J.J. Sarbo, "Lattice embedding", in Conceptual Structures: Knowledge Representation as Interlingua (ICCS'96), ed. by P.W. Eklund and Gerard Ellis and Graham Mann, vol. 1115, pp. 293-307, 1996. Home/Search Document Details and Download
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NLCA: Towards an algorithmic implementation - Grootjen (1998) (Correct)
....the NLCA project 1 took one step back, and examined the nature of hierarchical structure in general, and phrase structure in particular. It looked for ways to derive hierarchical structure from input, and to incorporate it in a mathematically well founded theory of knowledge representation ([Sar96]) The result ( KS98] is an approach in which hierarchical structure is found as the yield of the interaction between different, inherent combinatorial properties of linguistic units. The model identifies three different basic relations that underlie these combinatorial properties, at a level ....
J.J. Sarbo, "Lattice embedding", in Conceptual Structures: Knowledge Representation as Interlingua (ICCS'96), ed. by P.W. Eklund and Gerard Ellis and Graham Mann, vol. 1115, pp. 293-307, 1996.
Natural Language Concept Analysis: Towards a Theoretical.. - Farkas, Kamphuis, Sarbo (1997) Self-citation (Sarbo) (Correct)
....combinatorial properties, rather than being given in advance. Farkas and Sarbo have chosen a different starting point. Their research on FCA ( SF94, SF95] has proven the usefulness and elegance of concept lattices in knowledge representation. Having shown the importance of concept sublattices ([Sar96]) they were looking for applications of the theory in NL, amongst others. It turned out soon that the object attribute dichotomy of FCA could be applied to NL; and by introducing the idea of external and internal arguments of lexical items their bindings could be determined. 15 ....
J. Sarbo. Lattice embedding. In P.W. Eklund, Gerard Ellis, and Graham Mann, editors, Conceptual Structures: Knowledge Representation 16 as Interlingua (ICCS'96), volume 1115 of Springer-Verlag, pages 293-- 307, 1996.
Building Sub-Knowledge Bases Using Concept Lattices - Sarbo (1996) (2 citations) Self-citation (Sarbo) (Correct)
....of a node v, is de ned as out(v) fw j (v; w) 2 e.g. De nition 7.2 Let L be a lattice, the elements of L ordered by v and x 2 L. We de ne 4(x) the up set of x as 4(x) fy 2 L j x v yg; and 5(x) the down set of x as 5(x) fy 2 L j y v xg. We describe an algorithm for lattice embedding in [14]. This algorithm (cf. g. 5) determines for two lattices, L 1 and L 2 , whether L 1 contains a sublattice isomorphic to L 2 . The lattices are represented as graphs, and the nodes of L 2 are partitioned according to their depth (the depth of a node is the length of the shortest path from the root ....
....of L 1 topdown and the partitions of L 2 in depth order. In each step, nodes of a partition of L 2 are mapped to those nodes of L 1 that are below the nodes already involved in a map of some earlier partition. Having found a map, the algorithm checks whether it is order preserving. Example 7. 3 ([14]) Consider the lattices L 1 and L 2 of Fig. 4. Partitioning of V 2 by depth yields f(A) B; C) D)g. Below we show the stepwise computation of the match M = f(A; a) B; c) C; b) D; e)g. k = 1) m = f(A; a)g (k = 2) M 2 = fag, 5(M 2 ) fb; c; d; e; f; gg; m = f(B; c) C; b)g This is a ....
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Sarbo, J.J. (1996) Lattice embedding. In P.W. Eklund, Gerard Ellis, and Graham Mann (eds), Conceptual Structures: Knowledge Representation as Interlingua (ICCS'96), 1115, Springer-Verlag, 293-307. 11
A Data Representation for Abstract Reasoning - Sarbo, Farkas (1997) Self-citation (Sarbo) (Correct)
....exist a context embedding such that the following diagram commutes (the function to concept lattice from context, described in theorem 2. 6, is denoted by the symbol ) 2 ( 1 h G (G , M 2 1 , 1 M ) 2 j , R 2 R 1 B B b b An algorithm for concept sublattices is given in [Sar96]. This algorithm determines for two lattices, B 1 and B 2 , whether B 1 contains a sublattice isomorphic to B 2 . The lattices are represented as graphs, and the nodes of B 2 are partitioned according to their depth (the depth of a node is the length of the shortest path from the root to that ....
....2 in depth order. In each step, nodes of a partition of B 2 are mapped to those nodes of B 1 that are below the nodes already involved in a map of some earlier partition. Having found a map, the algorithm checks whether it is order preserving. The complexity of lattice embedding is exponential ([Sar96]) The algorithm can be optimized by only considering irreducible elements of B 2 . This optimization, however, does not change the worst case complexity, as the number of irreducible elements is in the order of the size of the lattice . De nition 4.4 Let B = B; be a concept lattice and fB j ....
J. Sarbo. Lattice embedding. In P.W. Eklund, Gerard Ellis, and Graham Mann, editors, Conceptual Structures: Knowledge Representation as Interlingua (ICCS'96), volume 1115 of Springer-Verlag, pages 293-307, 1996.
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