A toy world for logical exploration The Wumpus example

D. Goforth, fall Wumpus world  A four by four cave with locations identified by coordinates (3,4), etc.  Agent is at a location, facing a particular direction (L,R,D,U) Agent starts at (1,1) facing R >

D. Goforth, fall Wumpus world  In the cave is: A wumpus that smells  It can kill the agent if at same location  It can be killed by the agent shooting an arrow if facing the wumpus. When the wumpus dies, it SCREAMs ^

D. Goforth, fall Wumpus world  In the cave are: 3 Pits. Breezes blow from pits.  If an agent steps into a pit, it falls to its death. A heap of gold that glitters ^

D. Goforth, fall Wumpus world  Agent goal: get gold and get out alive  Agent actions: Move forward one square in current direction (Fwd) Turn left or right 90 o (TL,TR) Shoot arrow in current direction Grab gold  Agent perceptions at each location: [Stench, Breeze, Glitter, Bump, Scream]

D. Goforth, fall Wumpus world  Cave is created randomly (location of wumpus, pits and gold)  Perception / action loop  Agent must construct a model – knowledge base about the cave – as it tries to achieve its goal >

D. Goforth, fall Wumpus world knowledge  General knowledge (known at start) Location and direction Living Grab and holding Wumpus and stench, shooting, scream, life Pits and breeze Gold and glitter Movement and location, direction and bumps Starting state of agent Goal  Facts (not known) Location of wumpus, pits, gold

D. Goforth, fall Wumpus world in propositional logic  Facts are propositions: e.g., W 44 “Wumpus is at square (4,4) 96 propositions (16 each for wumpus, stench, pit, breeze, gold, glitter) to represent a particular cave  General knowledge in sentences: e.g., W 44  (S 44  S 43  S 34 ) “if the wumpus is at (4,4), there is stench at (4,4), (4,3) and (3,4)” “many” sentences

D. Goforth, fall Wumpus world in propositional logic  Facts that may change: Location of agent, direction of agent Agent holding gold Agent has shot arrow Agent, wumpus are alive  timed logic  proliferation of propositions

D. Goforth, fall Wumpus world in FOL  the objects in the environment terms: constants, variables, functions  constants: times: 0, 1, 2,... headings: R, L, D, U coordinates: 1, 2, 3, 4 locations: 16 squares percepts: Stench, Breeze, Glitter, Bump, Scream, None actions: Turn(Left), Turn(Right), Forward, Grab, Shoot Agent, Wumpus

D. Goforth, fall Wumpus world in FOL  the objects in the environment terms: constants, variables, functions  functions: Square(x,y) // [x,y] p.259 Home(Wumpus) Perception(s, b, g, h, y) // [s, b, g, h, y] p.258 Heading(t), Location(t)

D. Goforth, fall Wumpus world in FOL  the basic knowledge atomic sentences: predicates, term=term  predicates: (true or false) properties (of one term/object)  Breezy(t) // agent feeling breeze at time t  Breeze(s) // breeze blowing on square s  Pit(s), Gold(s), etc.  Time(x) // object x is a time  Coordinate(x), Action(x), Heading(x), etc.

D. Goforth, fall Wumpus world in FOL  the basic knowledge atomic sentences: predicates, term=term  predicates: (true or false) relations (of multiple terms/objects)  At(s,t) // agent on square s at time t*  Adjacent (r,s) // squares r and s are adjacent  Alive(x,t) // x is alive at time t  Percept(p,t) // perception at time t  BestAction(a,t) // action a to take at time t *compare with p.259

D. Goforth, fall Wumpus world in FOL  the basic knowledge atomic sentences: predicates, term=term  term = term: (true or false) Home(Wumpus) = [3,3] Heading(5) = U

D. Goforth, fall Wumpus world in FOL  the knowledge base General knowledge Facts that are fixed Facts that may change over time Atomic sentences Compound sentences

D. Goforth, fall Wumpus world in FOL  the knowledge base General knowledge Facts that are constant Facts that may change over time

D. Goforth, fall Exploring Wumpus world in FOL Initial conditions: known unknown After first perception P 0, action A 0 : knownnew unknown P0P0 A0A0

D. Goforth, fall Exploring Wumpus world in FOL After first perception P 0, action A 0 : knownnew unknown P0P0 A0A0 After second perception P 1, action A 1 P1P1 A1A1

D. Goforth, fall Exploring Wumpus world in FOL Timed atomic sentences: Initial conditions At([1,1],0) Heading(R,0) Alive(Agent,0) Alive(Wumpus,0) then First perception: Percept([Stench,None, None, None, None],0)

D. Goforth, fall Exploring Wumpus world in FOL Percept([Stench, None, None, None, None],0) Understanding what is perceived ∀ b ∀ g ∀ h ∀ y ∀ t Percept([Stench,b,g, h, y],t) ⇒ Stinky(t) ∀ s ∀ g ∀ h ∀ y ∀ t Percept([s,None,g, h, y],t) ⇒  Glittery(t) Stinky(0)  Glittery(0) ∀ r ∀ t Stinky(t)  At(r,t) ⇒ Stinks(r) ∀ r ∀ t  Glittery(t)  At(r,t) ⇒  Glitters(r) Stinks([1,1])  Glitters ([1,1]) Fixed knowledge

D. Goforth, fall Exploring Wumpus world in FOL Updating timed knowledge: All atomic sentences may be different from t to t+1 BUT Most are the same UNLESS An action changes them ∀ r ∀ t At(r,t)  (  BestAction(Forward,t)  (Bumped(t+1)) ⇒ At(r,t+1) ∀ t Screams(t) ⇒  Alive(Wumpus,t) Time t Time t+1

D. Goforth, fall Exploring Wumpus world in FOL Deciding the best action (incomplete description here): Need to reason about the cave conditions Diagnostic rules (p.259) ∀ s Breezy(s) ⇒ ∃ r Adjacent(r,s)  Pit(r) Causal rules (p.260) ∀ r Pit(r) ⇒ [ ∀ s Adjacent(r,s) ⇒ Breezy(s)]