of the original thinkers in semiotics were Charles. Sanders Peirce [4] and Ferdinand de Saussure [5]. Each of these thinkers posited a basic theory of signs and ...
Practical Semiotics:AFormal Theory Adam Pease,Ian Niles Teknowledge 1810 Embarcadero Palo Alto, CA 94303 USA [apease iniles]@teknowledge.com |
Abstract Weaddressthedevelopmentoafpracticaltheoryof semioticswithinthecontextoftheIEEEStandard UpperOntologyeffort. Thetheoryhastheformof ofpredicatesandothertermsthatareaxiomatized firstorderlogic. Wearguethatthistheoryisu forrepresentingmanyofthesubtletiesofsemantic representationthatarelikelytoariseinthecont interoperabilityoinformation f systems.
aset in fficient extof
Keywords:ontology, semiotics, logic
1.SUO Scope And Purpose Recognizingboththeneedforlargeontologies andtheneedforanopenprocessleadingtfree, oa publicstandard,adiversegroupofcollaborators fromthefieldsofengineering,philosophy,and informationsciencehavecometogethertowork onaStandardUpperOntology(SUO). TheSUO emaillistwascreatedinMayo2000 f and, shortly afterthatdate,hadover150subscribers. The Project Authorization Request (PAR),which detailsthescopeandpurposefortheSUOeffort wassubmittedtotheIEEEinOctoberandwas approved aworking s groupP1600.1iD n ecember. TheStandardUpperOntology(SUO)will providedefinitionsforgeneral-purposeterms,and itwillactasafoundationformorespecific domainontologies. Itisestimatedthatiw t ill eventuallycontainbetween1000and2500terms androughlytendefinitionalstatementsforeach term. TheSUO willhavethefollowing purposes: - Designonew f knowledgebasesand databases. Developerscancraftnew knowledgeanddefinenew dataelements in termsof caommonontology, and thereby gainsomedegreeof interoperability withother compliant systems.
- Reuse/integration olegacy f databases. Dataelementsfrom existing systemscan bemappedjustoncetcommon ao ontology. - Integration odomain-specific f ontologies. Such ontologies(ifthey arecompliant with theSUO)willbeabletointeroperate (to somedegree)by virtueoshared f terms and definitions. Therearetwoofficial“starterdocuments” approvedbytheSUOemaillist.Theformal semiotictheorytobeaddressedinthispaperis contained in one of those documents, the SuggestedUpperMergedOntology(SUMO)[1]. TheSUMOusesasimplifiedversionofKIF[2] calledSUO-KIF[3]asthelanguageforspecifying theontology.
2.SemioticsBackground Semioticsitshetheoryosigns, f andihas t aroused considerableinterestinawiderangeoffields, including linguistics, anthropology, literary criticism,politicalscience,andphilosophy. Two oftheoriginalthinkersinsemioticswereCharles SandersPeirce[4]andFerdinanddS e aussure[5]. Eachofthesethinkerspositedabasictheoryof signsandtheirmeanings.AccordingtoDe Saussure,asignismadeupoftwoelements,the signifiedandthesignifier. Thesignifieristhe soundoimage r thatstandsforsomethingelse,e.g. theword“bachelor”,andthesignifiedisthe conceptrepresentedbythesignifier,e.g.the conceptofbeinganunmarried,adultmale. Peirce complicatedthispicturesomewhatbyintroducing anadditionalelement. Accordingtohim,asign consistsoR af epresentamen(correspondingtoDe Saussure’s signifier), an Interpretant (correspondingtoDS e aussure’ssignified),andan
Object,thethingorsetofthingsintheactual world to which theRepresentamenrefers. Inthispaper,wewillfleshoutthesebasic picturesosfemioticsinthecontextofontological engineering. In particular, we will propose set a of formallyspecifiedpredicates,whichwebelieve canrepresentthatpartofsemioticsthatisrelevant to semantic interoperability between heterogeneous information systems. It is importanttopointoutthatthisconcernleavesout muchthatconventionallygoesundertheheading ofsemiotics. Anotherhelpfulreferenceinthis areai[s8]. However,wearenotconcernedwith branches of semiotics that address the interpretationofsigns,pictorialsemiotics[6], discourseanalysis,northebroaderapplicationof semioticsinculturalor politicalcontexts[7].
3.SUMO Semiotics TheSUOemaillisthascreatedawell-definedset ofsemioticspredicatesthatarenot,asfarasthe authorsotfhis paperareaware,availableinany otherpubliclyavailableontology. Themembers ofthelistwereabletoagreeonthisstockof predicates (and their corresponding formal definitions)afterworkingthroughsomeconcrete examplesrelatingtointellectual propertyissues. These examples concerned the appropriate representationothe f following items: • Thefictionalcharacter Hamlet • An editionothe f play Hamlet • A copy othe f play Hamlet • A performanceoHamlet f • AperformanceofHamletcapturedon video • The timelessinformationalcontentofthe play Hamlet Beforewediscusstheseexamplesandtheir representation,we’lldefineallofthepredicates thatweredevelopedotnheir basis. Note that these definitionswillbesomewhatinformal.The complete,formaldefinitionsofthesepredicates andtheirsupportingconceptsareavailableintext and hyperlinked, browsable format at http://ontology.teknowledge.com . ThecentralsemioticpredicateintheSUMO is represents. (represents THING ENTITY)means thatTHINGinsomewayexpresses,connotes, pictures,describes,etc.ENTITY.Thetwo
subrelations
of
containsInformation and
represents
are
realization The . former
predicaterelatesa ContentBearingObject tothe Proposition that is expressed by the ContentBearingObject. Examples include the relationshipsbetweenaphysicalnovelandits storyandbetweenaprintedscoreanditsmusical content. As for the other subrelation of represents, (realization PROCESS PROP)means thatPROCESSisa Processthatexpressesthe contentofthe PropositionE . xamplesincludea particularmusicalperformance,whichrealizesthe contentofamusicalscore,orthereadingofa poem.Notethattheonlydifferencebetween containsInformation and realization concernsthe typeofinstanceof Physical thatispermittedto occupy thefirstargumentposition. Thisis samall difference,butiitsreflectedprominentlybothin naturallanguagesandinsemioticsdiscussions, andsowedecidedtofindaplaceforiitnthe SUMO. Itisimportanttonotethat,insomecases,the binaryrelation represents istoogeneralinscope. Onthebasisofsuggestionsfrom SUO listmember PhilJackson, wehaveadded theternary predicates representsForAgent and representsInLanguage. Thesepredicatesareusefulwhenonewantsto relativizetherepresentationrelationshiptoa particular Agent or Language. Although representscanberegardedasthe centralsemioticspredicateintheSUMO,iitsa subrelationoaf nothersemioticspredicate refers. (refers OBJECT1 OBJECT2) meansthatOBJECT1 mentionsorincludesareferencetoOBJECT2. Thepredicate refersismoregeneralinmeaning than represents,becausepresumablysomething canrepresentsomething elseonlyifirtefersto thisotherthing. Forexample,anarticlewhose topicisarecentchangeinthepriceofoilmay refertomanyotherthings,e.g.thegeneralstateof theeconomy,theweatherinCalifornia,the prospectofglobalwarming,theoptionsfor alternativeenergysources,thestockpricesof variousoilcompanies, etc. Thepredicate refersanditssubrelationsall relate a ContentBearingObjectto something denotedbytheobject. Anotherclassopredicates f intheSUMOrelatestwo ContentBearingObjects or classes of ContentBearingObjectsto one another. These predicates are subsumesContentInstance,
equivalentContentInstance , subsumesContentClass,
ContentBearingObjectsthatexpressthem.A
and equivalentContentClass.
Proposition ispiece a oinformation, f e.g.thatthe
(subsumesContentInstance
OBJECT1
OBJECT2)
meansthatthecontentexpressedbyOBJECT2is partotfhecontentexpressedbyOBJECT1. An exampleitsherelationshipbetweenhandwritten a poemandoneofitsstanzas. Thisisarelation betweeninstances,ratherthanclasses.Ifone wantstoassertacontentrelationshipbetween classes,e.g.betweenaversionofanintellectual workandapartofthatwork,therelation subsumesContentClass isused. Notethatthis latter predicate ineeded s im n any cases. Consider, forexample,therelationbetweentheKingJames editionothe f BibleanditsBookoGenesis. f This relationholdsforeverycopyofthiseditionand notjustfor saingleinstance. Thepredicate equivalentContentInstance meansthatthetwo ContentBearingObjects related expressexactlythesamecontent. Anexample wouldbetherelationshipbetweenahandwritten draftof laetter toone'slawyer and typed a copy of the same letter. The predicate equivalentContentClass on , theotherhand,means thatthecontentexpressedbyasubclassof ContentBearingObject isidenticalwiththecontent expressed by another subclass of ContentBearingObject An .exampleotfhissortof relationshipholdsbetweenEnglishandRussian editionsoAgatha f Christie's'Murder on theOrient Express'. Notethat (equivalentContent OBJECT1 OBJECT2) is equivalent to (subsumesContent OBJECT1 OBJECT2)and (subsumesContent OBJECT2 OBJECT2)whether , oneitalking s aboutinstancesor subclassesof ContentBearingObject. Asidefromthepredicatesdiscussedinthe preceding paragraphs,itisimportant to understand the SUMO concepts of Proposition and ContentBearingObject Propositions . areabstract entitiesthatexpresscomplete a thoughtorsaetof suchthoughts.Asanexample,theformula '(instanceYojo Cat)' expresses the Proposition that theentitynamedYojoiasnelementoftheclassof cats. Note that propositions are not restricted ttohe contentexpressedbyindividualsentencesofa language.Theymayencompassthecontent expressedbytheories,books,andevenwhole libraries. ContentBearingObjects on , theotherhand, areobjectsthatexpressa PropositionI. tis importanttodistinguish Propositionsfromthe
catisonthe mat,buta ContentBearingObject isan object that represents this information. A Propositionisanabstractionthatmayhave multiplerepresentations:strings,sounds,icons, etc. Forexample,the Proposition thatthecatis onthematisrepresentedhereasastringof graphicalcharactersdisplayedomonitor na and/or printedonpaper,butict anberepresentedbya sequenceosfoundsobr yanon-latinalphabetor by cryptographic a form. Itmaybeusefultoseehowallofthese semiotics-relatedterms areorganizedintotype hierarchies. refers represents containsInformation realization Entity Physical Object ContentBearingObject subsumesContentInstance equivalentContentInstance subsumesContentClass equivalentContentClass
Notethatindentationindicatesasubsumption relationbetweentheindentedtermandthe preceding term. Now that we’ve presented the semiotics predicatesintheSUMO,let’sreturntothe representational challenge problems involving Hamlet. Returning tour “Hamlet”example, Hamletthefictionalcharacter (instance Hamlet Human)
Hamletan edition othe f printed play (subclass Hamlet-FolgerEdition ContentBearingObject) (subclass Hamlet-ScribnerEdition Hamlet-FolgerEdition) (equivalentContentClass Hamlet-ScribnerEdition Hamlet-FolgerEdition)
A copy othe f printed play (instance Hamlet-ScribnerEditionOnMyBookshelf Hamlet-ScribnerEdition)
A performanceoHamlet f (instance HamletPerformanceByRoyalSPCoOnJune18-99 IntentionalProcess) (realization HamletPerformanceByRoyalSPCoOnJune18-99 Hamlet-ThePlay)
A performanceoHamlet f capturedovnideo (instance VideoOfHamletPerfByRoyalSPCoOnJune18-99 ContentBearingObject) (refers VideoOfHamletPerfByRoyalSPCoOnJune18-99 HamletPerformanceByRoyalSPCoOnJune18-99)
Thetimelessinformationalcontentoftheplay (instance Hamlet-ThePlay Proposition) (containsInformation Hamlet-ScribnerEditionOnMyBookshelf Hamlet-ThePlay)
4.FormalDetails Inthisfinalsection,we’llpresenttheaxiomsthat providetheformal,semanticunderpinningtothe predicatesthatwereconsideredintheprevious section.Becausethesemioticssectionofthe SUMOisonlyonesmallpartofthislarge,upperlevelontology,thereareadditional,relevant axiomsthataretoonumeroustoreproducehere. Pleaseconsulttheon-linebrowserforcomplete information. Inthediscussionbelowitmayalsobe helpfultorefertotheon-linespecificationof SUO-KIF [3]. Inparticular,termsthatbeginwith aquestionmark‘?’denotevariables,and‘exists’, ’standforthe ‘forall’,‘and’,‘=>’,and‘ existentialquantifier,theuniversalquantifier,and thetruth-functionaloperatorsofconjunction, materialimplication,andmaterialequivalence, respectively. Realizing some proposition in a process requiresthattherebaenobjectthatrepresentsthe information itnhatproposition. (=> (realization ?PROCESS ?PROP) (exists (?OBJ) (and (instance ?OBJ ContentBearingObject) (containsInformation ?OBJ ?PROP))))
Ifoneclasssubsumestheinformationalcontentof another,instancesotfhesecondclassexpressall oftheinformationrepresentedbyinstancesotfhe firstclass. ( (subsumesContentClass ?CLASS1 ?CLASS2)
(forall (?INFO ?OBJ1 ?OBJ2) (=> (and (instance ?OBJ1 ?CLASS1) (instance ?OBJ2 ?CLASS2) (containsInformation ?OBJ1 ?INFO)) (containsInformation ?OBJ2 ?INFO))))
If oneinstancesubsumes the informational content ofanother,thenthefirstobjectcontainsallthe informationcontained itnhesecond object. ( (subsumesContentInstance ?OBJ1 ?OBJ2) (forall (?INFO) (=> (containsInformation ?OBJ1 ?INFO) (containsInformation ?OBJ2 ?INFO))))
Contentbearingobjectscontainsomesortof information (=> (instance ?OBJECT ContentBearingObject) (exists (?PROP) (containsInformation ?OBJECT ?PROP)))
Iftwoinstancesof ContentBearingObject subsume eachother’scontent,thentheseinstancesmust expressthesamecontent. ( (and (subsumesContentInstance ?OBJ1 ?OBJ2) (subsumesContentInstance ?OBJ2 ?OBJ1)) (equivalentContentInstance ?OBJ1 ?OBJ2))
If two subclasses of ContentBearingObject subsumeeachother’scontent,theneachsubclass mustexpressthesamecontent. ( (and (subsumesContentClass ?CLASS1 ?CLASS2) (subsumesContentClass ?CLASS2 ?CLASS1)) (equivalentContentClass ?CLASS1 ?CLASS2))
Iftwosentenceshaveequivalentcontent,they imply oneanother. (=> (and (equivalentContentInstance ?SENT1 ?SENT2) (instance ?SENT1 Sentence) (instance ?SENT2 Sentence)) ( ?SENT1 ?SENT2))
Onesentencesubsumesthecontentofanother sentenceonly iitimplies f theother sentence. (=> (and (subsumesContentInstance ?SENT1 ?SENT2) (instance ?SENT1 Sentence) (instance ?SENT2 Sentence)) (=> ?SENT1 ?SENT2))
Acknowledgments WewishtoacknowledgeourArmysponsorsfor fundingandguidingthiswork,andww e ouldlike tothankmembersotfheSUOemaillistfortheir many helpfulsuggestionsandcriticisms. References
[1] Niles,I.,& Pease, A. (2001)“Toward a Standard Upper Ontology”,in Proceedingsof Formal the2 ndInternationalConferenceon OntologyiInnformationSystems(FOIS-2001) Ogunquit,Maine, Oct.17-19. [2] Genesereth, M.(1991).“Knowledge InterchangeFormat,”Proceedingsofthe Second InternationalConferenceonthe PrinciplesofKnowledgeRepresentation and Reasoning (KR-91), J.Alleneal., t (eds), MorganKaufmanPublishers,1991, 238-249. Seealso http://logic.stanford.edu/kif/kif.html. [3] Pease,A.,(2000),StandardUpper Ontology KnowledgeInterchangeFormat,unpublished web documenteditedfrom (Genesereth, 1991), http://suo.ieee.org/suo-kif.html [4] Peirce,C. (1931-1958) S. Collected Papersof C.S.Peirce ed. , by CHartshorne, . P.Weiss,& A.Burks,8 vols.,HarvardUniversity Press, Cambridge,MA. [5] DeSaussure,F. (1916) CoursdeLinguistique Générale,translatedbW y Baskin . as Course in GeneralLinguistics (1959),Philosophical Library,New York. [6] Barthes,R.(1964)"Rhétoriquedle´image", Communications,4,40-51.AlsoiB n arthes, R., L´Obvieel´Obtus t (1982), Seuil, Paris, 25-42. [7] Lotman,M.,& Uspenskij, B. A. (1978)"On thesemioticmechanism ofculture", LiteraryHistory IX, , 2,211-232. [8] Eco,U.(1976) A TheoryoSemiotics f University Press, Bloomington.
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