From: Simon Spero <ses@unc.edu>

Date: Sat, 6 Feb 2010 17:24:51 -0500

Message-ID: <1af06bde1002061424v21823032x997c87f645b0cadd@mail.gmail.com>

To: Christophe Dupriez <christophe.dupriez@destin.be>

Cc: SKOS <public-esw-thes@w3.org>, Ed Summers <ehs@pobox.com>, Seth van Hooland <svhoolan@ulb.ac.be>, Bhojaraju Gunjal <bhojaraju.g@gmail.com>, Emmanuel Di Pretoro <edipretoro@gmail.com>, José Ramón Pérez Agüera <jose.aguera@gmail.com>, danbrickley@gmail.com

Date: Sat, 6 Feb 2010 17:24:51 -0500

Message-ID: <1af06bde1002061424v21823032x997c87f645b0cadd@mail.gmail.com>

To: Christophe Dupriez <christophe.dupriez@destin.be>

Cc: SKOS <public-esw-thes@w3.org>, Ed Summers <ehs@pobox.com>, Seth van Hooland <svhoolan@ulb.ac.be>, Bhojaraju Gunjal <bhojaraju.g@gmail.com>, Emmanuel Di Pretoro <edipretoro@gmail.com>, José Ramón Pérez Agüera <jose.aguera@gmail.com>, danbrickley@gmail.com

---- Useful sources: Croft, William and D. Alan Cruse (2004). *Cognitive linguistics*. Cambridge University Press. Cruse, D. Alan. (1986). *Lexical semantics*. Cambridge University Press. Riesthuis, Gerhard J. A. et al. (2008). *Guidelines for Multilingual Thesauri*. IFLA Professional Reports, No. 115. The Hague, NL: International Federation of Library Associations and Institutions. URL: http://www.ifla.org/VII/s29/pubs/Profrep115.pdf Soergel, Dagobert (1974). Indexing languages and thesauri: construction and maintenance. Information sciences series. Los Angeles: Melville Pub. Co. ISBN: 0471810479. In fact, read as much Soergel as you can find :-) ---------- I'm not sure if the semantics of SKOS are quite right for the mathematical symbols you're using Let the type Δ denote the domain of discourse to which labels might be attached. Let the type Σ denote the set of all possible label strings . Let the type CONCEPT denote a two-tuple, (Σ × ℙ(Δ)) containing a label and a set of elements of Δ . Let the type CONCEPT-SCHEME denote a 2-tuple (Σ × ℙ(CONCEPT)). Let c and k denote two arbitrary CONCEPTs Let C and K denote two arbitrary CONCEPT-SCHEMEs Let label(k) refer to the first element of CONCEPT k. Let documents(k) refer to the second element of CONCEPT k. Let label(C) refer to the first element of a CONCEPT-SCHEME C. Let concepts(C) refer to the second element of a CONCEPT-SCHEME C. Let the 2-tuple (c,C) denote a fully qualified concept (FQC) consisting of of a concept and a concept scheme, where c ∈ concepts(C). BT, NT, and EQ for a single CONCEPT scheme. Within a single CONCEPT-SCHEME C, such that c ∈ C ⋀ k ∈ C 1: ( BT) c < k iff documents(c) ⊂ documents(k) 2: (NT) c > k iff documents(c) ⊃ documents(k) 3: (SY) c ≍ k iff documents(c) ≡ documents(k) Unique Concept Scheme Name Assumption 4: ∀ C ∈ CONCEPT-SCHEME. ∀ K ∈ CONCEPT-SCHEME. label(C) ≡ label(D) → C ≡ D Within Scheme Unique Preferred Name Assumption 5: ∀ C ∈ CONCEPT-SCHEME. ∀ c ∈ concepts(C). ∀ d ∈ concepts(C). label(c) = label(d) → c ≡ d Identity 6: C = K iff label(c) ≡ label(k) ⋀ concepts(c) ≡ concepts(k) 7: c = k iff label(c) ≡ label(k) ⋀ documents(c) ≡ documents(k) ^ ∀ C ∈ CONCEPT-SCHEME. c ∈ concepts(C) iff k ∈ concepts(C) Mapping Relations Note that mapping relations are only defined between concepts in different concept schemes. Exact match, (c,C) ≍ (k,K) 8: For an exact match, (c,C) ≍ (k,K) (c,C) ≍ (k,K) iff C ≢ K ⋀ documents(c) ≡ documents(k) Broad Match: (c,C) ⪷ (k,K) 9: (c,C) ⪷ (k,K) iff ¬ (c,C) ≍ (k,K) ⋀ c < k ⋀ ∄d ∈ concepts(K). (c < d ⋀ d < k ⋀ d ≠ k) Narrower Match: (c,C) ⪸ (k,K) 10: (c,C) ⪸ (k,K) iff ¬ (c,C) ≍ (k,K) ⋀ c > k ⋀ ∄d ∈ concepts(K). (c > d ⋀ d > k ⋀ d ≠ k) Close Match: (c,C) ≈ (k,K) The semantics of close match are under determined: as a bare minimum, we must define a similarity function f ∈ (CONCEPT × CONCEPT → [0,1]), together with a threshold t below which two concepts are not considered to be a match. 11: (c,C) ≈ (k,K) iff ¬ (c,C) ≍ (k,K) ⋀ f(c,k) ≥ t ⋀ ∄d ∈ concepts(K). f(c,d) > f(c,k)Received on Saturday, 6 February 2010 22:25:24 UTC

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