits
2013
To become familiar with the new rules for predicate logic trees.
Colin Howson, [1997] Logic with trees Chapter 6
There are further rules for predicate logic trees (which we will come to shortly).
