CS 416 Artificial Intelligence Lecture Lecture 13 13 First Order First Order Logic Logic Chapter Chapter 88 Guest Speaker Topics Topics in in Optimal Optimal Control Control Minimax Minimax Control Control and and Game Game Theory Theory March March 28 28thth 22 p m p m OLS OLS 005 005 Onesimo Onesimo Hernandez Lerma Hernandez Lerma Department Department of of Mathematics Mathematics CINVESTAV IPN CINVESTAV IPN Mexico Mexico City City This This is is aa nontechnical nontechnical introduction introduction mainly mainly thru thru examples examples to to some some recent recent topics topics in in control control and and game game theory theory including including adaptive adaptive control control minimax minimax control control a k a a k a worst case worst case control control or or games games against against nature nature partially partially observable observable systems systems a k a a k a controlled controlled hidden hidden Markov Markov models models cooperative cooperative and and noncooperative noncooperative game game equilibria equilibria etc etc First order logic We We saw saw how how propositional propositional logic logic can can create create intelligent intelligent behavior behavior But But propositional propositional logic logic is is aa poor poor representation representation for for complex complex environments environments First order First order logic logic is is aa more more expressive expressive and and powerful powerful representation representation Diagnostic Rules Rules Rules leading leading from from observed observed effects effects to to hidden hidden causes causes After After you ve you ve observed observed something something this this rule rule offers offers an an explanation explanation These These rules rules explain explain what what happened happened in in the the past past Breezy Breezy implies implies pits pits Not Not breezy breezy implies implies no no pits pits Combining Combining Causal Rules Some Some hidden hidden property property causes causes percepts percepts to to be be generated generated These These are are predictions predictions of of perceptions perceptions you you expect expect to to have have in in the the future future given given current current conditions conditions A A pit pit causes causes adjacent adjacent squares squares to to be be breezy breezy IfIf all all squares squares adjacent adjacent to to aa square square aa pitless pitless itit will will not not be be breezy breezy Causal Rules The The causal causal rules rules formulate formulate aa model model Knowledge Knowledge of of how how the the environment environment operates operates Model Model can can be be very very useful useful and and important important and and replace replace straightforward straightforward diagnostic diagnostic approaches approaches Conclusion If If the the axioms axioms correctly correctly and and completely completely describe describe the the way way the the world world works works and and the the way way percepts percepts are are produced produced then then any any complete complete logical logical inference inference procedure procedure will will infer infer the the strongest strongest possible possible description description of of the the world world state state given given the the available available percepts percepts The The agent agent designer designer can can focus focus on on getting getting the the knowledge knowledge right right without without worrying worrying about about the the processes processes of of deduction deduction Discussion of models Let s Let s think think about about how how we we use use models models every every day day Daily Daily stock stock prices prices Seasonal Seasonal stock stock prices prices Seasonal Seasonal temperatures temperatures Annual Annual temperatures temperatures Knowledge Engineering Understand Understand aa particular particular domain domain How How does does stock stock trading trading work work Learn Learn what what concepts concepts are are important important in in the the domain domain features features Buyer Buyer confidence confidence strength strength of of the the dollar dollar company company earnings earnings interest interest rate rate Create Create aa formal formal representation representation of of the the objects objects and and relations relations in in the the domain domain Forall Forall stocks stocks price price low low confidence confidence high high profitability profitability high high Identify the task What What is is the the range range of of inputs inputs and and outputs outputs Will Will the the stock stock trading trading system system have have to to answer answer questions questions about about the the weather weather Perhaps Perhaps ifif you re you re buying buying wheat wheat futures futures Must Must the the agent agent store store daily daily temperatures temperatures or or can can itit use use another another agent agent Assemble the relevant knowledge You You know know what what information information is is relevant relevant How How can can you you accumulate accumulate the the information information Not Not formal formal description description of of knowledge knowledge at at this this point point Just Just principled principled understanding understanding of of where where information information resides resides Formalize the knowledge Decide Decide on on vocabulary vocabulary of of predicates predicates functions functions and and constants constants Beginning Beginning to to map map domain domain into into aa programmatic programmatic structure structure You re You re selecting selecting an an ontology ontology A A particular particular theory theory of of how how the the domain domain can can be be simplified simplified and and represented represented at at its its basic basic elements elements Mistakes Mistakes here here cause cause big big problems problems Encode general knowledge Write Write down down axioms axioms for for all all vocabulary vocabulary terms terms Define Define the the meaning meaning of of terms terms Errors Errors will will be be discovered discovered and and knowledge knowledge assembly assembly and and formalization formalization steps steps repeated repeated Map to this particular instance Encode Encode aa description description of of the the specific specific problem problem instance instance Should Should be be an an easy easy step step Write Write simple simple atomic atomic sentences sentences Derived Derived