Lecture 6 - Logic and Reasoning Notes | EduRev

: Lecture 6 - Logic and Reasoning Notes | EduRev

 Page 1


Logic and Reasoning
CS60001: Foundations of Computing Science
Pallab Dasgupta
Professor, Dept. of Computer Sc. & Engg.,
Indian Institute of Technology Kharagpur
Page 2


Logic and Reasoning
CS60001: Foundations of Computing Science
Pallab Dasgupta
Professor, Dept. of Computer Sc. & Engg.,
Indian Institute of Technology Kharagpur
Indian Institute of Technology Kharagpur
Pallab Dasgupta
Knowledge and Reasoning
? Representation, Reasoning and Logic
? Propositional Logic
? First-Order Logic
? Inference in first-order logic
¦ Generalized Modus Ponens
¦ Forward and backward chaining
¦ Resolution
? Logical Reasoning Systems
Page 3


Logic and Reasoning
CS60001: Foundations of Computing Science
Pallab Dasgupta
Professor, Dept. of Computer Sc. & Engg.,
Indian Institute of Technology Kharagpur
Indian Institute of Technology Kharagpur
Pallab Dasgupta
Knowledge and Reasoning
? Representation, Reasoning and Logic
? Propositional Logic
? First-Order Logic
? Inference in first-order logic
¦ Generalized Modus Ponens
¦ Forward and backward chaining
¦ Resolution
? Logical Reasoning Systems
Indian Institute of Technology Kharagpur
Pallab Dasgupta
The Wumpus World Environment
? Adjacent means left, right, top, or bottom
¦ Stench: In squares containing and adjacent to wumpus
¦ Breeze: In squares adjacent to a pit
? There can be one wumpus, one gold, and many pits. Agent starts from the 
bottom-left square of a grid.
? The agent dies if it enters a square containing a pit or the wumpus
? The agent can shoot the wumpus along a straight line
? The agent has only one arrow
3
Page 4


Logic and Reasoning
CS60001: Foundations of Computing Science
Pallab Dasgupta
Professor, Dept. of Computer Sc. & Engg.,
Indian Institute of Technology Kharagpur
Indian Institute of Technology Kharagpur
Pallab Dasgupta
Knowledge and Reasoning
? Representation, Reasoning and Logic
? Propositional Logic
? First-Order Logic
? Inference in first-order logic
¦ Generalized Modus Ponens
¦ Forward and backward chaining
¦ Resolution
? Logical Reasoning Systems
Indian Institute of Technology Kharagpur
Pallab Dasgupta
The Wumpus World Environment
? Adjacent means left, right, top, or bottom
¦ Stench: In squares containing and adjacent to wumpus
¦ Breeze: In squares adjacent to a pit
? There can be one wumpus, one gold, and many pits. Agent starts from the 
bottom-left square of a grid.
? The agent dies if it enters a square containing a pit or the wumpus
? The agent can shoot the wumpus along a straight line
? The agent has only one arrow
3
Indian Institute of Technology Kharagpur
Pallab Dasgupta
Logic
? A formal system for describing states of affairs, consisting of:
¦ Syntax: describes how to make sentences, and
¦ Semantics: describes the relation between the sentences and the states of 
affairs
? A proof theory – a set of rules for deducing the entailments of a set of 
sentences
? Improper definition of logic, or an incorrect proof theory can result in absurd 
reasoning
4
Page 5


Logic and Reasoning
CS60001: Foundations of Computing Science
Pallab Dasgupta
Professor, Dept. of Computer Sc. & Engg.,
Indian Institute of Technology Kharagpur
Indian Institute of Technology Kharagpur
Pallab Dasgupta
Knowledge and Reasoning
? Representation, Reasoning and Logic
? Propositional Logic
? First-Order Logic
? Inference in first-order logic
¦ Generalized Modus Ponens
¦ Forward and backward chaining
¦ Resolution
? Logical Reasoning Systems
Indian Institute of Technology Kharagpur
Pallab Dasgupta
The Wumpus World Environment
? Adjacent means left, right, top, or bottom
¦ Stench: In squares containing and adjacent to wumpus
¦ Breeze: In squares adjacent to a pit
? There can be one wumpus, one gold, and many pits. Agent starts from the 
bottom-left square of a grid.
? The agent dies if it enters a square containing a pit or the wumpus
? The agent can shoot the wumpus along a straight line
? The agent has only one arrow
3
Indian Institute of Technology Kharagpur
Pallab Dasgupta
Logic
? A formal system for describing states of affairs, consisting of:
¦ Syntax: describes how to make sentences, and
¦ Semantics: describes the relation between the sentences and the states of 
affairs
? A proof theory – a set of rules for deducing the entailments of a set of 
sentences
? Improper definition of logic, or an incorrect proof theory can result in absurd 
reasoning
4
Indian Institute of Technology Kharagpur
Pallab Dasgupta
Types of Logics
Language What exists Belief of agent
Propositional Logic Facts T / F / Unknown
First-Order Logic Facts, Objects, Relations T / F / Unknown
Temporal Logic Facts, Objects, Relations, Times T / F / Unknown
Probability Theory Facts Degree of belief   [0..1]
Fuzzy Logic Degree of truth Degree of belief [0..1]
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