lecch07 - CS2710,ISSP2610 Chapter7 PropositionalLogic...

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1 CS 2710, ISSP 2610 Chapter 7  Propositional Logic  Reasoning
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2 Knowledge Based Agents Central component:   knowledge base , or  KB . A set of sentences in a  knowledge representation language Generic Functions TELL   (add a fact to the knowledge base) ASK (get next action based on info in KB) Both often involve inference, which is? Deriving new sentences from old
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Note We’re all familiar with logic from mathematics In AI, we need to think about things we usually  can take  for granted To use the notion of prime number, you don’t have to think  about what  prime  means … or  number , for that matter In AI, we create knowledge representation schemes, which  define the objects, predicates, and functions which exist 3
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4 The Wumpus World Game is played in a MxN grid One player, one wumpus, one or more pits Goal:  find gold while avoiding wumpus and pits Percepts: Glitter (gold is in this square) Stench (wumpus is within 1 square N,E,S,W) Breeze (pit is within 1 square N, E, S, W) Bump (agent walks into a wall) Scream (when Wumpus dies; hear it anywhere)
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5 Wumpus Example stench [Wumpus] stench Glitter [gold] stench, breeze [start] breeze [Pit] breeze 0 0
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6 Wumpus Main difficulty:  player doesn’t know the  configuration Reason about configuration Knowledge evolves as new percepts arrive and  actions are taken.
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7 Examples of reasoning If the player is in square (1, 0) and the percept is breeze,  then there must be a pit in (0,0) or a pit in (2,0) or a pit in  (1,1). If the player is now in (0,0) [and still alive], there is not a  pit in (0,0). If there is no breeze percept in (0,0), there is no pit in (0,1) If there is also no breeze in (0,1) then there is no pit in  (1,1). Therefore, there must be a pit in (2,0)
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8 Fundamental Concepts of logical  representation and reasoning Information is represented in  sentences,  which must have correct  syntax ( 1 + 2 ) * 7 = 21 vs.  2 ) + 7 = * ( 1 21 The  semantics  of a sentence defines its  truth  with respect to each  possible world – an  interpretation  assigning T or F to all  propositions W  is a model of  S  means that sentence  S  is true under  interpretation  W What do the following mean? X |= Y X entails Y Y logically follows from X
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9 Which are true?
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