Co-evolution in Epistemic Networks Reconstructing Social Complex Systems Camille Roth CREA – CNRS / Ecole Polytechnique Presentation of the thesis — Nov 19, 2005
Framework and objectives Epistemic communities Micro-foundations The Reconstruction Problem Reconstruction is a reverse problem consisting in successfully reproducing several stylized facts observed in the original empirical system.
Framework and objectives Epistemic communities Micro-foundations The Reconstruction Problem Reconstruction is a reverse problem consisting in successfully reproducing several stylized facts observed in the original empirical system. Issues η e (i) Find P in order to deduce H H t+ ∆ t t high-level observations H from strictly low-level phenomena L . P? P? (ii) Find a low-level dynamics λ that rebuilds high-level evolution η e . e λ L L t+ ∆ t t
Framework and objectives Epistemic communities Micro-foundations The Reconstruction Problem Reconstruction is a reverse problem consisting in successfully reproducing several stylized facts observed in the original empirical system. Issues η e (i) Find P in order to deduce H H t+ ∆ t t high-level observations H from strictly low-level phenomena L . P P (ii) Find a low-level dynamics λ that rebuilds high-level evolution η e . λ? L L t+ ∆ t t
Framework and objectives Epistemic communities Micro-foundations Objectives A socio-semantic complex system Reproduce a hierarchic epistemic hypergraph of a 1 knowledge community that fits a high-level expert-based description Provide a low-level dynamics and a morphogenesis model 2 that rebuilds the empirically observed high-level structure Thesis The structure of a knowledge community, and in particular its epistemic hypergraph, is primarily produced by the co-evolution of agents and concepts.
Framework and objectives Epistemic communities Micro-foundations Objectives A socio-semantic complex system Reproduce a hierarchic epistemic hypergraph of a 1 knowledge community that fits a high-level expert-based description Provide a low-level dynamics and a morphogenesis model 2 that rebuilds the empirically observed high-level structure Thesis The structure of a knowledge community, and in particular its epistemic hypergraph, is primarily produced by the co-evolution of agents and concepts.
Framework and objectives Epistemic communities Micro-foundations Outline Epistemic communities 1 Rationale & definitions Epistemic community taxonomy and Galois lattices Partial taxonomies: rebuilding history Micro-foundations of epistemic networks 2 Networks Towards a rebuilding model Reconstruction of epistemic communities
Framework and objectives Epistemic communities Micro-foundations Outline Epistemic communities 1 Rationale & definitions Epistemic community taxonomy and Galois lattices Partial taxonomies: rebuilding history Micro-foundations of epistemic networks 2 Networks Towards a rebuilding model Reconstruction of epistemic communities
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Building taxonomies Rationale Describe the taxonomy of a knowledge community, in particular scientific communities, that matches high-level descriptions. η e H H t+ ∆ t t P P e λ L L t+ ∆ t t
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Building taxonomies Epistemic communities Epistemic Community: group of agents sharing a common set of subjects, concepts, issues; sharing a common goal of knowledge creation — Haas (1992), Cowan et al. (2000) Definition here: “an epistemic community is the largest set of agents sharing a given set of concepts” – as such strongly linked with structural equivalence
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Building taxonomies Epistemic communities Epistemic Community: group of agents sharing a common set of subjects, concepts, issues; sharing a common goal of knowledge creation — Haas (1992), Cowan et al. (2000) Definition here: “an epistemic community is the largest set of agents sharing a given set of concepts” – as such strongly linked with structural equivalence
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Building taxonomies Formal framework Consider a binary relation R between Concepts (C) agents & concepts Intent S ∧ of an agent set S : all Prs concepts used by every agent in S s 1 Extent C ⋆ of a concept set C Lng s Epistemic community : the extent of a 2 NS concept set C s “ ∧ ⋆ ” is a closure operation : 3 (idempotent) ( S ∧ ⋆ ) ∧ ⋆ = S ∧ ⋆ 1 s 4 (extensive) S ⊆ S ∧ ⋆ 2 (increasing) S ⊆ S ′ ⇒ S ∧ ⋆ ⊆ S ′∧ ⋆ 3 Agents ( S , C ) is closed iff C = S ∧ and S = C ⋆ (S)
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Building taxonomies Formal framework Consider a binary relation R between Concepts (C) agents & concepts Intent S ∧ of an agent set S : all Prs concepts used by every agent in S s 1 Extent C ⋆ of a concept set C Lng s Epistemic community : the extent of a 2 NS concept set C s “ ∧ ⋆ ” is a closure operation : 3 (idempotent) ( S ∧ ⋆ ) ∧ ⋆ = S ∧ ⋆ 1 s 4 (extensive) S ⊆ S ∧ ⋆ 2 (increasing) S ⊆ S ′ ⇒ S ∧ ⋆ ⊆ S ′∧ ⋆ 3 Agents ( S , C ) is closed iff C = S ∧ and S = C ⋆ (S)
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Building taxonomies Formal framework Consider a binary relation R between Concepts (C) agents & concepts Intent S ∧ of an agent set S : all Prs concepts used by every agent in S s 1 Extent C ⋆ of a concept set C Lng s Epistemic community : the extent of a 2 NS concept set C s “ ∧ ⋆ ” is a closure operation : 3 (idempotent) ( S ∧ ⋆ ) ∧ ⋆ = S ∧ ⋆ 1 s 4 (extensive) S ⊆ S ∧ ⋆ 2 (increasing) S ⊆ S ′ ⇒ S ∧ ⋆ ⊆ S ′∧ ⋆ 3 Agents ( S , C ) is closed iff C = S ∧ and S = C ⋆ (S)
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Building taxonomies From trees to lattices Representing epistemic communities structured into 1 fields, with common concerns, hierarchically: 2 generalization / specialization, overlapping. 3
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Building taxonomies From trees to lattices Representing epistemic mammal bird mammal bird communities platypus platypus platypus structured into 1 tree lattice fields, with common Italy Germany tree concerns, Rural Italy Urban Germany Rural Germany Urban Italy hierarchically: 2 generalization / Territories Habitat specialization, lattice Germany Rural Italy Urban overlapping. 3 Urban Italy Rural Italy Urban Germany Rural Germany
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Building taxonomies Galois lattices GL= { ( S ∧ ⋆ , S ) | S ⊆ S } is the partially-ordered set of all epistemic communities, with the partial order: ( X , X ∧ ) < ( X ′ , X ′∧ ) ⇔ X ⊂ X ′ ∅ ( s s s s ; ) GL 1 2 3 4 ( s s s ; Lng ) ( ; ) s s s NS 1 2 3 2 3 4 ; ( s s Lng Prs ) s s ; Lng NS ( ) 1 2 2 3 s ( ; Lng Prs NS ) 2
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Managing taxonomies Taxonomy selection & extraction Which ECs should we extract from ∅ ( s s s s ; ) 1 2 3 4 GL the lattice? s s s ; Lng ( ) ( s s s ; NS ) 1 2 3 2 3 4 Given the assumptions , a first criterion is agent set size — Small ( s s ; ) s s ; Lng Prs ( Lng NS ) 1 2 2 3 isolated ECs could be interesting s ( ; Lng Prs NS ) 2 too. poset ∅ ( s s s s ; ) In order to create a partial 1 2 3 4 taxonomy, with selection heuristics : ( s s s ; Lng ) ( s s s ; NS ) 1 2 3 2 3 4 partially-ordered set overlaying the lattice: “epistemic hypergraph”
Framework and objectives Epistemic communities Micro-foundations Epistemic community taxonomy and Galois lattices Managing taxonomies Taxonomy selection & extraction Which ECs should we extract from ∅ ( s s s s ; ) 1 2 3 4 GL the lattice? s s s ; Lng ( ) ( s s s ; NS ) 1 2 3 2 3 4 Given the assumptions , a first criterion is agent set size — Small ( s s ; ) s s ; Lng Prs ( Lng NS ) 1 2 2 3 isolated ECs could be interesting s ( ; Lng Prs NS ) 2 too. poset ∅ ( s s s s ; ) In order to create a partial 1 2 3 4 taxonomy, with selection heuristics : ( s s s ; Lng ) ( s s s ; NS ) 1 2 3 2 3 4 partially-ordered set overlaying the lattice: “epistemic hypergraph”
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