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1
A Concise Introduction to Logic
Every substitution instance of a valid form is a valid argument, but it is not the
case that every substitution instance of an invalid form is an invalid argument.
The reason is that some substitution instances of invalid forms are also
substitution ...
2
Cengage Advantage Books: Understanding Arguments: An ...
Perhaps a bit more surprisingly, our definitions allow “Roses are red and roses
are red” to be a substitution instance of “p & q.” This example makes sense if you
compare it to variables in mathematics. Using only positive integers, how many ...
Walter Sinnott-Armstrong, Robert Fogelin, 2014
3
A Concise Introduction to Logic:
Bs Cs This diagram suggests that we can prove the form invalid if we can find a
substitution instance having actually true premises and an actually false
conclusion. In such a substitution instance the As and the Cs would be separated
from ...
4
Handbook of Modal Logic
We shall call φ[ψ/P(x)] a substitution-instance of φ. It might be instructive to
consider an example of a substitution-instance: If φ is the formula ∀y(P(y) ∧ Q(y)
) and ψ is the formula R(z,x) where z is distinct from x and y, then φ[ψ/P(x)] is the
...
Patrick Blackburn, Johan F.A.K. van Benthem, Frank Wolter, 2006
5
Logic and Philosophy: A Modern Introduction
Here is the important rule to keep in mind regarding sentence forms: A sentence
is a substitution instance of a form if and only if you can produce exactly that
sentence by doing nothing other than replacing each variable in the form with a ...
Alan Hausman, Howard Kahane, Paul Tidman, 2012
6
Logic Identity and Consistency]
latter case as it is in the former. And if we drop this demand on 'y is a substitution
instance of "<)>x"' as well as on 'y is true', we have to drop it on '§x too. To see the
point clearly we can take first the substitutional version of 'For all x, <}>x', ...
7
Cengage Advantage Books: Understanding Arguments, Concise ...
Perhaps a bit more surprisingly, our definitions allow “Roses are red and roses
are red” to be a substitution instance of “p & q.” This example makes sense if you
compare it to variables in mathematics. Using only positive integers, how many ...
Walter Sinnott-Armstrong, Robert Fogelin, 2014
8
Mathematical Foundation of Computer Science
In (3), P is replaced Qand Qis replaced by P. In (4), P is replaced by Qand Qis
replaced by P A —.Q. Example. Consider the following formulae from P —-> -1Q
1. Substitute P v Qfor P and R for Qto get the substitution instance (P v Q) —-) wR
2.
Dr. J. Rajendra Prasad, T. Rama Rao, A. Madana Mohana Rao, 2009
9
Introducing Symbolic Logic
The antecedent is false and the consequent true, so this substitution instance is
true. All those three substitution instances are true. What would it take for there to
be a substitution instance which is false? There would have to be an instantiating
...
(ii) If every substitution instance of 4> is true in 971, then every substitution
instance of<j> is true in 971'. (iii) 7/SW Ih A then W Ih A. Proof. Item (i) follows by
induction on 4>. For the base case we have 971', w Ih p iff 971, w Ih 4>v,(p). As (-.
0)' ...
Patrick Blackburn, Maarten de Rijke, Yde Venema, 2002
