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]Read More

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