Logic

Question 1

What is Logic?

Answer 1

Logic provides reasoning techniques that enable deriving knowledge in a systematic way

Question 2

Define Logic;

Answer 2

Logic is about formalising knowledge & reasoning in a precise, unambiguous in a rigorous way.

Question 3

What do logical rules do?

Answer 3

Use rules to derive knowledge

Question 4

What is understanding /modelling?

Answer 4

Program follows its specification

Question 5

What is formalisation/ rigour?

Answer 5

Programs works as should before changing it

Question 6

What is proof/correctness?

Answer 6

Verify mathematical results

Question 7

What is computation/automation?

Answer 7

Prove things about your program
-What can be computed / How fast
-Solve hard problems

Question 8

What is Propositional Logic?

Answer 8

Sentence which states a fact
- That can be True/False

Question 9

What is an Argument

Answer 9

A list of Propositions
- Last is called CONCLUSION
- Others are called PREMISES

Question 10

When is an Argument Valid?

Answer 10

is Valid IF AND ONLY IF, when premise is true so is the conclusion

Question 11

Assumptions have to …

Answer 11

… perfectly fit the environment you want it set in

Question 12

Define Symbolic Logic

Answer 12

• Formal language that allows conducting logical reasoning through the manipulation of symbols.
• Defined by grammar that allows deriving formula from collection of symbols

Question 13

What are the 2 aspects of a Language?

Answer 13

• Syntax
• Semantics

Question 14

Define Syntax:

Answer 14

Well formed sequences of symbols
DEFINED BY GRAMMAR

Question 15

Define Semantics:

Answer 15

Assigns meaning to those Symbols

Question 16

What does BNF stand for?

Answer 16

BNF - Backus Naur Form

Question 17

What does BNF define?

Answer 17

Defines Context-Free-Grammar

Question 18

What does
lhs :: = rhs1 |…| rhsn represent?

Answer 18

Left hand side (lhs) can expand to any forms rhs1 to rhsn
Right hand side

Question 19

What is Non-Terminal?

Answer 19

-Left Hand Side of lhs :: = rhs1 |…| rhsn
- Can be expanded
- Occurs left to the rules

Question 20

What does rhsi represent?

Answer 20

Each rhsi is a sequence of non-terminal and terminal symbols

Question 21

What is Arity?

Answer 21

The number of Arguments terminal symbols take

Question 22

What is the Arity of +/*?

Answer 22

2
- Binary Infix Operators

Question 23

What is the Arity of 0/1?

Answer 23

1
- Called CONSTANTS
- NULLARY OPERATORS

Question 24

What is Arity of AND,OR & IMPLIES?

Answer 24

2

Question 25

What is Arity of NOT?

Answer 25

1

Question 26

Define Infix:

Answer 26

In between 2 expressions / arguments

Question 27

Define Fixity:

Answer 27

Place where it occurs with reference to its Arguments

Question 28

Define Prefix:

Answer 28

Goes before expression/ Argument

Question 29

Define Postfix:

Answer 29

Occurs after expressions/ Argument

Question 30

How to fix AMBIGUITY?

Answer 30

Use Brackets and Parentheses

Question 31

Give an Example of BNF arithmetic Expression:

Answer 31

exp ::= num |exp+exp|exp * exp -exp on LHS is non-terminal symbol - +,*,1,0 are terminal symbol - num ---> numeral is a sequence of digits -

Question 32

What is Meta Variables?

Answer 32

Act as placeholders for any variable -exp can act as placeholder

Question 33

How are Propositional Logic built?

Answer 33

Combining Atomic Proposition & Logical Connectives

Question 34

What is a ATOMIC PROPOSTION?

Answer 34

Can be True/ False - Cannot be decomposed further

Question 35

Define NEGATION:

Answer 35

if A is True - then ¬A is False