2/5/08 10Software
Hausman[2007] Logic and Philosophy Chapter 9
There also is a rule for adding a Universal Quantifier. This permits the step illustrated by the following proof fragments.
2/5/08 10Software
Hausman[2007] Logic and Philosophy Chapter 9
To understand the concepts of scope, free, bound. To meet substitution and a simplified version of the rule for removing a Universal Quantifier.
12/25/06
This video illustrates use of the downloadable application (and the symbol ∧ for 'and' and (∀x) for the universal quantifier, some systems use (x) for this). But, what the film depicts and explains is equally good if you happen to be using the web pages applets (or different symbols for 'and' and the universal quantifier).
10Software
Hausman[2007] Logic and Philosophy Chapter 7
We will certainly wish to discuss the truth and falsity of formulas with quantifiers in them.
Let us start with an Interpretation
Interpretation 1
Universe= {a,b}
F={a}
6/18/07 10 Software
To learn how to use the Universal and Existential Quantifiers in symbolizing propositions.
Hausman[2007] Logic and Philosophy Chapter 7
In Predicate Logic there are two new logical connectives, the Universal Quantifier (x) and the Existential Quantifier (∃x). These are used for symbolizing certain English constructions (they also have their own rules of inference and their own semantics, which we will learn about later).
10 Software
Hausman[2007] Logic and Philosophy Chapter 8
A few concepts are needed give a simple portrayal of the truth and falsity of predicate logic formulas.
There is the notion of an Interpretation which consists of a Universe together with an account of how the various symbols in the predicate logic formulas apply in this Universe.
There should be a Universe, which is the collection of the objects that the formulas is about. We write, for example,
Universe = {a,b,c}
6/6/09 10Software
To learn how to interpret simple predicate logic formulas as being true or false.
This helps in proving invalidity by the technique of displaying a counter-example.
Hausman[2007] Logic and Philosophy Chapter 8
In sentential logic, we just took it that each of the atomic sentences either is true or is false-- we did not look into the structure of the sentences.
Truth can be discussed in more detail in predicate logic.