trees

Help with Reading a Counter Example [Generic] martin Sun, 03/31/2013 - 13:50
Topic

2013

Reading a counter example from an open branch

[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.]

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The Tree Widget martin Fri, 03/01/2013 - 20:04
Topic

2013

An example of the tree widget in use (and we are showing a different parser here to the earlier ones)

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)

Reading a Counter Example from the Tree martin Wed, 06/20/2012 - 22:29
Topic
Logical System
Review of K Propositional Rules martin Thu, 06/07/2012 - 12:10
Topic
Logical System

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

The Modal Negation (MN) rules

 

Review of Additional S5 Propositional Rules martin Thu, 06/07/2012 - 11:25
Topic
Logical System



 

◊ S5 world, k, must be new [here the computer will choose for you]

 



 

□ S5 any world, stage 1, your choice

Review of Tree Propositional Rules martin Sat, 06/02/2012 - 16:35
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').

Tree Predicate Exercises: Roll your own martin Sat, 06/02/2012 - 11:40
Topic
Logical System
Review of Tree Predicate Rules martin Sat, 06/02/2012 - 11:39
Topic
Logical System

 

∃D. The constant, a, must be new to the branch [here the computer will choose for you]

 



 

∀D. Any closed term, stage 1, your choice


∀D. Any closed term, stage 2, the constant 'a' chosen

Set Theory (and Russell's Paradox) martin Thu, 05/31/2012 - 14:55
Logical System