Nicola Guarino CNR Institute for Cognitive Sciences and Technologies,

1. Ontologies, Conceptualizations,and Possible WorldsRevisiting “Formal Ontologies and Information Systems”10 years later Nicola Guarino CNR Institute for Cognitive Sciences and Technologies, Laboratory for Applied Ontology, Trento, Italy www.loa-cnr.it

2. Summary • Reality, perception, and conceptualizations • Computational ontologies as logical characterizations of conceptualizations • Differences betwen ontologies; kinds of ontology change • Evolution with respect to previous works of mine: • What are possible worlds? What is the domain of discourse? • Clearer distinction between possible worlds and logical models • Explicit role of perception in clarifying the notion of “conceptualization” • hPossible worlds as sensory states (also in a metaphorical sense: perception as observation perspective focusing on “raw data”) • More detailed account of kinds of ontology change

3. Ontology and Ontologies • Ontology: the philosophical discipline • Study of whatthereis (being qua being...) ...a liberal reinterpretation for computer science: content qua content, independently of the way it is represented • Study of the nature and structure of “reality” • ontologies: Specific (theoretical or computational) artifactsexpressing the intended meaning of a vocabularyin terms of primitive categories and relations describingthe nature and structure of a domain of discourse ...in order to account for the competent use of vocabulary in real situations! Gruber: “Explicit and formal specifications of a conceptualization”

4. apple LE same conceptualization mela LI What is a conceptualization • Formal structure of (a piece of) reality as perceived and organized by an agent, independently of: • the vocabulary used • the actual occurence of a specific situation • Different situations involving same objects, described by different vocabularies, may share the same conceptualization.

5. Example 1: the concept of red a b {a} {b} {a,b} {}

6. Example 2: the concept of on a {<a,b >} b b {<b,a >} a {} b a

7. n D r 2  n n D (Montague's intensional logic) 2 r : W  n Relations vs. Conceptual Relations ordinary relations are defined on a domain D: conceptual relations are defined on a domain space<D, W> But what are possible worlds? What are the elements of a domain of discourse?

8. What is a conceptualization? A cognitive approach • Humans isolate relevant invariances from physical reality (quality distributions) on the basis of: • Perception (as resulting from evolution) • Cognition and cultural experience (driven by actual needs) • (Language) • presentation: atomic event corresponding to the perception of an external phenomenon occurring in a certain region of space (the presentation space). • Presentation pattern(or input pattern):a pattern of atomic stimuli each associated to an atomic region of the presentation space. (Each presentation tessellates its presentation space in a sum of atomic regions, depending on the granularity of the sensory system). • Each atomic stimulus consists of a bundle of sensory quality values (qualia) related to an atomic region of timespace (e.g., there is red, here; it is soft and white, here). • Domain elements corresponds to invariants within and acrosspresentation patterns

9. State of affairs State of affairs State of affairs State of D's affairs Conceptualization State of affairs relevant invariants across world’s moments: D,  Presentationpatterns Conceptualization Perception Reality relevant invariantswithin andacross presentation patterns:D,  Phenomena cognitive domain (different from domain of discourse)! From experience to conceptualization Domain of Discourse D 1998: 2008:

10. Possible worlds as presentation patterns(or sensory states) Presentation pattern: unique (maximal) pattern of qualia ascribed to a spatiotemporal region tessellated at a certain granularity ...This corresponds to the notion of state for a sensory system (maximal combination of values for sensory variables) Possible worlds are (for our purposes)sensory states (or if you prefer, sensory situations)

11. Constructing the cognitive domain • Synchronic level: topological/morphological invariantswithin a single presentation pattern • Unity properties are verified on presentation patterns on the basis of pre-existing schemas: topological and morphological wholes (percepts) emerge • Diachronic level: temporal invariantsacross multiple presentation patterns • Objects: equivalence relationships among percepts belonging to different presentations are established on the basis of pre-existing schemas • Events: unity properties are ascribed to percept sequences belonging to different atomic presentations

12. The basic ingredients of a conceptualization (simplified view) • cognitive objects: mappings from presentation patterns into their parts • for every presentation, such parts constitute the perceptual reification of the object. • concepts and conceptual relations: functions from presentation patterns into sets of (tuples of) cognitive objects • if the value of such function (the concept’s extension) is not an empty set, the correponding perceptual state is a (positive) example of the given concept • Rigid concepts: same extension for all presentation patterns (possible worlds)

13. Conceptualization Perception Reality State of affairs State of affairs relevant invariants across presentation patterns:D,  Presentationpatterns Phenomena Bad Ontology Ontological commitmentK (selects D’D and ’) Models MD’(L) Ontology InterpretationsI Intended models for each IK(L) Ontology models Language L ~Good

14. Less good BAD WORSE Good Ontology Quality: Precision and Coverage High precision, max coverage Low precision, max coverage Max precision, limited coverage Low precision, limited coverage

15. b c c c c a a a a a Excluded conceptualizations Indistinguishable conceptualizations When precision is not enough Only one binary predicate in the language: on Only three blocks in the domain: a, b, c. Axioms (for all x,y,z): on(x,y) -> ¬on(y,x) on(x,y) -> ¬z (on(x,z)  on(z,y)) Non-intendedmodelsare excluded, but the rules for the competent usage ofonin differentsituationsare not captured.

16. The reasons for ontology inaccuracy • In general, a single intended model may not discriminate between positive and negative examplesbecause of amismatchbetween: • Cognitive domain and domain of discourse: lack of entities • Conceptual relations and ontology relations: lack of primitives • Capturing all intended models is not sufficient for a “perfect” ontology Precision: non-intended models are excluded Accuracy: negative examples are excluded

17. Kinds of ontology change(to be suitably encoded in versioning systems!) • Reality changes • Observed phenomena • Perception system changes • Observed qualities (different qualia) • Space/time granularity • Quality space granularity • Conceptualization changes • Changes in cognitive domain • Changes in conceptual relations • metaproperties like rigidity contribute to characterize them (OntoClean assumptions reflect a particular conceptualization) • Logical characterization changes • Domain • Vocabulary • Axiomatization (Correctness, Coverage, Precision) • Accuracy

18. Perception as a metaphor for the initial phase of conceptual modeling • Is student a rigid concept? • If you look at possible worlds, in the common understanding of this notion, your answer is no (it is rather antirigid: it is always possible to be a non-student) • If you focus your “perception” on a restricted point of view, then it may turn out to be rigid (in terms of the “possible worlds” you are able to perceive)