A Formal Interpretation of Frame Composition Wiebke Petersen & - PowerPoint PPT Presentation

Frames Classification of concepts Frame Composition Composition and Language A Formal Interpretation of Frame Composition Wiebke Petersen & Tanja Osswald Heinrich-Heine-Universit¨ at D¨ usseldorf Research group on “Functional Concepts and Frames” CTF 09, D¨ usseldorf Petersen & Osswald Frame Composition 1

Frames Classification of concepts Frame Composition Composition and Language outline Frames 1 Classification of concepts (L¨ obner) 2 Frame Composition 3 Composition and Language 4 Petersen & Osswald Frame Composition 2

Frames Classification of concepts Frame Composition Composition and Language outline Frames 1 Classification of concepts (L¨ obner) 2 Frame Composition 3 Composition and Language 4 Petersen & Osswald Frame Composition 3

Frames Classification of concepts Frame Composition Composition and Language frames Barsalou (1992) Frames, Concepts, and Conceptual Fields Frames provide the fundamental representation of knowledge in human cognition. At their core, frames contain attribute-value sets . Petersen & Osswald Frame Composition 4

Frames Classification of concepts Frame Composition Composition and Language feature structures typed feature structure untyped feature structure   phrase  CAT: phrase    noun     CAT: noun        agr      � �  PERS : 3   HEAD :   HEAD :       AGR : PERS : 3   AGR :       NUM : pl         NUM : pl  Petersen & Osswald Frame Composition 5

Frames Classification of concepts Frame Composition Composition and Language feature structures typed feature structure untyped feature structure   phrase  CAT: phrase    noun     CAT: noun        agr      � �  PERS : 3   HEAD :   HEAD :       AGR : PERS : 3   AGR :       NUM : pl         NUM : pl  phrase 3 3 PERS CAT S R E P HEAD AGR H E A D AGR phrase noun agr N CAT U NUM M noun num num Petersen & Osswald Frame Composition 5

Frames Classification of concepts Frame Composition Composition and Language frames as generalized feature structures feature structures (Carpenter 1992) feature structures are connected directed graphs with Crown CROWN one central node nodes labeled with types Bark TRUNK BARK arcs labeled with attributes no node with two outgoing arcs with DIAMETER the same label Dia and such that each node can be reached from the central node via directed arcs. Petersen & Osswald Frame Composition 6

Frames Classification of concepts Frame Composition Composition and Language frames as generalized feature structures Person Frames (Petersen 2007) R MOTHER E H Frames T O are connected directed graphs with M one central node nodes labeled with types arcs labeled with attributes no node with two outgoing arcs with the same label Bark BARK TRUNK DIAMETER Dia Petersen & Osswald Frame Composition 6

Frames Classification of concepts Frame Composition Composition and Language frames as generalized feature structures Person Frames (Petersen 2007) MOTHER MOTHER Frames are connected directed graphs with one central node nodes labeled with types arcs labeled with attributes no node with two outgoing arcs with the same label Bark BARK TRUNK D I A M E T E R Open argument nodes are marked as Dia rectangular nodes. Petersen & Osswald Frame Composition 6

Frames Classification of concepts Frame Composition Composition and Language outline Frames 1 Classification of concepts (L¨ obner) 2 Frame Composition 3 Composition and Language 4 Petersen & Osswald Frame Composition 7

Frames Classification of concepts Frame Composition Composition and Language concept classification person, pope, house, verb, sun, Mary, wood, brother, mother, meaning, distance, spouse, argument, entrance Petersen & Osswald Frame Composition 8

Frames Classification of concepts Frame Composition Composition and Language concept classification: relationality person, pope, house, verb, sun, Mary, non-relational wood brother, mother, meaning, distance, relational spouse, argument, entrance L¨ obner Petersen & Osswald Frame Composition 9

Frames Classification of concepts Frame Composition Composition and Language concept classification: uniqueness of reference non-unique refer- unique reference ence person, house, non-relational Mary, pope, sun verb, wood brother, argument, mother, meaning, relational entrance distance, spouse L¨ obner Petersen & Osswald Frame Composition 10

Frames Classification of concepts Frame Composition Composition and Language concept classification non-unique refer- unique reference ence individual con- non-relational sortal concept cept λ x . x = ι u . P ( u ) λ x . P ( x ) proper relational functional con- relational concept cept λ y λ x . x = f ( y ) λ y λ x . R ( x , y ) L¨ obner Petersen & Osswald Frame Composition 11

Frames Classification of concepts Frame Composition Composition and Language concept classification non-unique refer- unique reference ence individual con- non-relational sortal concept cept λ x . x = ι u . P ( u ) λ x . P ( x ) ι u . P ( u ) proper relational functional con- relational concept cept λ y λ x . x = f ( y ) λ y λ x . R ( x , y ) λ y . f ( y ) L¨ obner Petersen & Osswald Frame Composition 11

Frames Classification of concepts Frame Composition Composition and Language frames and functional concepts attributes describe functional relations, i.e., they represent functions Crown CROWN attributes correspond to Bark functional concepts TRUNK BARK ⇒ frames decompose DIAMETER concepts into functional concepts Dia ⇒ functional concepts embody the concept type on which categorization is based Petersen & Osswald Frame Composition 12

Frames Classification of concepts Frame Composition Composition and Language sortal concepts tree-Frame trunk-Frame Crown Bark CROWN K R A B TRUNK Bark DIAMETER TRUNK BARK Dia DIAMETER Dia λ x . TRUNK ( ε u . x = TRUNK ( u )) ∧ Bark ( BARK ( x )) ∧ Dia ( DIAMETER ( x )) λ x . Crown ( CROWN ( x )) ∧ Bark ( BARK ( TRUNK ( x ))) ∧ Dia ( DIAMETER ( TRUNK ( x ))) Petersen & Osswald Frame Composition 13

Frames Classification of concepts Frame Composition Composition and Language individual concepts Mary-frame pope-frame predicate constant ‘Mary’: predicate constant ‘pope’: HEAD Mary RCC λ x . x = ι y . ( y = Mary ) λ x . x = HEAD ( ι y . RCC ( y )) Petersen & Osswald Frame Composition 14

Frames Classification of concepts Frame Composition Composition and Language individual concepts Mary-frame pope-frame predicate constant ‘Mary’: predicate constant ‘pope’: HEAD Mary RCC λ x . x = ι y . ( y = Mary ) λ x . x = HEAD ( ι y . RCC ( y )) individual constant ‘Mary’: individual constant ‘pope’: HEAD Mary RCC ι x . x = Mary ι x . x = HEAD ( ι y . RCC ( y )) Petersen & Osswald Frame Composition 14

Frames Classification of concepts Frame Composition Composition and Language non-relational concepts sortal concepts individual concepts default frame: default frame: λ x . P ( x ) λ x . x = ι u . P ( u ) one open argument one open argument there is a direct path from a definite node to the central node Petersen & Osswald Frame Composition 15

Frames Classification of concepts Frame Composition Composition and Language proper relational concepts brother-frame co-parent-frame MOTHER MOTHER MOTHER FATHER SEX Male λ y λ x . MOTHER ( x ) = λ y λ x . x = MOTHER ( ε u . y = FATHER ( u )) MOTHER ( y ) ∧ Male ( SEX ( x )) child-frame MOTHER λ y λ x . y = MOTHER ( x ) Petersen & Osswald Frame Composition 16

Frames Classification of concepts Frame Composition Composition and Language functional concepts head-frame haircolor-frame predicate constant ‘head’: predicate constant ‘haircolor’: HEAD COLOR HAIR λ y λ x . x = HEAD ( y ) λ y λ x . x = COLOR ( HAIR ( y )) Petersen & Osswald Frame Composition 17

Frames Classification of concepts Frame Composition Composition and Language functional concepts head-frame haircolor-frame predicate constant ‘head’: predicate constant ‘haircolor’: HEAD COLOR HAIR λ y λ x . x = HEAD ( y ) λ y λ x . x = COLOR ( HAIR ( y )) function constant ‘head’: function constant ‘haircolor’: HEAD COLOR HAIR λ y . HEAD ( y ) λ y . COLOR ( HAIR ( y )) Petersen & Osswald Frame Composition 17

Frames Classification of concepts Frame Composition Composition and Language relational concepts proper relational concepts functional concepts default frame: default frame: λ y λ x . y = f ( x ) two open arguments λ y λ x . R ( x , y ) there is a direct path from the other open argument to two open arguments the central node no direct path from the other open argument to the central node Petersen & Osswald Frame Composition 18