Logic Flashcards
What is Logic?
Logic provides reasoning techniques that enable deriving knowledge in a systematic way
Define Logic;
Logic is about formalising knowledge & reasoning in a precise, unambiguous in a rigorous way.
What do logical rules do?
Use rules to derive knowledge
What is understanding /modelling?
Program follows its specification
What is formalisation/ rigour?
Programs works as should before changing it
What is proof/correctness?
Verify mathematical results
What is computation/automation?
Prove things about your program
-What can be computed / How fast
-Solve hard problems
What is Propositional Logic?
Sentence which states a fact
- That can be True/False
What is an Argument
A list of Propositions
- Last is called CONCLUSION
- Others are called PREMISES
When is an Argument Valid?
is Valid IF AND ONLY IF, when premise is true so is the conclusion
Assumptions have to …
… perfectly fit the environment you want it set in
Define Symbolic Logic
- Formal language that allows conducting logical reasoning through the manipulation of symbols.
- Defined by grammar that allows deriving formula from collection of symbols
What are the 2 aspects of a Language?
- Syntax
- Semantics
Define Syntax:
Well formed sequences of symbols
DEFINED BY GRAMMAR
Define Semantics:
Assigns meaning to those Symbols
What does BNF stand for?
BNF - Backus Naur Form
What does BNF define?
Defines Context-Free-Grammar
What does
lhs :: = rhs1 |…| rhsn represent?
Left hand side (lhs) can expand to any forms rhs1 to rhsn
Right hand side
What is Non-Terminal?
-Left Hand Side of lhs :: = rhs1 |…| rhsn
- Can be expanded
- Occurs left to the rules
What does rhsi represent?
Each rhsi is a sequence of non-terminal and terminal symbols
What is Arity?
The number of Arguments terminal symbols take
What is the Arity of +/*?
2
- Binary Infix Operators
What is the Arity of 0/1?
1
- Called CONSTANTS
- NULLARY OPERATORS
What is Arity of AND,OR & IMPLIES?
2
What is Arity of NOT?
1
Define Infix:
In between 2 expressions / arguments
Define Fixity:
Place where it occurs with reference to its Arguments
Define Prefix:
Goes before expression/ Argument
Define Postfix:
Occurs after expressions/ Argument
How to fix AMBIGUITY?
Use Brackets and Parentheses
Give an Example of BNF arithmetic Expression:
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
-
What is Meta Variables?
Act as placeholders for any variable
-exp can act as placeholder
How are Propositional Logic built?
Combining Atomic Proposition & Logical Connectives
What is a ATOMIC PROPOSTION?
Can be True/ False
- Cannot be decomposed further
Define NEGATION:
if A is True
- then ¬A is False
