EA C461 – Artificial Intelligence Logical Agent

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

To discuss… Knowledge-based agents Wumpus world Logic in general Models and entailment Propositional Logic : Review Vimal EA C461- Artificial Intelligence

Knowledge based Agents Partially Observable Environments & Knowledge and Reasoning Cope up with infinite variety of possible actions with the help of common sense. Flexibility Accept new tasks in the form of explicitly defined goals & achieve competence by being told/learned Vimal EA C461- Artificial Intelligence

Knowledge bases Knowledge base = set of sentences in a formal language Then it can Ask itself what to do - answers should follow from the KB Agents can be viewed at the knowledge level i.e., what they know, regardless of how implemented Implementation level i.e., data structures in KB and algorithms that manipulate them Vimal EA C461- Artificial Intelligence

A simple knowledge-based agent The agent must be able to: Represent states, actions, etc. Incorporate new percepts Update internal representations of the world Deduce hidden properties of the world Deduce appropriate actions Vimal EA C461- Artificial Intelligence

A simple knowledge-based agent MAKE-PERCEPT-SENTENCE (percept, t) Takes a percept and a time and return a sentence asserting that the agent perceived the percept at the given time MAKE-ACTION-QUERY (time) Takes as an input, time, and returns a sentence that asks what action should be performed at that time Vimal EA C461- Artificial Intelligence

A simple knowledge-based agent Build a KB by simply TELLing it what it need to know Declarative approach Vs. Procedural Approach Vimal EA C461- Artificial Intelligence

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 Vimal EA C461- Artificial Intelligence

Exploring a wumpus world Current Percept : [None, None, None, None, None] [Stench/None, Breeze/None, Glitter/None, Bump/None, Scream/None] Vimal EA C461- Artificial Intelligence

Exploring a wumpus world Current Percept : [Stench, None, None, None, None] [Stench/None, Breeze/None, Glitter/None, Bump/None, Scream/None] Vimal EA C461- Artificial Intelligence

Exploring a wumpus world Current Percept : [Stench, None, None, None, None] [Stench/None, Breeze/None, Glitter/None, Bump/None, Scream/None] Vimal EA C461- Artificial Intelligence

Exploring a wumpus world Current Percept : [None, Breeze, None, None, None] [Stench/None, Breeze/None, Glitter/None, Bump/None, Scream/None] Vimal EA C461- Artificial Intelligence

Exploring a wumpus world Current Percept : [None, Breeze, None, None, None] [Stench/None, Breeze/None, Glitter/None, Bump/None, Scream/None] Vimal EA C461- Artificial Intelligence

Exploring a wumpus world Current Percept : [None, None, None, None, None] [Stench/None, Breeze/None, Glitter/None, Bump/None, Scream/None] Vimal EA C461- Artificial Intelligence

Exploring a wumpus world Vimal EA C461- Artificial Intelligence

Exploring a wumpus world Current Percept : [None, None, None, None, None] [Stench/None, Breeze/None, Glitter/None, Bump/None, Scream/None] Vimal EA C461- Artificial Intelligence

Logic in general Logics are formal languages for representing information such that conclusions can be drawn Syntax defines the sentences in the language Semantics define the "meaning" of sentences; i.e., define truth of a sentence in a world Entailment means that a sentence logically follows from other sentence KB╞ α Knowledge base KB entails sentence α if and only if α is true in all worlds where KB is true E.g., the KB containing “the Giants won” and “the Reds won” entails “Either the Giants won or the Reds won” E.g., x+y = 4 entails 4 = x+y Entailment is a relationship between sentences (i.e., syntax) that is based on semantics Vimal EA C461- Artificial Intelligence

Models Logicians typically think in terms of models, which are formally structured worlds with respect to which truth can be evaluated We say m is a model of a sentence α if α is true in m M(α) is the set of all models of α Then KB ╞ α iff M(KB)  M(α) Vimal EA C461- Artificial Intelligence

Entailment in the wumpus world Situation after detecting nothing in [1,1], moving right, breeze in [2,1] Consider possible models for KB assuming only pits 3 Boolean choices  8 possible models Vimal EA C461- Artificial Intelligence

Wumpus models Vimal EA C461- Artificial Intelligence

Wumpus models KB = wumpus-world rules + observations Vimal EA C461- Artificial Intelligence

Wumpus models KB = wumpus-world rules + observations α1 = "[1,2] has no pit", KB ╞ α1, proved by model checking Vimal EA C461- Artificial Intelligence

Wumpus models α2 = "[2,2] has no pit ", KB ╞ α2 Vimal EA C461- Artificial Intelligence

Inference KB ├i α = sentence α can be derived from KB by procedure i Soundness: i is sound if whenever KB ├i α, it is also true that KB╞ α Completeness: i is complete if whenever KB╞ α, it is also true that KB ├i α Vimal EA C461- Artificial Intelligence

Review: Propositional logic: Syntax Propositional logic is the simplest logic – illustrates basic ideas The proposition symbols P1, P2 etc are sentences If S is a sentence, S is a sentence (negation) If S1 and S2 are sentences, S1  S2 is a sentence (conjunction) If S1 and S2 are sentences, S1  S2 is a sentence (disjunction) If S1 and S2 are sentences, S1  S2 is a sentence (implication) If S1 and S2 are sentences, S1  S2 is a sentence (biconditional) Vimal EA C461- Artificial Intelligence

Review: Propositional logic: Semantics Each model specifies true/false for each proposition symbol E.g. P1,2 P2,2 P3,1 false true false With these symbols, 8 possible models, can be enumerated automatically. Rules for evaluating truth with respect to a model m: S is true iff S is false S1  S2 is true iff S1 is true and S2 is true S1  S2 is true iff S1is true or S2 is true S1  S2 is true iff S1 is false or S2 is true i.e., is false iff S1 is true and S2 is false S1  S2 is true iff S1S2 is true and S2S1 is true Simple recursive process evaluates an arbitrary sentence, e.g., P1,2  (P2,2  P3,1) = true  (true  false) = true  true = true Vimal EA C461- Artificial Intelligence

Review: Truth tables for connectives Vimal EA C461- Artificial Intelligence

Wumpus world sentences Let Pi,j be true if there is a pit in [i, j]. Let Bi,j be true if there is a breeze in [i, j].  P1,1 B1,1 B2,1 "Pits cause breezes in adjacent squares" B1,1  (P1,2  P2,1) B2,1  (P1,1  P2,2  P3,1) Vimal EA C461- Artificial Intelligence

Truth tables for inference Vimal EA C461- Artificial Intelligence

Inference by enumeration Depth-first enumeration of all models is sound and complete For n symbols, time complexity is O(2n), space complexity is O(n) Vimal EA C461- Artificial Intelligence

Logical equivalence Two sentences are logically equivalent} iff true in same models: α ≡ ß iff α╞ β and β╞ α Vimal EA C461- Artificial Intelligence

Validity and satisfiability A sentence is valid if it is true in all models, e.g., True, A A, A  A, (A  (A  B))  B Validity is connected to inference via the Deduction Theorem: KB ╞ α if and only if (KB  α) is valid A sentence is satisfiable if it is true in some model e.g., A B, C A sentence is unsatisfiable if it is true in no models e.g., AA Satisfiability is connected to inference via the following: KB ╞ α if and only if (KB α) is unsatisfiable Vimal EA C461- Artificial Intelligence