EA C461 – Artificial Intelligence Logical Agent S.P.Vimal http://discovery.bits-pilani.ac.in/~vimalsp/1910AI/

To discuss… Propositional Inference in Wumpus World Circuit Based Agent Vimal EA C461- Artificial Intelligence

Wumpus World Let us look at sentences in the WW- KB The agent begins its exploration from a square known to be safe R1: P1,1 R2: W1,1 For every square [x,y], if the agent perceives breeze… R3 - R18: Bx,y  (Px,y+1  Px,y-1  Px+1,y  Px-1,y) Vimal EA C461- Artificial Intelligence

Wumpus World For every square [x,y], if the agent perceives stench… R19 – R34: Bx,y  (Px,y+1  Px,y-1  Px+1,y  Px-1,y) How do we express there is exactly one wumpus We can represent it 2 sentences There is at least one wumpus R35: W1,1  W1,2  …  W4,4 Vimal EA C461- Artificial Intelligence

Wumpus World We have used 64 distinct symbols in the KB For any two squares, one must be wumpus-free This should be stated for every pair of squares [n (n-1)] / 2 number of sentences R36 :W1,1  W1,2 R37 : W1,1  W1,3 … R155 : _________ We have used 64 distinct symbols in the KB Vimal EA C461- Artificial Intelligence

Wumpus World –Agent Program Additional Program Variables Vimal EA C461- Artificial Intelligence

Wumpus World –Agent Program ASK  Entailment computation TT-Entails -264 rows- DPLL / WALKSAT performs better For a large ww, the number of sentences in the KB will be huge WE could not capture the property “breeze in a square indicates pit in at least one of directly adjacent square” Can we keep track of location and orientation within the KB? Vimal EA C461- Artificial Intelligence

Location, Orientation in WW Can we add propositions like L1,1 Λ FacingRight Λ Forward  L2,1 KB will entail both L1,1 and L2,1. How??? What we intended to capture is this L1,1 (t) Λ FacingRight Λ Forward  L2,1(t+1) FacingRight Λ TurnLeft (t)  FacingUp(t+1) For every times steps, one such statements??? Assuming the problem is solvable in 100 time steps  10 thousands of additional sentences Vimal EA C461- Artificial Intelligence

Circuit Based Agents Reflex agent with state Percepts are inputs to sequential circuit Network of gates and registers Output are registers corresponding to actions Circuits are evaluated in a dataflow model Value stored at each proposition symbol gives the truth value of the corresponding symbol at the current time t. Vimal EA C461- Artificial Intelligence

Circuit Based Agents Vimal EA C461- Artificial Intelligence

Circuit Based Agents Vimal EA C461- Artificial Intelligence

Circuit Based Agents… Location??? One register for each Lxy. Agent is in [1,1] at t if The agent was in [1,1] at t-1 and has no moved, tried but bump It was at [1,2], facing down and moved forward It was at [2,1] facing left and move forward Vimal EA C461- Artificial Intelligence

Circuit Based Agents… Location??? Vimal EA C461- Artificial Intelligence

Circuit Based Agents… a problem What will be the initial truth value contained in B4,4 The agent cannot set a truth value for it Need to represent unknown Use knowledge propositions K(B4,4) , K(רB4,4) Vimal EA C461- Artificial Intelligence

Inference based agents vs. Circuit based Agents Declarative vs. Procedural Conciseness Computational Efficiency Completeness Vimal EA C461- Artificial Intelligence

Summary Logical agents apply inference to a knowledge base to derive new information and make decisions Basic concepts of logic: syntax: formal structure of sentences semantics: truth of sentences wrt models entailment: necessary truth of one sentence given another inference: deriving sentences from other sentences soundness: derivations produce only entailed sentences completeness: derivations can produce all entailed sentences Wumpus world requires the ability to represent partial and negated information, reason by cases, etc. Resolution is complete for propositional logic Forward, backward chaining are linear-time, complete for Horn clauses Propositional logic lacks expressive power Vimal EA C461- Artificial Intelligence