Logical Agents

Knowledge based agents use a process of reasoning over an internal representation of knowledge to decide what actions to take.

• Knowlege Base (KB): A set of sentences. Each sentence is expressed in a language called a knowledge representing language and represent some assertion about the world
• When a sentence is given that is not derived from other sentences, it’s called an axiom
• Inferece: Deriving new sentences from old.

Ex; Wumpus World

A cave consists of rooms connected by passageways. In the curve there is a wumpus. Wumpus can be shot by the agent, but the agent has one arrow. Some rooms contain bottomless pits.

• Performance measure: +1000 for climbing out of the cave with gold, -1000 for falling into a pit or wumpus, -1 for every action, -10 for using the arrow. Game ends when the agent dies or when climb out of cave
• Environment: a 4x4 grid of rooms. Agent always start at (1, 1), facing east.
• Actuators: Agent can move forward, turn left or right (by 90deg), Safe to enter a square with a dead wumpus. If agent tries to move forward and bump into a wall, then agent doesn’t move. Action shoot can be used to shoot the arrow, arrow continues until it kills the wumpus or hit a wall. Agent can use Climb action to climb out of cave (only from (1, 1) square)
• Sensors: Agent has 5 sensors, each of which gives a single bit of info
  • In squares adjacent to wumpus (not diagonal), agent will perceive a stench
  • In squares adjacent to a pit, agent will perceive a breeze
  • In the square with gold, agent will perceive a glitter
  • When agent walks into a wall, it will perceive a bump
  • When the wumpus is killed, it emits a scream that can be perceived anywhere in the cave
• This environment is:
  • Deterministic
  • Discrete
  • Static
  • Single Agent
  • Sequential
  • Partially observable

Logic

• Semantics: Define the truth of each sentence with respect to each possible word
• Model: Mathematical abstractions. Has a fixed truth value for every relevant sentence
• If a sentence is true in model m, we say that m satisfies , or m is a model of

Entailment:

Idea that a sentence follows logically from another sentence. Definition: if and only if, in every model where is true, is also true Example: if is true, then is true regardless of the value of y

• Logical Inference: Applying the definition of entailment to derive conclutions
• Model checking: Enumerate all possible models to check that is true in all models in which KB is true,

If an inference algorithm can derive from , we write An inference algorithm that derives only entailed sentences is called sound or truth-preserving

Propositional Logic: A very simple logic

• The atomic sentences consists of a single proposition symbol
• There are two propositional symbols with fixed meanings
  • : Always true
  • : Always false
• Complex sentences are created from simpler sentences, using parenthesis and operators called logical connectives.
  • (not): negation
  • (and): conjunction
  • (or): disjunction
  • (implies)
  • (if and only if): biconditional

Semantics

Semantics defines the rules for determining the truth of a sentence with respect to a particular model.