INTRODUCTION TO ARTIFICIAL INTELLIGENCE Massimo Poesio LECTURE 5: Ontologies and Formal Ontologies LOGIC vs ONTOLOGIES • Logic is not ‘knowledge’: is just a language for encoding knowledge and inferences • Already Aristotle realized that we need a separate theory of what types of objects there are, what properties they have, and how they are related, and made a first attempt in his CATEGORIES • Now this area of research is known as (Formal) ontology PHILOSOPHICAL BACKGROUND • Aristotle’s Metaphysics: – A list of 10 categories – Criteria for definition of categories • Tree of Porphiry: Organize categories under SUBSTANCE in a hierarchy • Brentano: all ten categories • Kant: neutral as to whether these categories really reflect the world or merely our conception of it ARISTOTLE’s CATEGORIES • • • • • • • • • • SUBSTANCE (man, horse) QUALITY (white, heavy) QUANTITY (four-foot, five-foot) ACTIVITY (cutting, burning) NB: simultaneously a PASSIVITY (being cut, being burned) classification of what is SPATIALITY / LOCATION (in the there Lyceum) and what TEMPORALITY / LOCATION (yesterday, propertieslast thereyear) may be RELATION (double, half) HAVING / STATE (has shoes on) SITUATEDNESS / POSTURE (is lying, is sitting) DEFINITION OF CONCEPTS (Aristotle’s Metaphysics, Book Z) “a definition is an account, and every account has parts, and part of the account stands to part of the thing in just the same way that the whole account stands to the whole thing” = Most concepts encode necessary and sufficient conditions for their own application DEFINITIONS BY GENUS AND DIFFERENTIA MAN = RATIONAL ANIMAL DEFINIENDUM DEFINIENS Definition by genus and differentia • The ‘method of division’: – Begin with the broadest genus containing the species to be defined (‘ANIMAL’) – Divide the genus in two sub-parts by some differentia (‘FOOTED’) – Then divide the two sub-types again (CLOVENFOOTED) THE TREE OF PORPHIRY Other philosophers The greatest part of the Ideas, that make our complex Idea of GOLD, are YELLOWNESS, great WEIGHT, FUSIBILITY, and SOLUBILITY IN AQUA REGIA (Locke) In the case of many words … it is possible to specify their meaning by reference to other words. E.g., “ARTHROPODES” are ANIMALS with SEGMENTED BODIES and JOINTED LEGS. (Carnap) `BOTTOM-UP’ ONTOLOGIES IN AI • The interest of Artificial Intelligence researchers in these ideas was born out of attempts to model knowledge in specific domains THE BLOCKS WORLD A BLOCKS WORLD ONTOLOGY OBJECT GRASPABLE grasp(arm,x) NON- GRASPABLE ~grasp(arm,x) STACKABLE stack(x,y) CUBE PYRAMID ~stack(x,y) TODAY’s DOMAIN-SPECIFIC ONTOLOGIES • Protein Ontology: developed to codify in a systematic way our knowledge about proteins – http://pir.georgetown.edu/pro/ • Other ontologies listed on OPEN BIOMEDICAL ONTOLOGY – http://www.obofoundry.org/ – Gene ontology, C. elegans, etc • Medical domain: UMLS PROTEIN ONTOLOGY UPPER ONTOLOGIES • The work on domain-specific ontologies eventually led to the desire to develop ontologies that could ‘connect’ formalizations in one domain with formalizations in other domains – E.g., an ontology for biology with an ontology for medicine – But also an ontology of art with an ontology for tourism • Whether this is actually possible is a deep philosophical question CYC • One of the first attempts in AI to produce such an overarching ontology was done in the CYC project – an effort to produce an enCYClopedia of commonsense knowledge THE CYC ONTOLOGY http://www.cyc.com/ PROBLEMS ENCOUNTERED IN CYC • The researchers working on CYC found themselves confronting every single issue in knowledge representation • E.g., how to define VIDEOTAPE? – A strip of coated plastic? (concrete) – The information contained on that strip? (abstract) FORMAL ONTOLOGIES • Work on formal ontologies is concerned with providing an inferential characterization of categories in terms of logic • A simple example of inference: – if X is a PHYSICAL OBJECT, then moving X from L1 to L2 implies that the LOCATION of X after the movement is L2 • A more complex inference: – Moving X with mass M from L1 to L2 implies that the total mass at L1 is reduced by M, whereas the total mass at L2 is increased by M (this is not true if X is an abstract object) UPPER ONTOLOGIES: DOLCE • Work on specifying the ‘categories of existence’ is exemplified by DOLCE, an upper ontology developed by the Lab for Applied Ontology of CNR (Povo) DOLCE’S TAXONOMY PT Particular ED Endurant PED Physical Endurant M Amount of Matter F Feature PD Perdurant NPED Non-physical Endurant POB Physical Object … AS Arbitrary Sum NPOB Non-physical Object Q Quality EV Event STV Stative ACH ACC Achievement Accomplishment … … TQ Temporal Quality ST State PRO Process … … … TL Temporal Location PQ Physical Quality AB Abstract … Fact AQ Abstract Quality … SL Spatial Location … TR Temporal Region … APO Agentive Physical Object NAPO Non-agentive Physical Object MOB Mental Object SOB Social Object ASO Agentive Social Object SAG Social Agent NASO Non-agentive Social Object SC Society T Time Interval Set PR Physical Region … S Space Region R Region AR Abstract Region … FUNDAMENTAL ONTOLOGICAL CHOICES IN DOLCE • CONCRETE: ‘rock’ – Exists in space / time • ABSTRACT: ‘law’ – Does not exists in space time FUNDAMENTAL ONTOLOGICAL CHOICES IN DOLCE • ENDURANT vs PERDURANT – ENDURANT OBJECTS: have a stable identity over a period of time (e.g., concrete objects) – PERDURANT OBJECTS: events that occur and then exist no more FUNDAMENTAL ONTOLOGICAL CHOICES IN DOLCE • QUALITIES – The particular qualities of specific objects (e.g., the specific color of this specific slide, the particular weight of this particular laptop, etc) – Each quality associated with a QUALITY SPACE that specifies the range of values that quality may take FORMALIZATIONS OF RELATIONS • Arguably most of the work on formal ontology is concerned with the formalization of RELATIONS – PARTS – SPACE – TIME PART-OF RELATION(S) • A great variety of relations between objects could be called ‘part’: – My hand is part of my body – The handle of the door – The top of the cupboard – This dish is made up of pepper and cod – This atom has one electron A SINGLE PART-OF RELATION? • In MEREOLOGY (Lesniewski, 1927-31; Link, 1983; Simons, 1987); a single transitive part-of relation is proposed • Problems: intransitivity – Marguerite’s tail is part of Marguerite the cow – Marguerite the cow is part of the herd – But: Marguerite’s tail is not part of the herd Winston et al’s classification • Winston et al (1987) distinguish between six types of part relation: – COMPONENT-INTEGRAL OBJECT (handle / cup) – PORTION-WHOLE(slice / pie) – SUBSTANCE-WHOLE(steel / bike) – MEMBER-COLLECTION (tree / forest) – FEATURE-ACTIVITY (paying / shopping) – PLACE-AREA (oasis / desert) VIEU & ARNAGUE 2007 • Vieu & Arnague show that many of the ‘part-of’ relations can be distinguished using a limited number of categories: – PLURALITY • Both ELEMENT-COLLECTION and SUB-COLLECTION –COLLECTION require one (or two) of the relata to be collections – SUBSTANCE • PORTION-WHOLE and SUBSTANCE-WHOLE require one of the relata to be a substance • This leaves out – ‘PART’ proper, Component-Integral Whole (CIW) – Temporal and spatial part COMPONENT-INTEGRAL-WHOLE • Main claim: an account of the ‘proper’ part relation requires an account of FUNCTIONALITY – Part of what makes a object a ‘hand’ or a ‘wheel’ is the function it performs – Previous accounts: Wright, Cummins, Searle • Wright: ‘proper function’ analyzed in terms of evolution – Problem: doesn’t apply to non-biological entities • Cummins: the function of a pigeon’s wing with respect to some analytical account of the pigeon’s capacity to fly is to generate lift and propulsion LEXICAL TYPES • Contrasts such as – The motor is part of the car – The motor is part of the vehicle – ?? The motor is part of the ARTEFACT • Suggest to Vieu & Arnague that CIW is a relation between LEXICAL TYPES not denotations – CIW-direct(x,X,y,Y,t) CIW: DEFINITION PHYSICAL PART INDIVIDUAL FUNCTIONAL DEPENDENCE GENERIC FUNCTIONAL DEPENDENCE CLASSIFIED AS OTHER AREAS OF RESEARCH IN FORMAL ONTOLOGY • Time • Space • Causality ONTOLOGIES ON THE WEB: THE SEMANTIC WEB • The Semantic Web (Berners-Lee et al, 2001) is a proposal to specify the type of objects mentioned in a Web page AN EXAMPLE OF SEMANTICALLY MARKED PAGE JIM HENDLER’S PAGE, SEMANTIC WEB INFO <BODY> <INSTANCE KEY="http://www.cs.umd.edu/users/hendler/"> <USE-ONTOLOGY ID="cs-dept-ontology" VERSION="1.0" PREFIX="cs" URL= "http://www.cs.umd.edu/projects/plus/SHOE/cs.html" /> <CATEGORY NAME="cs.Professor" FOR="http://www.cs.umd.edu/users/hendler/"/> <RELATION NAME="cs.member"> <ARG POS=1 VALUE="http://www.cs.umd.edu/projects/plus/"> <ARG POS=2 VALUE="http://www.cs.umd.edu/users/hendler/"> </RELATION> <RELATION NAME="cs.name"> <ARG POS=2 VALUE="Dr. James Hendler"> </RELATION> <RELATION NAME="cs.doctoralDegreeFrom"> <ARG POS=1 VALUE="http://www.cs.umd.edu/users/hendler/"> <ARG POS=2 VALUE="http://www.brown.edu"> </RELATION> <RELATION NAME="cs.emailAddress"> <ARG POS=2 VALUE="email@example.com"> </RELATION> ….. </INSTANCE> <b>As of January 1, 2007 Professor Hendler has moved from the University of Maryland to <a href="http://www.rpi.edu">Rensselaer Polytechnic Institute</a></b>. SEMANTIC WEB INGREDIENTS • XML as a language of markup • RDF as the basic tool for representing information • OWL (Web Ontology Language) to describe concepts, attributes, and relations • One or more ontologies RESOURCE DESCRIPTION FRAMEWORK (RDF) • A language to describe statements of the form: <RESOURCE, PROPERTY, VALUE> ‘Il presidente Ciampi vive a Roma’ RDF EXAMPLE <?xml version='1.0'?> <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:wikipedia="http://it.wikipedia.org/wiki/" xmlns:wikidizionario="http://it.wiktionary.org/wiki/"> <rdf:Description rdf:about="http://www.quirinale.it/presidente/ciampi.htm"> <wikidizionario:vivere rdf:resource="http://www.comune.roma.it/index.asp"/> <wikipedia:codice_fiscale> CMPCLZ20T09E625V </wikipedia:codice_fiscale> </rdf:Description> </rdf:RDF> OWL: A LANGUAGE TO DESCRIBE ONTOLOGIES • A series of languages allowing increasingly more complex descriptions – OWL-LITE: taxonomies, restrictions – OWL-DL: Description Logics (see next week) – OWL-FULL: Maximum expressivity OWL <owl:Class rdf:ID="ProteinComplex"> <owl:disjointWith> <owl:Class rdf:ID="SiteGroup"/> </owl:disjointWith> <owl:disjointWith> <owl:Class rdf:about="#Chains"/> </owl:disjointWith> <owl:disjointWith> <owl:Class rdf:about="#Residues"/> </owl:disjointWith> READINGS • Sowa, Knowledge Representation, Brooks & Cole, chapter 2 • Vieu & Arnague (2007), Part-of Relations, Functionality and Dependence, In Aurnague, M.; Hickmann, M. and Vieu, L. (eds.), The Categorization of Spatial Entities in Language and Cognition, John Benjamins, p. 307-337.