1Principles of Information and Database Management198:336Week 2 – Jan 31Matthew StoneTodayLogic and RepresentationEntities in IMDBRelationships in IMDBOverview of Design Methodology2Function of information managerStart from a formal languageSet of sentencesEach is a symbolic structure with an intended interpretation – as informationSupport operationsTELL a sentence to the IMGive the IM the information that S is trueFunction of information managerStart from a formal languageSet of sentencesEach is a symbolic structure with an intended interpretation – or as an information needSupport operationsASK a question to the IMExpress an information need to the IMGet back a sentence representing the IM’s answer3Pictorial viewTELLINFORMATIONMANAGERASKInformation Management as LogicFormal languages are sentences and proofsIM is a set of logical formulas STELL : gives the IM a logical formula j– The IM gets the information that j is trueASK : gives the IM a logical formula j– The IM should report its evidence about j– Answer is a set of proofs S®j4Abstract exampleStep 1: IM = ÆAbstract exampleStep 1: IM = ÆStep 2: TELL(IM, f(a,c))– Give IM the information that the individual represented by a stands in the relation represented by f to the individual represented by c.5Abstract exampleStep 1: IM = ÆStep 2: TELL(IM, f(a,c))– Give IM the information that the individual represented by a stands in the relation represented by f to the individual represented by c.– Result: IM = { f(a,c) }Abstract exampleStep 1: IM = ÆStep 2: TELL(IM, f(a,c))Step 3: ASK(IM, f(X,c))– Ask IM to report proofs that show that some individual X stands in the relation represented by f to the individual represented by c.6Abstract exampleStep 1: IM = ÆStep 2: TELL(IM, f(a,c))Step 3: ASK(IM, f(X,c))– Ask IM to report proofs that show that some individual X stands in the relation represented by f to the individual represented by c.– IM answers with a single proof of the formf(a,c) ® f(X,c) [X=a]Abstract exampleStep 1: IM = ÆStep 2: TELL(IM, f(a,c))Step 3: ASK(IM, f(X,c))Step 4: TELL(IM, f(b,c))– Give IM the information that the individual represented by b stands in the relation represented by f to the individual represented by c.7Abstract exampleStep 1: IM = ÆStep 2: TELL(IM, f(a,c))Step 3: ASK(IM, f(X,c))Step 4: TELL(IM, f(b,c))– Give IM the information that the individual represented by b stands in the relation represented by f to the individual represented by c.– Result: IM = { f(a,c), f(b,c) }Abstract exampleStep 1: IM = ÆStep 2: TELL(IM, f(a,c))Step 3: ASK(IM, f(X,c))Step 4: TELL(IM, f(b,c))Step 5: ASK(IM, f(X,c))– Ask IM to report proofs that show that some individual X stands in the relation represented by f to the individual represented by c.8Abstract exampleStep 1: IM = ÆStep 2: TELL(IM, f(a))Step 3: ASK(IM, f(X))Step 4: TELL(IM, f(b))Step 5: ASK(IM, f(X))– IM answers with two proofsf(a,c) ® f(X,c) [X=a]f(b,c) ® f(X,c) [X=b]The key ideaCausality + consequence Þ correspondence– If you design your system so that you only TELL the IM true facts (causality)– And if your system answers queries using correct logical inference (consequence)– Then all the answers you get from the IM are true (correspondence)9A big ideaUnderlies AI– How can we build a system that acts like it knows stuff?Underlies psychology– How can neural events in the brain be related to our ideas about the world?Shows up in philosophy– How is it possible, in principle, for sentences or thoughts to be true or false?PhotographsWhat’s a photograph about?1011It turns out…This is a photograph of Tobu World Square– A theme park in Nikko, Japan– 1/25 scale models of famous buildings• Eiffel tower, Great Pyramid, Empire State Building, Forbidden City, Leaning Tower of Pisa, etc.– Taken by Matt Machlis on vacation • Thanks, google!12Here’s an actual picture of St Peter’s Basilica in Vatican CityGoogled from Steve NatranA general fact about representationA representation is a causal record– Some entity interacted with the representer– A new structure was created there– This structure is patterned after the entity– If there’s enough detail, something bizarre would have to be going on for the structure to have been created any other way.13Same goes for mental representationsThought experiment: “Twin Earth”– Due to philosopher Hilary PutnamMental representationsScience fiction scenario– Imagine another planet exactly like Earth except that in place of H20 they have another substance XYZ.– You have an exact counterpart over there(a twin!)– When you are thinking about H20, your twin is thinking about…XYZ.14Same goes for IMDB designDatabases have symbols– Formalized expressions, such asbinary sequences, integers, character strings, or logical atoms.These are designed to correspond to world– Entities, properties, relationships, etc.This works as a representation– Provided causal connections are there.Example: bar codes15Products are labeledLabels are read very reliablyA fixed number of bars per character– To read code, each bar must be seen. Most characters are invalid– If size of one of the bars is misread,you will get an illegal character.16Codes identify product typesCompanies are part of UCC– “Uniform code council”–UPCsare NSC + MFC + PC + CD– NSC = number system code– UCC Member companies can get a UPC manufacturer code (MFC)– Each company makes up its product codes (PC)– Then there is a check digitResultWhen you scan a product, it reliably causes system to register a codethat (thus) represents the product typeSystem’s code 0-71641-81803-3 represents Sanford “Expo” white board cleaner.17NoteWe say – System’s code 0-71641-81803-3 represents Sanford “Expo” white board cleaner.Symbol: 0-71641-81803-3corresponds toReal-world stuff: Sanford “Expo” cleanerRememberMeanings ain’t in the head!– Photograph doesn’t know what it’s a photograph of.– Twin Earther thinks watery thoughts, but they’re about XYZ.– Database doesn’t necessarily have information about 0-71641-81803-3.18What does the system know?System needs explicit information to work with 0-71641-81803-3– Manufacturer name is “Sanford”– Product name is “Expo”– Product type is “cleaner”– Price is $5.99–Etc.AsideCheck outhttp://www.upcdatabase.com/For 56MB of product details.Normally, manufacturers supply UPC data to trading