More than the sum of its parts : compact preference representation over combinatorial domains - Index

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More than the sum of its parts : compact preference representation over

combinatorial domains

Uckelman, J.D.

Publication date 2009

Link to publication

Citation for published version (APA):

Uckelman, J. D. (2009). More than the sum of its parts : compact preference representation over combinatorial domains. Institute for Logic, Language and Computation.

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Index

AV, see Approval Voting bidding language, 26, 35, 138 big-O notation, 96 Boolean circuit, 65 Boolean game, 23 Borda count, 183 branch-and-bound, 150 branching policy, 154 BruteForce, 166, 169 CATS, 163 clause, 10 coalitional game, 26, 67 collective utility function

egalitarian, 116 elitist, 116 Nash product, 116 utilitarian, 116 committee election, 185 compilation, 65 complete cube, 10 completeness, 100 complexity class, 96 complementary, 97 computable function, 97 Condorcet rule, 183 CP-net, 14, 35 CPLEX, 147, 166, 171, 179 cube, 10 CubeBF, 169 CubeLex, 169

CUF, see utility function, collective cumulative voting, 183 data generation, 161 decision problem, 95 description logic, 23 dominated, 51 expansion policy, 154 expressive intersection, 62 formula active, 51 atom, 10 clause, 10 Horn, 10 positive, 10 cube, 10 complete, 10 positive, 10 224

INDEX 225 definition, 10 dominated, 51 Horn clause, 10 k-, 10 k-clause, 10 k-cube, 10 k-form, 10 k-Horn clause, 10 k-pclause, 10 k-pcube, 10 k-pform, 10 k-spcube, 10 k-spform, 10 length, 61 literal, 10 ω-clause, 11 ω-cube, 11 ω-formula, 11 pclause, 10 pcube, 10 pform, 10 positive, 10 strictly, 10 spclause, 10 spcube, 10 spform, 10 state, 11 superfluous, 33 Fourier coefficient, 75 Fourier transform, 74 Fourier-Walsh expansion, 75 function problem, 111 GA-decomposition, 25

generalized additive independence, 25 goalbase, 11 equivalence, 13, 35, 53 language, 13 minimality, 64 represented, 34 uniquely, 34 size, 62 summation, 13 hardness, 99 heuristic, 154 lower bound, 154 upper bound, 154 Horn clause, 10 hornsat, 125 integer program, 148 IP, see integer program k-additive function, 33 k-clause, 10 k-cube, 10 k-form, 10 k-Horn clause, 10 k-pclause, 10 k-pcube, 10 k-pform, 10 k-spcube, 10 k-spform, 10 L-eval, 144 linear program, 147 literal, 10 logic program, 127 manipulability, 200 many-one reduction, 99 max-cuf, 101 max-util, 100 decision problem, 100 function problem, 122 k-, 196 max-util∗, 124 MC-net, 26, 67, 77 min-util, 100 model, 10 least, 125 modular, 32 M¨obius inversion, 36 monotone, 32

negation normal form, 87 NNF, 87

226 INDEX nonnegative, 32 normalized, 32 ω-clause, 11 ω-cube, 11 ω-formula, 11 OR/XOR language, 27, 35, 68, 139 OR∗ language, 139 parity function, 74

PAV, see Approval Voting, Property pclause, 10 PClauseBF, 169 PClauseLex, 169 pcube, 10 PCubeBF, 166, 175 PCubeLex, 166 PDAG, 66 penalty logic, 16 pform, 10

PLP, see propositional logic programming

plurality rule, 182 positive clause, 10 positive cube, 10 positive formula, 10

propositional directed acyclic graph, see PDAG propositional logic, 9

propositional logic programming, 125 self-reducible, 124 sincerity, 200 singleton consistency, 117 spclause, 10 spcube, 10 spform, 10

strictly positive cube, 10 strictly positive formula, 10 subadditive, 32 submodular, 32 succinctness, 62, 140 absolute, 79 cross-aggregator, 90 incomparable, 62 superadditive, 32 superfluous, 33 supermodular, 32 translation invariant, 44 unanimity rule, 182 uniform substitution, 14 unique representations, 34, 36, 80 unit-demand, 32, 51 simple, 12 utility function, 11 class of, 13 collective, 100 generated, 12

valued constraint satisfaction problem, see VCSP VCSP, 24 voting rule approval, 182 Borda count, 183 Condorcet, 183 cumulative, 183 dictatorship, 184 plurality, 182 unanimity, 182

WDP, see Winner Determination Problem

weighted goal, 11 size, 61

Winner Determination Problem, 101, 145