### 7.2.1 What's that

I won't be able to explain everything, since various previous concepts are needed, but I will try to say a little about them. First, some changes:

Now we won't talk just about general facts (it rains, it's warm, etc.), but we will have a domain of known things, and we will have to say which property is true for each element.

For instance: we have the domain , which represent respectively to PROLOG (a logical programming language), a telephone, and a radio. p, t, r.

We also add a predicate letter (they're not called propositional letters anymore) , which will have the following meaning: when we write (read `` of '', but written together) we mean that is an electronic device. We will also have to say that is a piece of software, and which will mean that is a text processor.

Now we know that are true , , and nothing else.

Quantifiers make possible to write truths referring to some elements from the domain. There exist two quantifiers:

• Universal quantifier: . When we put (``for all , of ''), we mean that all elements on the domain make true the property .
• Existential quantifier: . (``there exists such that of '') we mean that at least one element from the domain makes true the property .
For instance, now are true the following formulas: , , , and several more. Quantifiers have the same priority as the operator .

The rules explained here will work only with free substitutions. Sorry for not saying what that means, but I don't want to go out of topic.

Daniel Clemente Laboreo 2005-05-17