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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-7470
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of extensions of a default theory. We give a complete solution to the problem of representability by means of default theories with finite set of defaults, and by means of normal default theories. We obtain partial results on representability by arbitrary (infinite, non-normal) default theories. We construct examples of denumerable families of non-including theories that are not representable. We also study the concept of equivalence between default theories.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1573-7470
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we introduce the notion of anF-program, whereF is a collection of formulas. We then study the complexity of computing withF-programs.F-programs can be regarded as a generalization of standard logic programs. Clauses (or rules) ofF-programs are built of formulas fromF. In particular, formulas other than atoms are allowed as “building blocks” ofF-program rules. Typical examples ofF are the set of all atoms (in which case the class of ordinary logic programs is obtained), the set of all literals (in this case, we get the class of logic programs with classical negation [9]), the set of all Horn clauses, the set of all clauses, the set of all clauses with at most two literals, the set of all clauses with at least three literals, etc. The notions of minimal and stable models [16, 1, 7] of a logic program have natural generalizations to the case ofF-programs. The resulting notions are called in this paperminimal andstable answer sets. We study the complexity of reasoning involving these notions. In particular, we establish the complexity of determining the existence of a stable answer set, and the complexity of determining the membership of a formula in some (or all) stable answer sets. We study the complexity of the existence of minimal answer sets, and that of determining the membership of a formula in all minimal answer sets. We also list several open problems.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Order 2 (1985), S. 1-8 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; N-free poset ; linear extension ; Jump number ; matroid ; greedy algorithm ; Rado-Edmonds theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let L=x 1 x 2...x n be a linear extension of a poset P. Each pair (x i , x i+1) such that x i ≮ x i+1in P is called a jump of L. It is well known that for N-free posets a natural ‘greedy’ procedure constructing linear extensions yields a linear extension with a minimum number of jumps. We show that there is a matroid corresponding to any N-free poset and apply the Rado-Edmonds Theorem to obtain another proof of this result.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Order 1 (1985), S. 345-350 
    ISSN: 1572-9273
    Keywords: 05C70 ; Uniform hypergraph ; graph ; tournament ; poset ; Ramsey type theorem ; decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We determine a minimum cardinality family ℱ n, k (resp. ℋ n, k ) ofn-uniform,k-edge hypergraphs satisfying the following property: all, except for finitely many,n-uniform hypergraphs satisfying the divisibility condition have an ℱ n, k -decomposition (resp. vertex ℋ n, k -decomposition).
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Graphs and combinatorics 3 (1987), S. 67-73 
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A coloring of the edges of a graph is called alocal k-coloring if every vertex is incident to edges of at mostk distinct colors. For a given graphG, thelocal Ramsey number, r loc k (G), is the smallest integern such that any localk-coloring ofK n , (the complete graph onn vertices), contains a monochromatic copy ofG. The following conjecture of Gyárfás et al. is proved here: for each positive integerk there exists a constantc = c(k) such thatr loc k (G) ≤ cr k (G), for every connected grraphG (wherer k (G) is theusual Ramsey number fork colors). Possible generalizations for hypergraphs are considered.
    Type of Medium: Electronic Resource
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