- Preview
- Why do we need formal logic?
- Inferences About Birds
- Exercise: Inferences About Foos
- Predicates
- Conjunctions and Disjunctions
- Implies
- Notation Equivalency
- Exercise: Practicing Formal Logic
- Truth Tables
- Exercise: Truth Tables I
- Exercise: Commutative Property
- Exercise: Distributive Property
- Exercise: Associative Property
- Exercise: De Morgan’s Law
- Truth of Implications
- Implication Elimination
- Rules of Inference
- Prove Harry is a bird
- Universal Quantifiers and Existential Quantifier
- A Simple Proof
- exercise
- Wrap Up
- The Cognitive Connection

# Preview

- Logic is a language allows to make association of the world in a precise way.
- it form the basis of planning

# Why do we need formal logic?

Knowledge base: sentence in the language of logic; complete and correct Rules of Inference engine:

## Inferences About Birds

## Exercise: Inferences About Foos

The sentences are language of logic

## Predicates

”:” means indicates.
`If Feathers(animal): Then Bird(animal)`

reads if animal has feathers, then animal is bird.

## Conjunctions and Disjunctions

## Implies

## Notation Equivalency

## Exercise: Practicing Formal Logic

## Truth Tables

## Exercise: Truth Tables I

Exercise: Truth Tables II (more complicated sentence)

In theory, we can calculate True or False values for very complicated sentences.

## Exercise: Commutative Property

A & B is the same as B & A

## Exercise: Distributive Property

- A &(B or C) is equivalent to (A and B) or (A and C) Exercise: Associative Property

## Exercise: Associative Property

- The associate property applies when there is only conjunction or disjunctions.

## Exercise: De Morgan’s Law

## Truth of Implications

This is hard to understand: need to go back to the examples
But remember `A=> B`

is actually `!A | B`

.

## Implication Elimination

## Rules of Inference

- The rules here can be used for reasoning.

## Prove Harry is a bird

Although the rules exist for a long times, it’s hard to use these rules in AI agent because the computation is not feasible.

## Universal Quantifiers and Existential Quantifier

- Propositional logic (zero-order logic): no variables.
- Existential and Universal Quantifier can be used with variables.
- Universal Quantifier mean given all values for the variable
- Existential Quantifier means at least one value

## A Simple Proof

- convert every sentence into a conjunctive normal form.
`not finished for this part. did not understand`

## exercise

- A efficient way to proof sentences

## Wrap Up

## The Cognitive Connection

- Formal and precise way to reason
- Human uses logic sometimes.. but its not a fundamental method.
- Human uses induction and abduction more for reasoning. logic is deductive.