## The Reading a Counter Example from a Tree Widget

Topic

Logical System

Topic

2013

*[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.] *

Your browser does not support html5 video.

Topic

2013

The logical symbols in use 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)

Logical System

**There are the ordinary (non-modal) tree propositional rules plus **

**The Modal Negation (MN) rules**

Logical System

Topic

Logical System

6/2/12
##
Review of Tree Propositional Rules, shown as patterns

Here the letters 'P' and 'Q' are being used to stand for entire well formed formulas (so, on a particular occasion, 'P' might stand for the atomic formula 'F' and, on another occasion, it might stand for the compound formula 'F&G').

Topic

Logical System