Wumpus World Propositional Logic

Wumpus World PEAS description Performance measure gold +1000, death -1000 -1 per step, -10 for using the arrow Environment Squares adjacent to wumpus are smelly Squares adjacent to pit are breezy Glitter iff gold is in the same square Shooting kills wumpus if you are facing it Shooting uses up the only arrow Grabbing picks up gold if in same square Releasing drops the gold in same square Sensors: Stench, Breeze, Glitter, Bump, Scream Actuators: Left turn, Right turn, Forward, Grab, Release, Shoot

Wumpus world characterization Single-agent? Yes – Wumpus is essentially a natural feature

Wumpus world sentences Let Pi,j be true if there is a pit in [i, j]; Pi,j Let Bi,j be true if there is a breeze in [i, j]; Bi,j  P1,1 , B1,1 , B2,1 "Pits cause breezes in adjacent squares" Bi, j  (Pi-1, j  Pi, j-1  Pi, j+1  Pj+1, j) B1,1  (P1,2  P2,1) B2,1  (P1,1  P2,2  P3,1) “Wumpus causes stench in adjacent squares“ (???)

Wumpus world sentences “No Stench means there is no wumpus in adjacent Square"  Si, j  (Wi-1, j  Wi, j-1  Wi, j+1  Wj+1, j)  S2,2  (W1,2  W2,1  W2,3  W3,2) “No Breeze means there is no pits in adjacent Square“  Bi, j  (Pi-1, j  Pi, j-1  Pi, j+1  Pj+1, j)  B2,2  (P1,2  P2,1  P2,3  P3,2)

Exploring Wumpuss World -1 A Agent Knowldege Ke mana agent akan berjalan dengan aman?  W1,1,  P1,1 , B1,1 , S1,1 B1,1  (P1,2  P2,1) S1,1  (W1,2  W2,1) Perlu Inferensi. Untuk kasus ini dapat digunakan resolusi.

Contoh Resolusi (Last Slide) ¬P V ¬Q V R ¬R 2 P ¬P V ¬Q 1 ¬T V Q ¬Q 4 ¬T T 5

Contoh Resolusi KB = (B1,1  (P1,2 P2,1))  B1,1 α = P1,2

Exploring Wumpuss World -2 A Agent Knowldege Setelah Inferensi di posisi (1,1) W1,2 W2,1 P1,2  P2,1,  W1,1,  P1,1 , B1,1 , S1,1 Dapat dikembangkan menjadi: B1,1  (P1,2  P2,1) S1,1  (W1,2  W2,1) Agent dapat memutuskan berjalan ke kanan atau ke atas

Exploring Wumpuss World -3 ok ok S W? P? A P? ok ok B ok ok B P A P? P? Di (2,1), agent mendeteksi BREEZE. B2,1  (P1,1  P2,2  P3,1) agent mendapatkan pengetahuan baru bahwa ada PIT di (2,2) atau di (3,1), tidak ada langkah valid selain kembali ke (1,1) Agent kembali ke (1,1) dan melanjutkan ke (1,2) Di (1,2) agent mendeteksi adanya STENCH dan tidak ada BREEZE S1,2  (W1,1  W2,2  W13) Tugas1: Lakukan Inferensi apakah (2,2) Aman!

Finding Wumpuss P TUGAS 2: (2,2) aman: P2,2 ,  W2,2 Agent sekarang mempunyai pengetahuan: P1,1 ,  W1,1 , P1,2 ,  W1,2, P2,1 ,  W2,1, P2,2 ,  W2,2 W? ok S ok W? A P? ok ok B P P? TUGAS 2: Dengan knowledge base yang dimiliki, temukanlah di mana wumpuss berada?

Exploring Wumpuss World Agent Perspective

Pro dan Kontra  Propositional logic is declarative  Propositional logic allows partial/disjunctive/negated information (unlike most data structures and databases)  Propositional logic is compositional: meaning of B1,1  P1,2 is derived from meaning of B1,1 and of P1,2  Meaning in propositional logic is context-independent (unlike natural language, where meaning depends on context)  Propositional logic has very limited expressive power (unlike natural language) E.g., cannot say "pits cause breezes in adjacent squares“ except by writing one sentence for each square

Kelemahan Proposisional Logic  Satu proposisi untuk satu statemen. Tidak bisa menunjukkan obyek dan hubungan antar obyek  Terlalu banyak proposisi yang harus digunakan. Metode Lain: Logika Predikat (First Order Logic)