Flashcards in Logic Deck (22)

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1

## What does logic deal with?

### Whether statements are true or false + chains of reasoning which enable us to decide this. Work with boolean + truth tables + de Morgan's laws.

2

## What are the symbols for and, or not?

### and = ^. Or = v. Not = ¬.

3

## What is the opposite of A^B?

### ¬A v ¬B. We find opposite by negating variable + swapping and/or symbols.

4

## When is A ⇒ B false?

### When A is true and B is false.

5

## What is the contrapositive of A ⇒ B?

### ¬B ⇒ ¬A. They mean the same thing.

6

## If you chain logical deductions together, how do you know when it's always true?

### If the truth table is true in every scenario.

7

## What is forward chaining?

### Search from initial conditions to goal. Start with what we know. Could end up with lots of intermediate deductions that aren't needed for final answer.

8

## What is backward chaining?

### From goal back to initial conditions. Start with what we want to know. Can end up with lots of questions which we don't need an answer to.

9

## What is propositional logic?

### Logic used when something must be proved/disproved (proposition)

10

## What is predicate logic?

### When we need to find out more about unknown variable before we can prove/disprove it. It tells you something about the subject and so is a Boolean function applied to 1 or more variables.

11

## What happens when you add values to a predicate?

### It becomes a proposition.

12

## What is the domain/universe of discourse?

### Set of values which can be assigned to predicate variable.

13

## What are the quantifiers?

### For all (∀) or there exists (∃) to indicate num of values for which predicate is true. For all shows all values are true. There exists shows at least one (possibly all) values are true for predicate. E.g. ∀x∈D .P(x) (for all possible values of x in domain D, P(x) is true.

14

## What is a counterexample?

### With for all, there must be at least 1case where p(x) is false so ¬( ∀x∈D.P(x)) = ∃x∈D.¬P(x) AND ¬( ∃x∈D .P(x) ) = ∀x∈D.¬P(x). You flip rule + negate predicate. Domain not affected.

15

## How do you prove 'there exists'?

### You just need 1 example.

16

## What is the lovers relationship?

### Use 2 different quantifiers. Let L(a,b) be ‘a loves b’. Can use statements such as ∀x∈D. ∃y∈D.L(y,x) meaning everyone is loved by someone

17

## What is the difference between a finite and infinite sequence?

### Finite sequences we know length and can specify each term's index, we limit domain to num of terms in sequence. Strong parallel between ∀i + for loops for arrays. With infinite, we don't know how many there are but if there's a pattern we can make a conjecture about subsequent terms so can make a predicate rule for this.

18

## What is the difference between an ordered and a sorted sequence?

### A sequence is already ordered but sorted means in asc/desc order.

19

## What is the Fibonacci sequence?

### Addition of previous 2 numbers in sequence but have to declare first 2 values as don’t have 2 previous values.

20

## How do we concatenate sequences?

### Tie symbol means concatenation, join 2 sequences together (⌢).

21

## How do we declare a subsequence in predicate logic?

### Use subseq(S,T) to state if something is a subsequence, but not in VDMLab. To ref subsequence, use S(starti,…,endi)

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