Kecerdasan Buatan M. Ali Fauzi

Size: px
Start display at page:

Download "Kecerdasan Buatan M. Ali Fauzi"

Transcription

1 Kecerdasan Buatan M. Ali Fauzi

2 Artificial Intelligence M. Ali Fauzi

3 Logical Agents M. Ali Fauzi

4 In which we design agents that can form representations of the would, use a process of inference to derive new representations about the world, and use these new representations to deduce what to do.

5 TODAY

6 ~ Knowledge-based agents

7 ~ Knowledge-based agents ~ Wumpus world

8 ~ Knowledge-based agents ~ Wumpus world ~ Logic in general - models and entailment

9 ~ Knowledge-based agents ~ Wumpus world ~ Logic in general - models and entailment ~ Propositional (Boolean) logic

10 ~ Knowledge-based agents ~ Wumpus world ~ Logic in general - models and entailment ~ Propositional (Boolean) logic ~ Inference rules and theorem proving

11 Knowledge-based agents

12 Problem Solving Agent Knowledge-based Agent VS

13 Problem Solving Agent ~ choose a solution among the available possibilities ~ The knowledge is very specific and inflexible. What he "knew" about the world does not evolve ~ problem solution (initial state, successor function, goal test)

14 Knowledge-based Agent ~ smarter ~ The knowledge is very flexible. What he "knew" about the world evolve ~ can do reasoning for ; - imperfect/partial information - Choosing better action

15 Knowledge-based Agent ~ Can represent world, state, action, etc. ~ Can percept new information (and update the representation) ~ Can deduce implicit knowledge (hidden property) ~ Can deduce the best action

16 Knowledge-based Agent

17 Knowledge Base ~ The central component of a knowledge-based agent is its knowledge base, or KB

18 Knowledge-base ~ What agent knew ~ a set of sentences. ~ Each sentence is expressed in a formal language (so it can be processed) called a knowledge representation language ~ Each sentence represents some fact about the world.

19 Knowledge-base ~ There must be a way to add new sentences to the knowledge base and a way to query what is known. ~ KB (TELL) : add new sentences to the KB ~ KB (ASK) : asking what the best action based on KB

20 Inference Engine ~ Deduce new facts that can be derived from the knowledge that already exists in KB ~ update the new representation from the new fact (TELL) ~ asking what the best action based on KB (ASK)

21 Knowledge-based Agent

22 Knowledge-based Agent ~ Knowledge Level : what he knows? a robot "knows" that the A building is between E building and C building

23 Knowledge-based Agent ~ Implementation level : how is the representation - Logical sentence: between(gda,gde,gdc) - Natural language: Gedung A ada di antara gedung E dan gedung C - Building coordinate location - Filkom maps (bitmap? vector?) ~ Representation is very influential on what can be done by inference engine

24 Declarative approach to building an agent ~ Tell it what it needs to know ~ Then it can ask itself what to do - answers follow from the knowledge base

25 Procedural approach to building an agent ~ Tell it what to do ~ If the program is not correct? (error?)

26 Knowledge representation ~ Expressive: can represent facts about the world ~ Tractable: can be processed by the inference engine

27 Knowledge is power Representation + Reasoning = Intelligence!!

28 Wumpus World

29 Wumpus World PEAS description Performance measure gold +1000, death 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 Actuators Left turn, Right turn, Forward, Grab, Release, Shoot Sensors Breeze, Glitter, Smell Stench Breeze Stench Gold Stench Breeze START Breeze PIT Breeze PIT PIT Breeze Breeze B. Beckert: KI für IM p.4

30 Wumpus World Characterization Observable Deterministic Episodic Static Discrete Single agent B. Beckert: KI für IM p.5

31 Wumpus World Characterization Observable No only local perception Deterministic Episodic Static Discrete Single agent B. Beckert: KI für IM p.5

32 Wumpus World Characterization Observable Deterministic No only local perception Yes outcome of action exactly specified Episodic Static Discrete Single agent B. Beckert: KI für IM p.5

33 Wumpus World Characterization Observable Deterministic Episodic No only local perception Yes outcome of action exactly specified No sequential at the level of actions Static Discrete Single agent B. Beckert: KI für IM p.5

34 Wumpus World Characterization Observable Deterministic Episodic Static No only local perception Yes outcome of action exactly specified No sequential at the level of actions Yes wumpus and pits do not move Discrete Single agent B. Beckert: KI für IM p.5

35 Wumpus World Characterization Observable Deterministic Episodic Static Discrete No only local perception Yes outcome of action exactly specified No sequential at the level of actions Yes wumpus and pits do not move Yes Single agent B. Beckert: KI für IM p.5

36 Wumpus World Characterization Observable Deterministic Episodic Static Discrete Single agent No only local perception Yes outcome of action exactly specified No sequential at the level of actions Yes wumpus and pits do not move Yes Yes wumpus is essentially a natural feature B. Beckert: KI für IM p.5

37 Exploring a Wumpus World OK OK A OK B. Beckert: KI für IM p.6

38 Exploring a Wumpus World B OK A OK OK A B. Beckert: KI für IM p.6

39 Exploring a Wumpus World P? B OK P? A OK OK A B. Beckert: KI für IM p.6

40 Exploring a Wumpus World P? B OK P? A OK S OK A A B. Beckert: KI für IM p.6

41 Exploring a Wumpus World P P? B A OK P? OK A OK S A OK W B. Beckert: KI für IM p.6

42 Exploring a Wumpus World P P? B A OK P? OK A A OK S A OK W B. Beckert: KI für IM p.6

43 Exploring a Wumpus World P P? OK B A OK P? OK A OK OK S OK A A W B. Beckert: KI für IM p.6

44 Exploring a Wumpus World P P? OK B A OK P? OK A BGS A OK OK S OK A A W B. Beckert: KI für IM p.6

45 Problematic Situations P? Problem B A OK P? P? Breeze in (1,2) and (2,1) no safe actions A OK B A OK P? B. Beckert: KI für IM p.7

46 Problematic Situations P? Problem B A OK P? P? Breeze in (1,2) and (2,1) no safe actions Possible solution A OK B A OK P? Assuming pits uniformly distributed: (2,2) has pit with probability 0.86 (1,3) and (3,1) have pit with probab B. Beckert: KI für IM p.7

47 Problematic Situations Problem Smell in (1,1) no safe actions S A B. Beckert: KI für IM p.8

48 Problematic Situations Problem Smell in (1,1) no safe actions Possible solution S A Strategy of coercion: shoot straight ahead wumpus was there dead safe wumpus wasn t there safe B. Beckert: KI für IM p.8

49 Logic in General

50 Logic in General Logics Formal languages for representing information, such that conclusions can be drawn Syntax Defines the sentences in the language Semantics Defines the meaning of sentences; i.e., defines truth of a sentence in a world B. Beckert: KI für IM p.9

51 Example: Language of Arithmetic Syntax x + 2 y x2 + y > is a sentence is not a sentence B. Beckert: KI für IM p.10

52 Example: Language of Arithmetic Syntax x + 2 y x2 + y > is a sentence is not a sentence Semantics x + 2 y is true iff the number x + 2 is no less than the number y x + 2 y is true in a world where x = 7, y = 1 x + 2 y is false in a world where x = 0, y = 6 B. Beckert: KI für IM p.10

53 Entailment Definition Knowledge base KB entails sentence α if and only if α is true in all worlds where KB is true Notation KB = α B. Beckert: KI für IM p.11

54 Entailment Definition Knowledge base KB entails sentence α if and only if α is true in all worlds where KB is true Notation KB = α Note Entailment is a relationship between sentences (i.e., syntax) that is based on semantics B. Beckert: KI für IM p.11

55 Entailment Example The KB containing the shirt is green and the shirt is striped entails the shirt is green or the shirt is striped Example x + y = 4 entails 4 = x + y B. Beckert: KI für IM p.12

56

57 Models Intuition Models are formally structured worlds, with respect to which truth can be evaluated B. Beckert: KI für IM p.13

58 Models Intuition Models are formally structured worlds, with respect to which truth can be evaluated Definition m is a model of a sentence α if α is true in m M(α) is the set of all models of α Note KB = α if and only if M(KB) M(α) B. Beckert: KI für IM p.13

59 Models: Example KB = The shirt is green and striped α = The shirt is green M( ) M(KB) x x x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x B. Beckert: KI für IM p.14

60 Entailment in the Wumpus World Situation after detecting nothing in [1,1], moving right, breeze in [2,1]?? Consider possible models for? s (considering only pits) 3 Boolean choices A B A? 8 possible models B. Beckert: KI für IM p.15

61 Wumpus Models 2 2 PIT 1 Breeze PIT 1 Breeze PIT 2 2 PIT 1 Breeze Breeze Breeze PIT PIT 2 PIT PIT 1 Breeze PIT PIT PIT 1 Breeze Breeze PIT B. Beckert: KI für IM p.16

62 Wumpus Models 2 2 PIT 1 Breeze PIT 1 Breeze KB PIT 2 2 PIT 1 Breeze Breeze Breeze PIT PIT 2 PIT PIT 1 Breeze PIT PIT PIT 1 Breeze Breeze PIT KB = wumpus-world rules + observations B. Beckert: KI für IM p.16

63 Wumpus Models KB = α PIT 1 Breeze PIT 1 Breeze KB PIT 2 2 PIT 1 Breeze Breeze Breeze PIT PIT 2 PIT PIT 1 Breeze PIT PIT PIT 1 Breeze Breeze PIT KB = wumpus-world rules + observations α 1 = [1,2] is safe B. Beckert: KI für IM p.16

64 Wumpus Models 2 2 PIT 1 Breeze PIT 1 Breeze KB PIT 2 2 PIT 1 Breeze Breeze Breeze PIT PIT 2 PIT PIT 1 Breeze PIT PIT PIT 1 Breeze Breeze PIT KB = wumpus-world rules + observations B. Beckert: KI für IM p.16

65 Wumpus Models KB = α PIT KB 1 Breeze PIT Breeze PIT 2 2 PIT 1 Breeze Breeze Breeze PIT PIT 2 PIT PIT 1 Breeze PIT PIT PIT 1 Breeze Breeze PIT KB = wumpus-world rules + observations α 2 = [2,2] is safe B. Beckert: KI für IM p.16

66 Inference Definition KB i α means sentence α can be derived from KB by inference procedure i B. Beckert: KI für IM p.17

67 Inference Definition KB i α means sentence α can be derived from KB by inference procedure i Soundness (of i) Whenever KB i α, it is also true that KB = α Completeness (of i) Whenever KB = α, it is also true that KB i α B. Beckert: KI für IM p.17

68 Preview First-order Logic We will define a logic (first-order logic) that is expressive enough to say almost anything of interest, and for which there exists a sound and complete inference procedure. That is, the procedure will answer any question whose answer follows from what is known by the KB. B. Beckert: KI für IM p.18

69 Propositional (Boolean) Logic

70 Propositional Logic: Syntax Definition Propositional symbols A, B, P 1, P 2, ShirtIsGreen, etc. are (atomic) sentences If S,S 1,S 2 are sentences, then S (negation) S 1 S 2 (con junction) S 1 S 2 (dis junction) S 1 S 2 (implication) S 1 S 2 (equivalence) are sentences B. Beckert: KI für IM p.19

71 Propositional logic: Semantics Propositional Models Each model specifies true/false for each proposition symbol B. Beckert: KI für IM p.20

72 Propositional logic: Semantics Propositional Models Each model specifies true/false for each proposition symbol Example A B C true true false (For three symbols, there are 8 possible models) B. Beckert: KI für IM p.20

73 Propositional logic: Semantics Propositional Models Each model specifies true/false for each proposition symbol Example A B C true true false (For three symbols, there are 8 possible models) Rules for evaluating truth with respect to a model S is true iff S is false S 1 S 2 is true iff S 1 is true and S 2 is true S 1 S 2 is true iff S 1 is true or S 2 is true S 1 S 2 is true iff S 1 is false or S 2 is true S 1 S 2 is true iff S 1 and S 2 have the same truth value B. Beckert: KI für IM p.20

74 Truth Tables for Connectives A B A A B A B A B A B false false true false false true true false true true false true true false true false false false true false false true true false true true true true B. Beckert: KI für IM p.21

75 Wumpus World Sentences Propositional symbols P i, j means: B i, j means: there is a pit in [i, j] there is a breeze in [i, j] P 1,1 B 1,1 B 2,1 B. Beckert: KI für IM p.22

76 Wumpus World Sentences Propositional symbols P i, j means: B i, j means: there is a pit in [i, j] there is a breeze in [i, j] P 1,1 B 1,1 B 2,1 Sentences Pits cause breezes in adjacent squares P 1,2 (B 1,1 B 1,3 B 2,2 ) A square is breezy if and only if there is an adjacent pit B 1,1 (P 1,2 P 2,1 ) B 2,1 (P 1,1 P 2,2 P 3,1 ) B. Beckert: KI für IM p.22

77 Propositional Inference: Enumeration Method Example α = A B KB = (A C) (B C) Checking that KB = α A B C A C B C KB α false false false false false true false true false false true true true false false true false true true true false true true true B. Beckert: KI für IM p.23

78 Propositional Inference: Enumeration Method Example α = A B KB = (A C) (B C) Checking that KB = α A B C A C B C KB α false false false false false false true true false true false false false true true true true false false true true false true true true true false true true true true true B. Beckert: KI für IM p.23

79 Propositional Inference: Enumeration Method Example α = A B KB = (A C) (B C) Checking that KB = α A B C A C B C KB α false false false false true false false true true false false true false false true false true true true true true false false true true true false true true false true true false true true true true true true true B. Beckert: KI für IM p.23

80 Propositional Inference: Enumeration Method Example α = A B KB = (A C) (B C) Checking that KB = α A B C A C B C KB α false false false false true false false false true true false false false true false false true false false true true true true true true false false true true true true false true true false false true true false true true true true true true true true true B. Beckert: KI für IM p.23

81 Propositional Inference: Enumeration Method Example α = A B KB = (A C) (B C) Checking that KB = α A B C A C B C KB α false false false false true false false false false true true false false false false true false false true false true false true true true true true true true false false true true true true true false true true false false true true true false true true true true true true true true true true true B. Beckert: KI für IM p.23

82 Propositional Inference: Enumeration Method Example α = A B KB = (A C) (B C) Checking that KB = α A B C A C B C KB α false false false false true false false false false true true false false false false true false false true false true false true true true true true true true false false true true true true true false true true false false true true true false true true true true true true true true true true true B. Beckert: KI für IM p.23

83 Propositional Inference: Enumeration Method Example α = A B KB = (A C) (B C) Checking that KB = α Note A B C A C B C KB α false false false false true false false false false true true false false false false true false false true false true false true true true true true true true false false true true true true true false true true false false true true true false true true true true true true true true true true true Table has 2 n rows for n symbols B. Beckert: KI für IM p.23

84 Logical Equivalence Definition Two sentences are logically equivalent, denoted by α β iff they are true in the same models, i.e., iff: α = β and β = α B. Beckert: KI für IM p.24

85 Logical Equivalence Definition Two sentences are logically equivalent, denoted by α β iff they are true in the same models, i.e., iff: α = β and β = α Example (A B) ( B A) (contraposition) B. Beckert: KI für IM p.24

86 Logical Equivalence Theorem If α β γ is the result of replacing a subformula α of δ by β, then γ δ B. Beckert: KI für IM p.25

87 Logical Equivalence Theorem If α β γ is the result of replacing a subformula α of δ by β, then γ δ Example A B B A implies (C (A B)) D (C (B A)) D B. Beckert: KI für IM p.25

88 Important Equivalences (α β) (β α) commutativity of (α β) (β α) commutativity of ((α β) γ) (α (β γ)) associativity of ((α β) γ) (α (β γ)) associativity of (α α) α idempotence for (α α) α idempotence for α α double-negation elimination (α β) ( β α) contraposition (α β) ( α β) implication elimination (α β) ((α β) (β α)) equivalence elimination (α β) ( α β) de Morgan s rules (α β) ( α β) de Morgan s rules (α (β γ)) ((α β) (α γ)) distributivity of over (α (β γ)) ((α β) (α γ)) distributivity of over B. Beckert: KI für IM p.26

89 The Logical Constants true and false Semantics true evaluates to true in all models false evaluates to false in all models B. Beckert: KI für IM p.27

90 The Logical Constants true and false Semantics true evaluates to true in all models false evaluates to false in all models Important equivalences with true and false (α α) false (α α) true tertium non datur (α true) α (α false) false (α true) true (α false) α B. Beckert: KI für IM p.27

91 Validity Definition A sentence is valid if it is true in all models Examples A A, A A, (A (A B)) B B. Beckert: KI für IM p.28

92 Validity Definition A sentence is valid if it is true in all models Examples A A, A A, (A (A B)) B Deduction Theorem (connects inference and validity) KB = α if and only if KB α is valid B. Beckert: KI für IM p.28

93 Satisfiability Definition A sentence is satisfiable if it is true in some model Examples A B, A, A (A B) B. Beckert: KI für IM p.29

94 Satisfiability Definition A sentence is satisfiable if it is true in some model Examples A B, A, A (A B) Definition A sentence is unsatisfiable if it is true in no models, i.e., if it is not satisfiable Example A A B. Beckert: KI für IM p.29

95 Satisfiability Theorem (connects validity and unsatisfiability) α is valid if and only if α is unsatisfiable B. Beckert: KI für IM p.30

96 Satisfiability Theorem (connects validity and unsatisfiability) α is valid if and only if α is unsatisfiable Theorem (connects inference and unsatisfiability) KB = α if and only if (KB α) is unsatisfiable B. Beckert: KI für IM p.30

97 Satisfiability Theorem (connects validity and unsatisfiability) α is valid if and only if α is unsatisfiable Theorem (connects inference and unsatisfiability) KB = α if and only if (KB α) is unsatisfiable Note Validity and inference can be proved by reductio ad absurdum B. Beckert: KI für IM p.30

98 Inference Rules and Theorem Proving

99 Two Kinds of Proof Methods 1. Application of inference rules Legitimate (sound) generation of new sentences from old Construction of / search for a proof (proof = sequence of inference rule applications) B. Beckert: KI für IM p.31

100 Two Kinds of Proof Methods 1. Application of inference rules Legitimate (sound) generation of new sentences from old Construction of / search for a proof (proof = sequence of inference rule applications) Properties Typically requires translation of sentences into a normal form B. Beckert: KI für IM p.31

101 Two Kinds of Proof Methods 1. Application of inference rules Legitimate (sound) generation of new sentences from old Construction of / search for a proof (proof = sequence of inference rule applications) Properties Typically requires translation of sentences into a normal form Different kinds Tableau calculus, resolution, forward/backward chaining,... B. Beckert: KI für IM p.31

102 Two Kinds of Proof Methods 2. Model checking Construction of / search for a satisfying model B. Beckert: KI für IM p.32

103 Two Kinds of Proof Methods 2. Model checking Construction of / search for a satisfying model Different kinds Truth table enumeration (always exponential number of symbols) Improved backtracking search for models e.g.: Davis-Putnam-Logemann-Loveland Heuristic search in model space e.g.: hill-climbing algorithms (sound but incomplete) B. Beckert: KI für IM p.32

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127 Two Kinds of Proof Methods 2. Model checking Construction of / search for a satisfying model Different kinds Truth table enumeration (always exponential number of symbols) Improved backtracking search for models e.g.: Davis-Putnam-Logemann-Loveland Heuristic search in model space e.g.: hill-climbing algorithms (sound but incomplete) B. Beckert: KI für IM p.32

128 Normal Forms Literal A literal is an atomic sentence (propositional symbol), or the negation of an atomic sentence B. Beckert: KI für IM p.33

129 Normal Forms Literal A literal is an atomic sentence (propositional symbol), or the negation of an atomic sentence Clause A disjunction of literals B. Beckert: KI für IM p.33

130 Normal Forms Literal A literal is an atomic sentence (propositional symbol), or the negation of an atomic sentence Clause A disjunction of literals Conjunctive Normal Form (CNF) A conjunction of disjunctions of literals, i.e., a conjunction of clauses Example (A B) (B C D) B. Beckert: KI für IM p.33

131 Resolution Inference rule P 1 P i 1 Q P i+1... P k R 1 R j 1 Q R j+1... R n P 1 P i 1 P i+1... P k R 1 R j 1 R j+1... R n B. Beckert: KI für IM p.34

132 Resolution Inference rule P 1 P i 1 Q P i+1... P k R 1 R j 1 Q R j+1... R n P 1 P i 1 P i+1... P k R 1 R j 1 R j+1... R n Example P 1,3 P 2,2 P 2,2 P 1,3 P P? B OK A P? OK A A OK S A OK W B. Beckert: KI für IM p.34

133 Resolution Correctness theorem Resolution is sound and complete for propositional logic, i.e., given a formula α in CNF (conjunction of clauses): α is unsatisfiable iff the empty clause can be derived from α with resolution B. Beckert: KI für IM p.35

134 Conversion to CNF 0. Given B 1,1 (P 1,2 P 2,1 ) B. Beckert: KI für IM p.36

135 Conversion to CNF 0. Given B 1,1 (P 1,2 P 2,1 ) 1. Eliminate, replacing α β with (α β) (β α) (B 1,1 (P 1,2 P 2,1 )) ((P 1,2 P 2,1 ) B 1,1 ) B. Beckert: KI für IM p.36

136 Conversion to CNF 0. Given B 1,1 (P 1,2 P 2,1 ) 1. Eliminate, replacing α β with (α β) (β α) (B 1,1 (P 1,2 P 2,1 )) ((P 1,2 P 2,1 ) B 1,1 ) 2. Eliminate, replacing α β with α β ( B 1,1 P 1,2 P 2,1 ) ( (P 1,2 P 2,1 ) B 1,1 ) B. Beckert: KI für IM p.36

137 Conversion to CNF 0. Given B 1,1 (P 1,2 P 2,1 ) 1. Eliminate, replacing α β with (α β) (β α) (B 1,1 (P 1,2 P 2,1 )) ((P 1,2 P 2,1 ) B 1,1 ) 2. Eliminate, replacing α β with α β ( B 1,1 P 1,2 P 2,1 ) ( (P 1,2 P 2,1 ) B 1,1 ) 3. Move inwards using de Morgan s rules (and double-negation) ( B 1,1 P 1,2 P 2,1 ) (( P 1,2 P 2,1 ) B 1,1 ) B. Beckert: KI für IM p.36

138 Conversion to CNF 0. Given B 1,1 (P 1,2 P 2,1 ) 1. Eliminate, replacing α β with (α β) (β α) (B 1,1 (P 1,2 P 2,1 )) ((P 1,2 P 2,1 ) B 1,1 ) 2. Eliminate, replacing α β with α β ( B 1,1 P 1,2 P 2,1 ) ( (P 1,2 P 2,1 ) B 1,1 ) 3. Move inwards using de Morgan s rules (and double-negation) ( B 1,1 P 1,2 P 2,1 ) (( P 1,2 P 2,1 ) B 1,1 ) 4. Apply distributivity law ( over ) and flatten ( B 1,1 P 1,2 P 2,1 ) ( P 1,2 B 1,1 ) ( P 2,1 B 1,1 ) B. Beckert: KI für IM p.36

139 Resolution Example Given KB = (B 1,1 (P 1,2 P 2,1 )) B 1,1 α = P 1,2 B. Beckert: KI für IM p.37

140 Resolution Example Given KB = (B 1,1 (P 1,2 P 2,1 )) B 1,1 α = P 1,2 Resolution proof for KB = α Derive empty clause from KB α in CNF B. Beckert: KI für IM p.37

141 Resolution Example Given KB = (B 1,1 (P 1,2 P 2,1 )) B 1,1 α = P 1,2 Resolution proof for KB = α Derive empty clause from KB α in CNF P 2,1 B 1,1 B 1,1 P 1,2 P 2,1 P 1,2 B 1,1 B 1,1 P 1,2 B 1,1 P 1,2 B 1,1 P 1,2 P 2,1 P 1,2 B 1,1 P 2,1 B 1,1 P1,2 P 2,1 P 2,1 P 2,1 P 1,2 B. Beckert: KI für IM p.37

142 Summary Logical agents apply inference to a knowledge base to derive new information and make decisions B. Beckert: KI für IM p.38

143 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 w.r.t. models entailment: necessary truth of one sentence given another inference: deriving sentences from other sentences soundess: derivations produce only entailed sentences completeness: derivations can produce all entailed sentences B. Beckert: KI für IM p.38

144 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 w.r.t. models entailment: necessary truth of one sentence given another inference: deriving sentences from other sentences soundess: 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. B. Beckert: KI für IM p.38

145 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 w.r.t. models entailment: necessary truth of one sentence given another inference: deriving sentences from other sentences soundess: 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 sound and complete for propositional logic B. Beckert: KI für IM p.38

146 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 w.r.t. models entailment: necessary truth of one sentence given another inference: deriving sentences from other sentences soundess: 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 sound and complete for propositional logic Propositional logic lacks expressive power B. Beckert: KI für IM p.38

Introduction to Artificial Intelligence. Logical Agents

Introduction to Artificial Intelligence. Logical Agents Introduction to Artificial Intelligence Logical Agents (Logic, Deduction, Knowledge Representation) Bernhard Beckert UNIVERSITÄT KOBLENZ-LANDAU Winter Term 2004/2005 B. Beckert: KI für IM p.1 Outline Knowledge-based

More information

Logical Agents. Outline

Logical Agents. Outline Logical Agents *(Chapter 7 (Russel & Norvig, 2004)) Outline Knowledge-based agents Wumpus world Logic in general - models and entailment Propositional (Boolean) logic Equivalence, validity, satisfiability

More information

Intelligent Agents. Pınar Yolum Utrecht University

Intelligent Agents. Pınar Yolum Utrecht University Intelligent Agents Pınar Yolum p.yolum@uu.nl Utrecht University Logical Agents (Based mostly on the course slides from http://aima.cs.berkeley.edu/) Outline Knowledge-based agents Wumpus world Logic in

More information

Logical Agents. Chapter 7

Logical Agents. Chapter 7 Logical Agents Chapter 7 Outline Knowledge-based agents Wumpus world Logic in general - models and entailment Propositional (Boolean) logic Equivalence, validity, satisfiability Inference rules and theorem

More information

Logical agents. Chapter 7. Chapter 7 1

Logical agents. Chapter 7. Chapter 7 1 Logical agents Chapter 7 Chapter 7 Outline Knowledge-based agents Wumpus world Logic in general models and entailment Propositional (Boolean) logic Equivalence, validity, satisfiability Inference rules

More information

TDT4136 Logic and Reasoning Systems

TDT4136 Logic and Reasoning Systems TDT436 Logic and Reasoning Systems Chapter 7 - Logic gents Lester Solbakken solbakke@idi.ntnu.no Norwegian University of Science and Technology 06.09.0 Lester Solbakken TDT436 Logic and Reasoning Systems

More information

EE562 ARTIFICIAL INTELLIGENCE FOR ENGINEERS

EE562 ARTIFICIAL INTELLIGENCE FOR ENGINEERS EE562 ARTIFICIAL INTELLIGENCE FOR ENGINEERS Lecture 10, 5/9/2005 University of Washington, Department of Electrical Engineering Spring 2005 Instructor: Professor Jeff A. Bilmes Logical Agents Chapter 7

More information

Inf2D 06: Logical Agents: Knowledge Bases and the Wumpus World

Inf2D 06: Logical Agents: Knowledge Bases and the Wumpus World Inf2D 06: Logical Agents: Knowledge Bases and the Wumpus World School of Informatics, University of Edinburgh 26/01/18 Slide Credits: Jacques Fleuriot, Michael Rovatsos, Michael Herrmann Outline Knowledge-based

More information

7. Logical Agents. COMP9414/ 9814/ 3411: Artificial Intelligence. Outline. Knowledge base. Models and Planning. Russell & Norvig, Chapter 7.

7. Logical Agents. COMP9414/ 9814/ 3411: Artificial Intelligence. Outline. Knowledge base. Models and Planning. Russell & Norvig, Chapter 7. COMP944/984/34 6s Logic COMP944/ 984/ 34: rtificial Intelligence 7. Logical gents Outline Knowledge-based agents Wumpus world Russell & Norvig, Chapter 7. Logic in general models and entailment Propositional

More information

Class Assignment Strategies

Class Assignment Strategies Class Assignment Strategies ì Team- A'ack: Team a'ack ì Individualis2c: Search for possible ì Poli2cal: look at others and make decision based on who is winning, who is loosing, and conversa;on ì Emo2on

More information

Artificial Intelligence

Artificial Intelligence Artificial Intelligence Propositional Logic Marc Toussaint University of Stuttgart Winter 2015/16 (slides based on Stuart Russell s AI course) Outline Knowledge-based agents Wumpus world Logic in general

More information

Revised by Hankui Zhuo, March 21, Logical agents. Chapter 7. Chapter 7 1

Revised by Hankui Zhuo, March 21, Logical agents. Chapter 7. Chapter 7 1 Revised by Hankui Zhuo, March, 08 Logical agents Chapter 7 Chapter 7 Outline Wumpus world Logic in general models and entailment Propositional (oolean) logic Equivalence, validity, satisfiability Inference

More information

Logical Agents. Knowledge based agents. Knowledge based agents. Knowledge based agents. The Wumpus World. Knowledge Bases 10/20/14

Logical Agents. Knowledge based agents. Knowledge based agents. Knowledge based agents. The Wumpus World. Knowledge Bases 10/20/14 0/0/4 Knowledge based agents Logical Agents Agents need to be able to: Store information about their environment Update and reason about that information Russell and Norvig, chapter 7 Knowledge based agents

More information

Logic. proof and truth syntacs and semantics. Peter Antal

Logic. proof and truth syntacs and semantics. Peter Antal Logic proof and truth syntacs and semantics Peter Antal antal@mit.bme.hu 10/9/2015 1 Knowledge-based agents Wumpus world Logic in general Syntacs transformational grammars Semantics Truth, meaning, models

More information

Chapter 7 R&N ICS 271 Fall 2017 Kalev Kask

Chapter 7 R&N ICS 271 Fall 2017 Kalev Kask Set 6: Knowledge Representation: The Propositional Calculus Chapter 7 R&N ICS 271 Fall 2017 Kalev Kask Outline Representing knowledge using logic Agent that reason logically A knowledge based agent Representing

More information

Logical Agents: Propositional Logic. Chapter 7

Logical Agents: Propositional Logic. Chapter 7 Logical Agents: Propositional Logic Chapter 7 Outline Topics: Knowledge-based agents Example domain: The Wumpus World Logic in general models and entailment Propositional (Boolean) logic Equivalence, validity,

More information

Artificial Intelligence

Artificial Intelligence Artificial Intelligence Propositional Logic Marc Toussaint University of Stuttgart Winter 2016/17 (slides based on Stuart Russell s AI course) Motivation: Most students will have learnt about propositional

More information

Last update: March 4, Logical agents. CMSC 421: Chapter 7. CMSC 421: Chapter 7 1

Last update: March 4, Logical agents. CMSC 421: Chapter 7. CMSC 421: Chapter 7 1 Last update: March 4, 00 Logical agents CMSC 4: Chapter 7 CMSC 4: Chapter 7 Outline Knowledge-based agents Wumpus world Logic in general models and entailment Propositional (oolean) logic Equivalence,

More information

Logical Agent & Propositional Logic

Logical Agent & Propositional Logic Logical Agent & Propositional Logic Berlin Chen 2005 References: 1. S. Russell and P. Norvig. Artificial Intelligence: A Modern Approach. Chapter 7 2. S. Russell s teaching materials Introduction The representation

More information

Logical Agents. Outline

Logical Agents. Outline ogical gents Chapter 6, Ie Chapter 7 Outline Knowledge-based agents Wumpus world ogic in general models and entailment ropositional (oolean) logic Equivalence, validity, satisfiability Inference rules

More information

Artificial Intelligence Chapter 7: Logical Agents

Artificial Intelligence Chapter 7: Logical Agents Artificial Intelligence Chapter 7: Logical Agents Michael Scherger Department of Computer Science Kent State University February 20, 2006 AI: Chapter 7: Logical Agents 1 Contents Knowledge Based Agents

More information

Logical Agent & Propositional Logic

Logical Agent & Propositional Logic Logical Agent & Propositional Logic Berlin Chen Department of Computer Science & Information Engineering National Taiwan Normal University References: 1. S. Russell and P. Norvig. Artificial Intelligence:

More information

Lecture 6: Knowledge 1

Lecture 6: Knowledge 1 rtificial Intelligence, CS, Nanjing University Spring, 08, Yang Yu Lecture 6: Knowledge http://cs.nju.edu.cn/yuy/course_ai8.ash Previously... Basic ability: search Path-based search Iterative-improvement

More information

Lecture 7: Logical Agents and Propositional Logic

Lecture 7: Logical Agents and Propositional Logic Lecture 7: Logical Agents and Propositional Logic CS 580 (001) - Spring 2018 Amarda Shehu Department of Computer Science George Mason University, Fairfax, VA, USA March 07, 2018 Amarda Shehu (580) 1 1

More information

CS 188: Artificial Intelligence Spring 2007

CS 188: Artificial Intelligence Spring 2007 CS 188: Artificial Intelligence Spring 2007 Lecture 8: Logical Agents - I 2/8/2007 Srini Narayanan ICSI and UC Berkeley Many slides over the course adapted from Dan Klein, Stuart Russell or Andrew Moore

More information

Logical Agents. Chapter 7

Logical Agents. Chapter 7 Logical Agents Chapter 7 Outline Knowledge-based agents Wumpus world Logic in general - models and entailment Propositional (Boolean) logic Equivalence, validity, satisfiability Inference rules and theorem

More information

CS 380: ARTIFICIAL INTELLIGENCE PREDICATE LOGICS. Santiago Ontañón

CS 380: ARTIFICIAL INTELLIGENCE PREDICATE LOGICS. Santiago Ontañón CS 380: RTIFICIL INTELLIGENCE PREDICTE LOGICS Santiago Ontañón so367@drexeledu Summary of last day: Logical gents: The can reason from the knowledge they have They can make deductions from their perceptions,

More information

CS 380: ARTIFICIAL INTELLIGENCE LOGICAL AGENTS. Santiago Ontañón

CS 380: ARTIFICIAL INTELLIGENCE LOGICAL AGENTS. Santiago Ontañón CS 380: RTIFICIL INTELLIGENCE LOGICL GENTS Santiago Ontañón so367@dreel.edu Summary so far: What is I? Rational gents Problem solving: Systematic search Uninformed search: DFS, BFS, ID Informed search:

More information

CS 771 Artificial Intelligence. Propositional Logic

CS 771 Artificial Intelligence. Propositional Logic CS 771 Artificial Intelligence Propositional Logic Why Do We Need Logic? Problem-solving agents were very inflexible hard code every possible state E.g., in the transition of 8-puzzle problem, knowledge

More information

CS 380: ARTIFICIAL INTELLIGENCE

CS 380: ARTIFICIAL INTELLIGENCE CS 380: RTIFICIL INTELLIGENCE PREDICTE LOGICS 11/8/2013 Santiago Ontañón santi@cs.drexel.edu https://www.cs.drexel.edu/~santi/teaching/2013/cs380/intro.html Summary of last day: Logical gents: The can

More information

A simple knowledge-based agent. Logical agents. Outline. Wumpus World PEAS description. Wumpus world characterization. Knowledge bases.

A simple knowledge-based agent. Logical agents. Outline. Wumpus World PEAS description. Wumpus world characterization. Knowledge bases. simple knowledge-based agent ogical agents Chapter 7 function K-gent( percept) returns an action static: K, a knowledge base t, a counter, initially, indicating time Tell(K, ake-ercept-entence( percept,

More information

Proof Methods for Propositional Logic

Proof Methods for Propositional Logic Proof Methods for Propositional Logic Logical equivalence Two sentences are logically equivalent iff they are true in the same models: α ß iff α β and β α Russell and Norvig Chapter 7 CS440 Fall 2015 1

More information

Logical agents. Chapter 7. Chapter 7 1

Logical agents. Chapter 7. Chapter 7 1 Logical agents Chapter 7 Chapter 7 1 Outline Knowledge-based agents Logic in general models and entailment Propositional (oolean) logic Equivalence, validity, satisfiability Inference rules and theorem

More information

Propositional Logic: Logical Agents (Part I)

Propositional Logic: Logical Agents (Part I) Propositional Logic: Logical Agents (Part I) This lecture topic: Propositional Logic (two lectures) Chapter 7.1-7.4 (this lecture, Part I) Chapter 7.5 (next lecture, Part II) Next lecture topic: First-order

More information

Title: Logical Agents AIMA: Chapter 7 (Sections 7.4 and 7.5)

Title: Logical Agents AIMA: Chapter 7 (Sections 7.4 and 7.5) B.Y. Choueiry 1 Instructor s notes #12 Title: Logical Agents AIMA: Chapter 7 (Sections 7.4 and 7.5) Introduction to Artificial Intelligence CSCE 476-876, Fall 2018 URL: www.cse.unl.edu/ choueiry/f18-476-876

More information

Logic. Introduction to Artificial Intelligence CS/ECE 348 Lecture 11 September 27, 2001

Logic. Introduction to Artificial Intelligence CS/ECE 348 Lecture 11 September 27, 2001 Logic Introduction to Artificial Intelligence CS/ECE 348 Lecture 11 September 27, 2001 Last Lecture Games Cont. α-β pruning Outline Games with chance, e.g. Backgammon Logical Agents and thewumpus World

More information

Outline. Logic. Knowledge bases. Wumpus world characteriza/on. Wumpus World PEAS descrip/on. A simple knowledge- based agent

Outline. Logic. Knowledge bases. Wumpus world characteriza/on. Wumpus World PEAS descrip/on. A simple knowledge- based agent Outline Logic Dr. Melanie Mar/n CS 4480 October 8, 2012 Based on slides from hap://aima.eecs.berkeley.edu/2nd- ed/slides- ppt/ Knowledge- based agents Wumpus world Logic in general - models and entailment

More information

Outline. Logical Agents. Logical Reasoning. Knowledge Representation. Logical reasoning Propositional Logic Wumpus World Inference

Outline. Logical Agents. Logical Reasoning. Knowledge Representation. Logical reasoning Propositional Logic Wumpus World Inference Outline Logical Agents ECE57 Applied Artificial Intelligence Spring 007 Lecture #6 Logical reasoning Propositional Logic Wumpus World Inference Russell & Norvig, chapter 7 ECE57 Applied Artificial Intelligence

More information

CS:4420 Artificial Intelligence

CS:4420 Artificial Intelligence CS:4420 rtificial Intelligence Spring 2018 Logical gents Cesare Tinelli The University of Iowa Copyright 2004 18, Cesare Tinelli and Stuart Russell a a These notes were originally developed by Stuart Russell

More information

INF5390 Kunstig intelligens. Logical Agents. Roar Fjellheim

INF5390 Kunstig intelligens. Logical Agents. Roar Fjellheim INF5390 Kunstig intelligens Logical Agents Roar Fjellheim Outline Knowledge-based agents The Wumpus world Knowledge representation Logical reasoning Propositional logic Wumpus agent Summary AIMA Chapter

More information

Logical Agents (I) Instructor: Tsung-Che Chiang

Logical Agents (I) Instructor: Tsung-Che Chiang Logical Agents (I) Instructor: Tsung-Che Chiang tcchiang@ieee.org Department of Computer Science and Information Engineering National Taiwan Normal University Artificial Intelligence, Spring, 2010 編譯有誤

More information

Foundations of Artificial Intelligence

Foundations of Artificial Intelligence Foundations of Artificial Intelligence 7. Propositional Logic Rational Thinking, Logic, Resolution Wolfram Burgard, Maren Bennewitz, and Marco Ragni Albert-Ludwigs-Universität Freiburg Contents 1 Agents

More information

Foundations of Artificial Intelligence

Foundations of Artificial Intelligence Foundations of Artificial Intelligence 7. Propositional Logic Rational Thinking, Logic, Resolution Joschka Boedecker and Wolfram Burgard and Bernhard Nebel Albert-Ludwigs-Universität Freiburg May 17, 2016

More information

CS 331: Artificial Intelligence Propositional Logic I. Knowledge-based Agents

CS 331: Artificial Intelligence Propositional Logic I. Knowledge-based Agents CS 331: Artificial Intelligence Propositional Logic I 1 Knowledge-based Agents Can represent knowledge And reason with this knowledge How is this different from the knowledge used by problem-specific agents?

More information

Knowledge-based Agents. CS 331: Artificial Intelligence Propositional Logic I. Knowledge-based Agents. Outline. Knowledge-based Agents

Knowledge-based Agents. CS 331: Artificial Intelligence Propositional Logic I. Knowledge-based Agents. Outline. Knowledge-based Agents Knowledge-based Agents CS 331: Artificial Intelligence Propositional Logic I Can represent knowledge And reason with this knowledge How is this different from the knowledge used by problem-specific agents?

More information

Outline. Logical Agents. Logical Reasoning. Knowledge Representation. Logical reasoning Propositional Logic Wumpus World Inference

Outline. Logical Agents. Logical Reasoning. Knowledge Representation. Logical reasoning Propositional Logic Wumpus World Inference Outline Logical Agents ECE57 Applied Artificial Intelligence Spring 008 Lecture #6 Logical reasoning Propositional Logic Wumpus World Inference Russell & Norvig, chapter 7 ECE57 Applied Artificial Intelligence

More information

Propositional Logic: Logical Agents (Part I)

Propositional Logic: Logical Agents (Part I) Propositional Logic: Logical Agents (Part I) First Lecture Today (Tue 21 Jun) Read Chapters 1 and 2 Second Lecture Today (Tue 21 Jun) Read Chapter 7.1-7.4 Next Lecture (Thu 23 Jun) Read Chapters 7.5 (optional:

More information

The Wumpus Game. Stench Gold. Start. Cao Hoang Tru CSE Faculty - HCMUT

The Wumpus Game. Stench Gold. Start. Cao Hoang Tru CSE Faculty - HCMUT The Wumpus Game Stench Stench Gold Stench Start 1 The Wumpus Game Stench in the square containing the wumpus and in the directly adjacent squares in the squares directly adjacent to a pit Glitter in the

More information

Foundations of Artificial Intelligence

Foundations of Artificial Intelligence Foundations of Artificial Intelligence 7. Propositional Logic Rational Thinking, Logic, Resolution Joschka Boedecker and Wolfram Burgard and Frank Hutter and Bernhard Nebel Albert-Ludwigs-Universität Freiburg

More information

CS 4700: Foundations of Artificial Intelligence

CS 4700: Foundations of Artificial Intelligence CS 4700: Foundations of Artificial Intelligence Bart Selman selman@cs.cornell.edu Module: Knowledge, Reasoning, and Planning Part 2 Logical Agents R&N: Chapter 7 1 Illustrative example: Wumpus World (Somewhat

More information

7. Propositional Logic. Wolfram Burgard and Bernhard Nebel

7. Propositional Logic. Wolfram Burgard and Bernhard Nebel Foundations of AI 7. Propositional Logic Rational Thinking, Logic, Resolution Wolfram Burgard and Bernhard Nebel Contents Agents that think rationally The wumpus world Propositional logic: syntax and semantics

More information

Chương 3 Tri th ức và lập luận

Chương 3 Tri th ức và lập luận Chương 3 Tri thức và lập luận Nội dung chính chương 3 Lecture 1 Lecture 2 Lecture 3,4 I. Logic ngôn ngữ của tư duy II. Logic mệnh đề (cú pháp, ngữ nghĩa, sức mạnh biểu diễn, các thuật toán suy diễn) III.

More information

Adversarial Search & Logic and Reasoning

Adversarial Search & Logic and Reasoning CSEP 573 Adversarial Search & Logic and Reasoning CSE AI Faculty Recall from Last Time: Adversarial Games as Search Convention: first player is called MAX, 2nd player is called MIN MAX moves first and

More information

Logical Agents. Santa Clara University

Logical Agents. Santa Clara University Logical Agents Santa Clara University Logical Agents Humans know things Humans use knowledge to make plans Humans do not act completely reflexive, but reason AI: Simple problem-solving agents have knowledge

More information

Introduction to Intelligent Systems

Introduction to Intelligent Systems Logical Agents Objectives Inference and entailment Sound and complete inference algorithms Inference by model checking Inference by proof Resolution Forward and backward chaining Reference Russel/Norvig:

More information

Introduction to Intelligent Systems

Introduction to Intelligent Systems Logical Agents Objectives Inference and entailment Sound and complete inference algorithms Inference by model checking Inference by proof Resolution Forward and backward chaining Reference Russel/Norvig:

More information

Knowledge base (KB) = set of sentences in a formal language Declarative approach to building an agent (or other system):

Knowledge base (KB) = set of sentences in a formal language Declarative approach to building an agent (or other system): Logic Knowledge-based agents Inference engine Knowledge base Domain-independent algorithms Domain-specific content Knowledge base (KB) = set of sentences in a formal language Declarative approach to building

More information

7 LOGICAL AGENTS. OHJ-2556 Artificial Intelligence, Spring OHJ-2556 Artificial Intelligence, Spring

7 LOGICAL AGENTS. OHJ-2556 Artificial Intelligence, Spring OHJ-2556 Artificial Intelligence, Spring 109 7 LOGICAL AGENS We now turn to knowledge-based agents that have a knowledge base KB at their disposal With the help of the KB the agent aims at maintaining knowledge of its partially-observable environment

More information

Lecture 7: Logic and Planning

Lecture 7: Logic and Planning Lecture 7: Logic and Planning Planning and representing knowledge Logic in general Propositional (Boolean) logic and its application to planning COMP-424, Lecture 8 - January 30, 2013 1 What is planning?

More information

Artificial Intelligence. Propositional logic

Artificial Intelligence. Propositional logic Artificial Intelligence Propositional logic Propositional Logic: Syntax Syntax of propositional logic defines allowable sentences Atomic sentences consists of a single proposition symbol Each symbol stands

More information

Knowledge- Based Agents. Logical Agents. Knowledge Base. Knowledge- Based Agents 10/7/09

Knowledge- Based Agents. Logical Agents. Knowledge Base. Knowledge- Based Agents 10/7/09 Knowledge- Based Agents Logical Agents CISC481/681, Lecture #8 Ben Cartere>e A knowledge- based agent has a base of knowledge about the world It uses that base to make new inferences about the world From

More information

Logic & Logic Agents Chapter 7 (& background)

Logic & Logic Agents Chapter 7 (& background) Lecture Notes, Advanced Artificial Intelligence (SCOM7341) Sina Institute, University of Birzeit 2 nd Semester, 2012 Advanced Artificial Intelligence (SCOM7341) Logic & Logic Agents Chapter 7 (& background)

More information

Introduction to Arti Intelligence

Introduction to Arti Intelligence Introduction to Arti Intelligence cial Lecture 4: Constraint satisfaction problems 1 / 48 Constraint satisfaction problems: Today Exploiting the representation of a state to accelerate search. Backtracking.

More information

Logic: Propositional Logic (Part I)

Logic: Propositional Logic (Part I) Logic: Propositional Logic (Part I) Alessandro Artale Free University of Bozen-Bolzano Faculty of Computer Science http://www.inf.unibz.it/ artale Descrete Mathematics and Logic BSc course Thanks to Prof.

More information

Price: $25 (incl. T-Shirt, morning tea and lunch) Visit:

Price: $25 (incl. T-Shirt, morning tea and lunch) Visit: Three days of interesting talks & workshops from industry experts across Australia Explore new computing topics Network with students & employers in Brisbane Price: $25 (incl. T-Shirt, morning tea and

More information

Logical Agents. Course material: Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 7

Logical Agents. Course material: Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 7 Logical Agents CE417: Introduction to Artificial Intelligence Sharif University of Technology Soleymani In which we design agents that can form representations of a complex world, use a process of inference

More information

Logical Agents. Soleymani. Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 7

Logical Agents. Soleymani. Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 7 Logical Agents CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2016 Soleymani Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 7 Knowledge-based agents

More information

Agenda. Artificial Intelligence. Reasoning in the Wumpus World. The Wumpus World

Agenda. Artificial Intelligence. Reasoning in the Wumpus World. The Wumpus World Agenda Artificial Intelligence 10. Propositional Reasoning, Part I: Principles How to Think About What is True or False 1 Introduction Álvaro Torralba Wolfgang Wahlster 2 Propositional Logic 3 Resolution

More information

Logic & Logic Agents Chapter 7 (& Some background)

Logic & Logic Agents Chapter 7 (& Some background) Lecture Notes on Logic & Logic Agents University of Birzeit, Palestine 2013 Artificial Intelligence Logic & Logic Agents Chapter 7 (& Some background) Dr. Mustafa Jarrar Sina Institute, University of Birzeit

More information

Description Logics. Foundations of Propositional Logic. franconi. Enrico Franconi

Description Logics. Foundations of Propositional Logic.   franconi. Enrico Franconi (1/27) Description Logics Foundations of Propositional Logic Enrico Franconi franconi@cs.man.ac.uk http://www.cs.man.ac.uk/ franconi Department of Computer Science, University of Manchester (2/27) Knowledge

More information

Inference in Propositional Logic

Inference in Propositional Logic Inference in Propositional Logic Deepak Kumar November 2017 Propositional Logic A language for symbolic reasoning Proposition a statement that is either True or False. E.g. Bryn Mawr College is located

More information

Logical Inference. Artificial Intelligence. Topic 12. Reading: Russell and Norvig, Chapter 7, Section 5

Logical Inference. Artificial Intelligence. Topic 12. Reading: Russell and Norvig, Chapter 7, Section 5 rtificial Intelligence Topic 12 Logical Inference Reading: Russell and Norvig, Chapter 7, Section 5 c Cara MacNish. Includes material c S. Russell & P. Norvig 1995,2003 with permission. CITS4211 Logical

More information

Propositional Logic: Methods of Proof (Part II)

Propositional Logic: Methods of Proof (Part II) Propositional Logic: Methods of Proof (Part II) You will be expected to know Basic definitions Inference, derive, sound, complete Conjunctive Normal Form (CNF) Convert a Boolean formula to CNF Do a short

More information

CS:4420 Artificial Intelligence

CS:4420 Artificial Intelligence CS:4420 Artificial Intelligence Spring 2018 Propositional Logic Cesare Tinelli The University of Iowa Copyright 2004 18, Cesare Tinelli and Stuart Russell a a These notes were originally developed by Stuart

More information

Propositional Logic: Methods of Proof (Part II)

Propositional Logic: Methods of Proof (Part II) Propositional Logic: Methods of Proof (Part II) This lecture topic: Propositional Logic (two lectures) Chapter 7.1-7.4 (previous lecture, Part I) Chapter 7.5 (this lecture, Part II) (optional: 7.6-7.8)

More information

CSCI 5582 Artificial Intelligence. Today 9/28. Knowledge Representation. Lecture 9

CSCI 5582 Artificial Intelligence. Today 9/28. Knowledge Representation. Lecture 9 CSCI 5582 Artificial Intelligence Lecture 9 Jim Martin Today 9/28 Review propositional logic Reasoning with Models Break More reasoning Knowledge Representation A knowledge representation is a formal scheme

More information

Propositional Logic: Methods of Proof. Chapter 7, Part II

Propositional Logic: Methods of Proof. Chapter 7, Part II Propositional Logic: Methods of Proof Chapter 7, Part II Inference in Formal Symbol Systems: Ontology, Representation, ti Inference Formal Symbol Systems Symbols correspond to things/ideas in the world

More information

CS 4700: Artificial Intelligence

CS 4700: Artificial Intelligence CS 4700: Foundations of Artificial Intelligence Fall 2017 Instructor: Prof. Haym Hirsh Lecture 12 Prelim Tuesday, March 21 8:40-9:55am Statler Auditorium Homework 2 To be posted on Piazza 4701 Projects:

More information

COMP3702/7702 Artificial Intelligence Week 5: Search in Continuous Space with an Application in Motion Planning " Hanna Kurniawati"

COMP3702/7702 Artificial Intelligence Week 5: Search in Continuous Space with an Application in Motion Planning  Hanna Kurniawati COMP3702/7702 Artificial Intelligence Week 5: Search in Continuous Space with an Application in Motion Planning " Hanna Kurniawati" Last week" Main components of PRM" Collision check for a configuration"

More information

Logical Agents. Soleymani. Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 7

Logical Agents. Soleymani. Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 7 Logical Agents CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2018 Soleymani Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 7 Wumpus world Wumpus

More information

CSC242: Intro to AI. Lecture 11. Tuesday, February 26, 13

CSC242: Intro to AI. Lecture 11. Tuesday, February 26, 13 CSC242: Intro to AI Lecture 11 Propositional Inference Propositional Inference Factored Representation Splits a state into variables (factors, attributes, features, things you know ) that can have values

More information

COMP219: Artificial Intelligence. Lecture 20: Propositional Reasoning

COMP219: Artificial Intelligence. Lecture 20: Propositional Reasoning COMP219: Artificial Intelligence Lecture 20: Propositional Reasoning 1 Overview Last time Logic for KR in general; Propositional Logic; Natural Deduction Today Entailment, satisfiability and validity Normal

More information

Lecture Overview [ ] Introduction to Artificial Intelligence COMP 3501 / COMP Lecture 6. Motivation. Logical Agents

Lecture Overview [ ] Introduction to Artificial Intelligence COMP 3501 / COMP Lecture 6. Motivation. Logical Agents Lecture Overview [7.1-7.4] COMP 3501 / COMP 4704-4 Lecture 6 Prof. JGH 318 Logical Agents Wumpus World Propositional Logic Inference Theorem Proving via model checking Motivation Existing techniques help

More information

Inference Methods In Propositional Logic

Inference Methods In Propositional Logic Lecture Notes, Artificial Intelligence ((ENCS434)) University of Birzeit 1 st Semester, 2011 Artificial Intelligence (ENCS434) Inference Methods In Propositional Logic Dr. Mustafa Jarrar University of

More information

COMP219: Artificial Intelligence. Lecture 19: Logic for KR

COMP219: Artificial Intelligence. Lecture 19: Logic for KR COMP219: Artificial Intelligence Lecture 19: Logic for KR 1 Overview Last time Expert Systems and Ontologies Today Logic as a knowledge representation scheme Propositional Logic Syntax Semantics Proof

More information

Agents that reason logically

Agents that reason logically Artificial Intelligence Sanguk Noh Logical Agents Agents that reason logically A Knowledge-Based Agent. function KB-Agent (percept) returns an action Tell(KB, Make-Percept-Sentence(percept,t)) action Ask(KB,

More information

Inference Methods In Propositional Logic

Inference Methods In Propositional Logic Lecture Notes, Advanced Artificial Intelligence (SCOM7341) Sina Institute, University of Birzeit 2 nd Semester, 2012 Advanced Artificial Intelligence (SCOM7341) Inference Methods In Propositional Logic

More information

Propositional Logic: Methods of Proof (Part II)

Propositional Logic: Methods of Proof (Part II) Propositional Logic: Methods of Proof (Part II) You will be expected to know Basic definitions Inference, derive, sound, complete Conjunctive Normal Form (CNF) Convert a Boolean formula to CNF Do a short

More information

CS 7180: Behavioral Modeling and Decision- making in AI

CS 7180: Behavioral Modeling and Decision- making in AI CS 7180: Behavioral Modeling and Decision- making in AI Review of Propositional Logic Prof. Amy Sliva September 7, 2012 Outline General properties of logics Syntax, semantics, entailment, inference, and

More information

AI Programming CS S-09 Knowledge Representation

AI Programming CS S-09 Knowledge Representation AI Programming CS662-2013S-09 Knowledge Representation David Galles Department of Computer Science University of San Francisco 09-0: Overview So far, we ve talked about search, which is a means of considering

More information

20/c/applet/more.html Local Beam Search The best K states are selected.

20/c/applet/more.html Local Beam Search The best K states are selected. Have some fun Checker: http://www.cs.caltech.edu/~vhuang/cs 20/c/applet/more.html 1 Local Beam Search Run multiple searches to find the solution The best K states are selected. Like parallel hill climbing

More information

Part 1: Propositional Logic

Part 1: Propositional Logic Part 1: Propositional Logic Literature (also for first-order logic) Schöning: Logik für Informatiker, Spektrum Fitting: First-Order Logic and Automated Theorem Proving, Springer 1 Last time 1.1 Syntax

More information

Logical Agents. Administrative. Thursday: Midterm 1, 7p-9p. Next Tuesday: DOW1013: Last name A-M DOW1017: Last name N-Z

Logical Agents. Administrative. Thursday: Midterm 1, 7p-9p. Next Tuesday: DOW1013: Last name A-M DOW1017: Last name N-Z Logical Agents Mary Herchenhahn, mary-h.com EECS 492 February 2 nd, 2010 Administrative Thursday: Midterm 1, 7p-9p DOW1013: Last name A-M DOW1017: Last name N-Z Next Tuesday: PS2 due PS3 distributed---

More information

Logic and Inferences

Logic and Inferences Artificial Intelligence Logic and Inferences Readings: Chapter 7 of Russell & Norvig. Artificial Intelligence p.1/34 Components of Propositional Logic Logic constants: True (1), and False (0) Propositional

More information

Propositional inference, propositional agents

Propositional inference, propositional agents ropositional inference, propositional agents Chapter 7.5 7.7 Chapter 7.5 7.7 1 Outline Inference rules and theorem proving forward chaining backward chaining resolution Efficient model checking algorithms

More information

COMP219: Artificial Intelligence. Lecture 19: Logic for KR

COMP219: Artificial Intelligence. Lecture 19: Logic for KR COMP219: Artificial Intelligence Lecture 19: Logic for KR 1 Overview Last time Expert Systems and Ontologies Today Logic as a knowledge representation scheme Propositional Logic Syntax Semantics Proof

More information

Artificial Intelligence Knowledge Representation I

Artificial Intelligence Knowledge Representation I Artificial Intelligence Knowledge Representation I Agents that reason logically knowledge-based approach implement agents that know about their world and reason about possible courses of action needs to

More information

Overview. Knowledge-Based Agents. Introduction. COMP219: Artificial Intelligence. Lecture 19: Logic for KR

Overview. Knowledge-Based Agents. Introduction. COMP219: Artificial Intelligence. Lecture 19: Logic for KR COMP219: Artificial Intelligence Lecture 19: Logic for KR Last time Expert Systems and Ontologies oday Logic as a knowledge representation scheme Propositional Logic Syntax Semantics Proof theory Natural

More information

Deliberative Agents Knowledge Representation I. Deliberative Agents

Deliberative Agents Knowledge Representation I. Deliberative Agents Deliberative Agents Knowledge Representation I Vasant Honavar Bioinformatics and Computational Biology Program Center for Computational Intelligence, Learning, & Discovery honavar@cs.iastate.edu www.cs.iastate.edu/~honavar/

More information

Artificial Intelligence

Artificial Intelligence Torralba and Wahlster Artificial Intelligence Chapter 10: Propositional Reasoning, Part I 1/46 Artificial Intelligence 10. Propositional Reasoning, Part I: Principles How to Think About What is True or

More information