Conge 精进

2019-01-01

# 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:

The sentences are language of logic

## Predicates

”:” means indicates. `If Feathers(animal): Then Bird(animal)` reads if animal has feathers, then animal is bird.

## 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.

## Truth of Implications

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

## 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

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

## exercise

• A efficient way to proof sentences

## 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.