Maggie Johnson Handout #3

CS103A

Introduction to Propositional Logic

Key Topics

* Why Study Logic?

* Atomic Sentences

* Translations

* Tarski's World

* Valid & Sound Arguments

· Definition 1: Atomic Sentences correspond to the simplest sentences of English, sentences consisting of some names connected by a predicate.

· Some rules:

Every individual constant must name an existing object.

No constant can name more than one object

An object can have more than one name.

· Predicate symbols are used to express some property of objects or some relation between objects

· In FOL, each predicate has a fixed number of arguments or arity. This is the number of constants the predicate needs to form a sentence.

· Every predicate is interpreted by a determinate property or relation, i.e., it is possible to determine definitively whether or not an object has the property.

· Definition 2: An Atomic Sentence is a predicate followed by the right number of names (as defined by the arity of the predicate) which makes a claim that must be either true or false.

· When designing our own FOL, we want a language that can say everything we want but with the smallest "vocabulary".

Translate the following into FOL making up predicates as needed:

1. Elliot shook hands with Caroline.

2. AIDS is less contagious then influenza.

3. Spain is between France and Portugal, in size.

4. Misery loves company.

· An argument is a series of statements in which one, called the conclusion is meant to be a consequence of the others, called premises.

· An argument is valid if the conclusion must be true in any circumstance in which the premises are true.

· An argument is sound if it is valid and the premises are all true.