Upward Refinement for Conceptual Blending in Description Logic — An ASP-based Approach and Case Study in EL ++ — Roberto Confalonieri 1 Manfred Eppe 1 , 2 Marco Schorlemmer 1 Oliver Kutz 3 Rafael Peñaloza 3 Enric Plaza 1 1 IIIA-CSIC, Barcelona, Spain 2 International Computer Science Institute, Berkeley, USA 3 Free University of Bozen-Bolzano, Italy ONTOLP 2015, 25 July, 2015, Buenos Aires, Argentina
Outline Introduction 1 Computational Conceptual Blending Overview 2 Upward Refinement Operator for EL ++ 3 Generalisation as Search Problem in Answer Set Programming 4 Conclusion and Future Works 5 Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 2 / 23
Introduction COINVENT Project goals: ◮ Computationally feasible model of conceptual blending ⋆ Cognitive theory described by Fauconnier and Turner [1998, 2002]. The universal creative engine of human thinking. ⋆ Model concept invention ◮ Symbolic approach, based on formal logic (CASL, OWL) ◮ Applications areas: Mathematics, Music, and Computer Icon Design This paper goals: ◮ Define an upward refinement operator for EL ++ ◮ Use ASP to generate and search for EL ++ concept generalisations Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 3 / 23
Introduction COINVENT Project goals: ◮ Computationally feasible model of conceptual blending ⋆ Cognitive theory described by Fauconnier and Turner [1998, 2002]. The universal creative engine of human thinking. ⋆ Model concept invention ◮ Symbolic approach, based on formal logic (CASL, OWL) ◮ Applications areas: Mathematics, Music, and Computer Icon Design This paper goals: ◮ Define an upward refinement operator for EL ++ ◮ Use ASP to generate and search for EL ++ concept generalisations Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 3 / 23
Creating Icons by Conceptual Blending Designer “Give me an icon with meaning Preview- Document” Amalgamation OWL2ASP ICON LIBRARY ASP2OWL Evaluation OWL Conceptual Blending Engine Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 4 / 23
Computational Model of Conceptual Blending - Amalgamation Amalgamation originates from the notion of amalgam Ontañón and Plaza [2010] in case-based reasoning It applies to any language L such that �L , ⊑� is a poset G ¯ I 1 ¯ I 2 I 1 B I 2 An amalgam of two input concepts is a new concept that combines parts from the original descriptions ◮ Find Generic Space ( G ) of input concepts (commonalities) and try to combine non-common elements in I 1 and I 2 ◮ Often, input concepts I 1 and I 2 cannot be combined directly (inconsistency or insatisfaction of some properties) ◮ Input concepts have to be first generalised into I ′ 1 and I ′ 2 ◮ I ′ 1 and I ′ 2 can be finally blended to obtain a ‘good’ B Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 5 / 23
Creating Icons by Conceptual Blending Generic Space Input 1 Input 2 Blend Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 6 / 23
Modeling Computer Icons in EL ++ N C = { Icon , Sign , Document , MagnifyingGlass , Pen , HardDisk } N r = { hasSign , isAbove , isLeft , isRight , isBelow , isSpatialRelation } Background Knowledge Icon ⊑ Thing domain ( isInSpatialRelation ) ⊑ Sign Sign ⊑ Thing range ( isInSpatialRelation ) ⊑ Sign Document ⊑ Sign . . . HardDisk ⊑ Sign . . . MagnifyingGlass ⊑ Sign isAbove ⊑ isInSpatialRelation Pen ⊑ Sign isBehind ⊑ isInSpatialRelation domain ( hasSign ) ⊑ Icon isLeft ⊑ isInSpatialRelation range ( hasSign ) ⊑ Sign isRight ⊑ isInSpatialRelation Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 7 / 23
Modeling Computer Icons in EL ++ N C = { Icon , Sign , Document , MagnifyingGlass , Pen , HardDisk } N r = { hasSign , isAbove , isLeft , isRight , isBelow , isSpatialRelation } Background Knowledge Icon ⊑ Thing domain ( isInSpatialRelation ) ⊑ Sign Sign ⊑ Thing range ( isInSpatialRelation ) ⊑ Sign Document ⊑ Sign . . . HardDisk ⊑ Sign . . . MagnifyingGlass ⊑ Sign isAbove ⊑ isInSpatialRelation Pen ⊑ Sign isBehind ⊑ isInSpatialRelation domain ( hasSign ) ⊑ Icon isLeft ⊑ isInSpatialRelation range ( hasSign ) ⊑ Sign isRight ⊑ isInSpatialRelation Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 7 / 23
Modeling Computer Icons in EL ++ N C = { Icon , Sign , Document , MagnifyingGlass , Pen , HardDisk } N r = { hasSign , isAbove , isLeft , isRight , isBelow , isSpatialRelation } Background Knowledge Icon ⊑ Thing domain ( isInSpatialRelation ) ⊑ Sign Sign ⊑ Thing range ( isInSpatialRelation ) ⊑ Sign Document ⊑ Sign . . . HardDisk ⊑ Sign . . . MagnifyingGlass ⊑ Sign isAbove ⊑ isInSpatialRelation Pen ⊑ Sign isBehind ⊑ isInSpatialRelation domain ( hasSign ) ⊑ Icon isLeft ⊑ isInSpatialRelation range ( hasSign ) ⊑ Sign isRight ⊑ isInSpatialRelation Domain Knowledge Input 1 Input 2 Icon ⊓ ∃ hasSign.HardDisk ⊓ ∃ hasSign. Icon ⊓ ∃ hasSign.Document ⊓ ∃ hasSign. (MagnifyingGlass ⊓ ∃ isAbove.HardDisk) (Pen ⊓ ∃ isAbove.Document) Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 7 / 23
Blending Computer Icons Input 1 Input 2 ? Icon ⊓ ∃ hasSign.HardDisk ⊓ ∃ hasSign. Icon ⊓ ∃ hasSign.Document ⊓ ∃ hasSign. (MagnifyingGlass ⊓ ∃ isAbove.HardDisk) (Pen ⊓ ∃ isAbove.Document) Blend Icon ⊓ ∃ hasSign.HardDisk ⊓ ∃ hasSign. (MagnifyingGlass ⊓ ∃ isAbove.HardDisk) ⊓ Icon ⊓ ∃ hasSign.Document ⊓ ∃ hasSign. (Pen ⊓ ∃ isAbove.Document) Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 8 / 23
Generalising Icon Concepts Input 1 Input 2 Icon ⊓ ∃ hasSign.HardDisk ⊓ ∃ hasSign. Icon ⊓ ∃ hasSign.Document ⊓ ∃ hasSign. (MagnifyingGlass ⊓ ∃ isAbove.HardDisk) (Pen ⊓ ∃ isAbove.Document) Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 9 / 23
Generalising Icon Concepts Generic Space Icon ⊓ ∃ hasSign.Sign ⊓ ∃ hasSign. (Sign ⊓ ∃ isAbove.Sign) Input 1 Input 2 Icon ⊓ ∃ hasSign.HardDisk ⊓ ∃ hasSign. Icon ⊓ ∃ hasSign.Document ⊓ ∃ hasSign. (MagnifyingGlass ⊓ ∃ isAbove.HardDisk) (Pen ⊓ ∃ isAbove.Document) Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 9 / 23
Generalising Icon Concepts Generic Space Icon ⊓ ∃ hasSign.Sign ⊓ ∃ hasSign. (Sign ⊓ ∃ isAbove.Sign) Generalisation Generalisation Icon ⊓ ∃ hasSign.Sign ⊓ ∃ hasSign. Icon ⊓ ∃ hasSign.Document ⊓ ∃ hasSign. (MagnifyingGlass ⊓ ∃ isAbove.Sign) (Sign ⊓ ∃ isAbove.Document) Input 1 Input 2 Icon ⊓ ∃ hasSign.HardDisk ⊓ ∃ hasSign. Icon ⊓ ∃ hasSign.Document ⊓ ∃ hasSign. (MagnifyingGlass ⊓ ∃ isAbove.HardDisk) (Pen ⊓ ∃ isAbove.Document) Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 9 / 23
Generalisation and Refinement operators The generalisation in the amalgamation algorithm is based on a search in the poset �L ( T ) , ⊑ T � The generalisation of an EL ++ concept can be done through an upward refinement operator γ Refinement operator properties Local finiteness Properness Completeness Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 10 / 23
Generalisation of EL ++ concepts The upward refinement operator generalises an EL ++ concept by: ◮ generalising a concept ◮ generalising the concept filling the range of a role ◮ generalising a role ◮ ‘removing’ a role/concept Properties Trade-off between completeness and finiteness ◮ The operator is finite but not proper and complete ◮ It is possible that the generic space is not least general ◮ Not a big issue for conceptual blending, the important thing is to find the commonalities between the concepts Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 11 / 23
Generalisation in ASP The search for generalisations is modeled as an ASP search problem where the ‘goal’ is to find a generic space for two input EL ++ concepts: EL ++ concept in background and domain knowledge are translated to 1 ASP facts (base part) Generalisation operators are implemented as a step-wise process to 2 generalise EL ++ concepts in the domain knowledge until they are not equal (cumulative part) Each ASP stable model returns a generalisation path from the input 3 specifications to a generic space Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 12 / 23
Modeling EL ++ concepts in ASP Background knowledge in ASP Sign ⊑ Thing concept(concept_Sign). subConcept(concept_Document,concept_Thing). Document ⊑ Sign concept(concept_Document). subConcept(concept_Document,concept_Sign). . . . . . . domain ( hasSign ) ⊑ Icon role(role_hasSign). range ( hasSign ) ⊑ Sign domain(role_hasSign,concept_Icon). range(role_hasSign,concept_Sign). . . . . . . isAbove ⊑ isInSpatialRelation subRole(role_isAbove,role_isInSpatialRelation). . . . . . . Upward Refinement for EL ++ in ASP Confalonieri, et al 25/07/2015 13 / 23
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