Knowledge Representation Use of logic
Artificial agents need Knowledge and reasoning power Can combine GK with current percepts Build up KB incrementally Logic primary vehicle K always definite ( T/F)
Problem for a robot If red light is ON or it is morning shift or supervisor absent then door is locked. If door is locked it implies that the red light is turned ON or it is morning shift or the supervisor is absent If load is small in size or load is light then the conveyor belt moves If the conveyor belt is moving then it means the load has a small size or load is light The Red light is off, the Conveyor belt is not moving and the Door is locked. The robot wants to know if the load is heavy (not light).
Robot needs a Knowledge Base and reasoning ability
Knowledge base Central component of a K based agent Set of sentences INFERENCE – Deriving new info from old Language to enable building KB
Interpretations Language semantics defines TRUTH of each sentence w.r.t. each possible world
Similarity with CSP Constraint solving is a form of Logical reasoning Constraint languages: LOGICS
Wff and logical reasoning Entailment: – Sentence follows logically from another sentence KB |= s iff in every model in which KB is true, s is also true
Inference algorithm Enumerate the models Check if s is true in every model (interpretation) for which KB is also true Backtracking search – recursively assign values to variables Exponential complexity
definitions Validity Tautology Deduction theorem Satisfiability inconsistancy
Reasoning patterns in Propositional logic
Inference rules Modus Ponens And Elimination Standard logical equivalances – De Morgan – Contra positive – Distributive laws – Associative laws
Deduction With the knowledge base that the robot has, and what it currently perceives (more knowledge added to the KB), the robot wants to deduce that the load is not light
Knowledge that robot has If red light is ON or it is morning shift or supervisor absent then door is locked. If door is locked it implies that the red light is turned ON or it is morning shift or the supervisor is absent If load is small in size or load is light then the conveyor belt moves If the conveyor belt is moving then it means the load has a small size or load is light
Observations by the robot Red light is off Conveyor belt is not moving Door is locked
What the robot wants to establish? The load is not light ( or in other words it is heavy)
Knowledge + Observation (K.B.) If red light is ON or it is morning shift or supervisor absent then door is locked. If door is locked it implies that the red light is turned ON or it is morning shift or the supervisor is absent If load is small in size or load is light then the conveyor belt moves If the conveyor belt is moving then it means the load has a small size or load is light Red light is off Conveyor belt is not moving Door is locked
Propositions P: red light is ON M: it is morning shift N: supervisor absent D: door is locked. Q: load is small in size R: load is light B: the conveyor belt is moving
Next? Now generate wffs and start the inference process
Steps to help the robot (inferencing) Consider a relevant rule for conveyor belt Use And-elimination Use contra-positive relation Use modus ponens Use de morgan’s law
PROOF? PROOF: Sequence of application of Inference rules. Finding proofs is like finding solutions to search problems. Successor function generates all possible application of inference rules In worst case, search for proof would be as bad as enumerating all the models Some irrelevant propositions can be ignored to speed up search.
Monotonicity Set of entailed sentences can only increase as info is added to KB. Rules can be applied wherever suitable
Resolution What about completeness? Can everything be inferred? Resolution rule forms basis for a family of complete inference procedures.
Refutation completeness Resolution can be used to either CONFIRM or REFUTE a sentence
Artificial Intelligence
Intelligent?
What is intelligence? computational part of the ability to achieve goals in the world