Semiring induced valuation algebras: Exact and approximate local computation algorithms
Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra. There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non...
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| Veröffentlicht in: | Artificial intelligence Jg. 172; H. 11; S. 1360 - 1399 |
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| Abstract | Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra. There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible. |
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| AbstractList | Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra. There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible. |
| Author | Kohlas, J. Wilson, N. |
| Author_xml | – sequence: 1 givenname: J. surname: Kohlas fullname: Kohlas, J. email: juerg.kohlas@unifr.ch organization: Department of Informatics, University of Fribourg, Switzerland – sequence: 2 givenname: N. surname: Wilson fullname: Wilson, N. email: n.wilson@4c.ucc.ie organization: Cork Constraint Computation Centre, Department of Computer Science, Ireland |
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| Cites_doi | 10.1145/256303.256306 10.1073/pnas.28.12.535 10.1093/logcom/9.5.651 10.1109/18.825794 10.2140/pjm.1960.10.313 10.1111/j.2517-6161.1988.tb01721.x 10.1016/j.artint.2003.09.002 10.1016/0165-0114(95)00052-6 10.1016/S0888-613X(97)89135-9 10.2996/kmj/1138843534 10.1016/0004-3702(87)90002-6 10.1111/j.0824-7935.2004.00239.x 10.1016/S0004-3702(99)00059-4 10.1016/0165-0114(95)00133-6 10.1016/B978-0-08-051489-5.50008-4 10.1023/A:1018953016172 10.24033/asens.1015 10.1145/636865.636866 10.1016/j.ijar.2003.10.009 10.1007/3-540-45578-7_24 10.1016/j.artint.2005.04.004 10.1016/j.artint.2004.05.004 10.1016/0004-3702(86)90090-1 10.1023/A:1026441215081 10.1007/978-94-015-9540-7 |
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| Issue | 11 |
| Keywords | Valuation networks Uncertainty Join tree decompositions Valuation algebras Local computation Semirings Soft constraints Hypergraph Algebraic structure Probabilistic approach Relational database Network architecture Constraint satisfaction Semiring Semigroup Graph theory Soft constraint Modeling Bayes network Artificial intelligence |
| Language | English |
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| References | Spohn (bib060) 1988 Kohlas, Shenoy (bib037) 2000 Dechter, Pearl (bib023) 1987; 34 Hewitt, Zuckermann (bib028) 1956; 83 Cooper, Schiex (bib016) 2004; 154 L. Chang, Semiring-based unifying framework for constraint-based inference, Master's thesis, University of British Columbia, 2005 Lauritzen, Jensen (bib040) 1997; 21 Klement, Mesiar, Pap (bib033) 2000 Shafer (bib054) 1996; vol. 67 Croisot (bib017) 1953; 79 Clifford, Preston (bib015) 1967 Dechter (bib021) 1999; 113 M. Pouly, Nenok 1.1 user guide, Tech. Rep. 06-02, Department of Informatics, University of Fribourg, 2006 N. Wilson, Bounds and pre-processing for local computation of semiring valuations, in: J. Kohlas, J. Mengin, N. Wilson (Eds.), ECAI'2004, Workshop 22: Local Computation for Logics and Uncertainty, 2004, pp. 53–56 Larrosa, Schiex (bib039) 2004; 159 Bistarelli, Montanari, Rossi, Schiex, Verfaillie, Fargier (bib009) 1999; 4 Kask, Dechter, Larrosa, Dechter (bib032) 2005; 166 Schiex, T., Fargier, H., Verfaillie, G., Valued constraint satisfaction problems: Hard and easy problems, in: Proc. IJCAI-95, 1995, pp. 631–637 Bistarelli, Fruewirth, Marthe, Rossi (bib005) 2004 Kohlas, Haenni, Moral (bib036) 1999; 9 Tamura, Kimura (bib061) 1954 Maier (bib042) 1983 J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., 1988 Shenoy (bib058) 1997; 17 Haenni (bib026) 2004; 37 Kohlas (bib034) 2003 Menger (bib044) 1942; 28 Yager, Rybalov (bib063) 1996; 80 G. Shafer, An axiomatic study of computation in hypertrees, Working Paper 232, School of Business, University of Kansas, 1991 Schneuwly, Pouly, Kohlas (bib051) 2004 L. Chang, A.K. Mackworth, Generalized constraint-based inference, Tech. Rep. TR-2005-10, Dept. of Computer Science, Univ. of British Columbia, 2005 Aji, McEliece (bib001) 2000; 46 E. Amir, Efficient approximation for triangulation of minimum treewidth, in: Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence, 2001, pp. 7–15 Mengin, Wilson (bib045) 1999 Bodlaender (bib011) 2006; vol. 4271 R. Dechter, Mini-buckets: A general scheme for generating approximations in automated reasoning, in: Proc. Fifteenth International Joint Conference of Artificial Intelligence (IJCAI97), 1997, pp. 1297–1303 K. Kask, R. Dechter, Mini-bucket heuristics for improved search, in: Proc. UAI99, 1999, pp. 314–323 Shenoy (bib056) 1992 Schweizer, Sklar (bib052) 1960; 10 Baccelli, Cohen, Olsder, Quadrat (bib003) 1992 R. Dechter, K. Kask, J. Larrosa, A general scheme for multiple lower bound computation in constraint optimization, in: Proc. CP2001, 2001, pp. 346–360 Bistarelli, Montanari, Rossi (bib008) 1997; 44 Kolokoltsov, Maslov (bib038) 1997 Kohlas (bib035) 2004 Lauritzen, Spiegelhalter (bib041) 1988; 50 M. Pouly, J. Kohlas, Minimizing communication costs of distributed local computation, Tech. rep., Department of Informatics, University of Fribourg, 2005 S. Bistarelli, F. Gadducci, Enhancing constraints manipulation in semiring-based formalisms, in: Proc. 17th European Conference on Artificial Intelligence (ECAI 2006), 2006, pp. 63–67 Bodlaender (bib010) 1993; 11 Beeri, Fagin, Maier, Mendelzon, Ullman, Yannakakis (bib004) 1981 Haenni, Kohlas, Lehmann (bib027) 2000 Shenoy, Shafer (bib059) 1990; vol. 9 De Kleer, Brown (bib019) 1986; 29 Schiex (bib049) 1992 Dechter, Rish (bib024) 2003; 50 Shenoy (bib057) 1996 De Baets (bib018) 1996; 118 R. Mateescu, R. Dechter, K. Kask, Tree approximation for belief updating, in: Proc. AAAI-2002, 2002, pp. 553–559 K. Kask, R. Dechter, Branch and bound with mini-bucket heuristics, in: Proc. International Joint Conference on Artificial Intelligence (IJCAI99), 1999, pp. 426–433 S. Bistarelli, S.K.L. Fung, J.H.M. Lee, H. Leung, A local search framework for semiring-based constraint satisfaction problems, in: Proc. CP2003 Workshop on Soft Constraints (Soft-2003), 2003 Jensen, Lauritzen, Olesen (bib029) 1990; 4 V. Gogate, R. Dechter, A complete anytime algorithm for treewidth, in: Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence UAI-04, 2004, pp. 201–208 G. Shafer, P. Shenoy, Local computation in hypertrees, Tech. Rep. 201, School of Business, University of Kansas, Lawrence, 1988 Cechlárová, Plávka (bib012) 1996; 77 10.1016/j.artint.2008.03.003_bib025 10.1016/j.artint.2008.03.003_bib062 10.1016/j.artint.2008.03.003_bib020 10.1016/j.artint.2008.03.003_bib022 Larrosa (10.1016/j.artint.2008.03.003_bib039) 2004; 159 Aji (10.1016/j.artint.2008.03.003_bib001) 2000; 46 Baccelli (10.1016/j.artint.2008.03.003_bib003) 1992 Kolokoltsov (10.1016/j.artint.2008.03.003_bib038) 1997 Schneuwly (10.1016/j.artint.2008.03.003_bib051) Hewitt (10.1016/j.artint.2008.03.003_bib028) 1956; 83 Dechter (10.1016/j.artint.2008.03.003_bib023) 1987; 34 Shenoy (10.1016/j.artint.2008.03.003_bib057) 1996 Lauritzen (10.1016/j.artint.2008.03.003_bib040) 1997; 21 Menger (10.1016/j.artint.2008.03.003_bib044) 1942; 28 Schweizer (10.1016/j.artint.2008.03.003_bib052) 1960; 10 De Kleer (10.1016/j.artint.2008.03.003_bib019) 1986; 29 Maier (10.1016/j.artint.2008.03.003_bib042) 1983 Cechlárová (10.1016/j.artint.2008.03.003_bib012) 1996; 77 Croisot (10.1016/j.artint.2008.03.003_bib017) 1953; 79 Clifford (10.1016/j.artint.2008.03.003_bib015) 1967 Tamura (10.1016/j.artint.2008.03.003_bib061) 1954 10.1016/j.artint.2008.03.003_bib013 10.1016/j.artint.2008.03.003_bib014 Bodlaender (10.1016/j.artint.2008.03.003_bib010) 1993; 11 Kohlas (10.1016/j.artint.2008.03.003_bib034) 2003 Kohlas (10.1016/j.artint.2008.03.003_bib035) Dechter (10.1016/j.artint.2008.03.003_bib021) 1999; 113 10.1016/j.artint.2008.03.003_bib050 Lauritzen (10.1016/j.artint.2008.03.003_bib041) 1988; 50 10.1016/j.artint.2008.03.003_bib053 Shenoy (10.1016/j.artint.2008.03.003_bib059) 1990; vol. 9 10.1016/j.artint.2008.03.003_bib055 Cooper (10.1016/j.artint.2008.03.003_bib016) 2004; 154 Haenni (10.1016/j.artint.2008.03.003_bib026) 2004; 37 Mengin (10.1016/j.artint.2008.03.003_bib045) 1999 Kohlas (10.1016/j.artint.2008.03.003_bib037) 2000 Shafer (10.1016/j.artint.2008.03.003_bib054) 1996; vol. 67 Spohn (10.1016/j.artint.2008.03.003_bib060) 1988 Kohlas (10.1016/j.artint.2008.03.003_bib036) 1999; 9 Yager (10.1016/j.artint.2008.03.003_bib063) 1996; 80 Jensen (10.1016/j.artint.2008.03.003_bib029) 1990; 4 Bistarelli (10.1016/j.artint.2008.03.003_bib005) 2004 Klement (10.1016/j.artint.2008.03.003_bib033) 2000 10.1016/j.artint.2008.03.003_bib002 De Baets (10.1016/j.artint.2008.03.003_bib018) 1996; 118 10.1016/j.artint.2008.03.003_bib046 Bodlaender (10.1016/j.artint.2008.03.003_bib011) 2006; vol. 4271 10.1016/j.artint.2008.03.003_bib047 10.1016/j.artint.2008.03.003_bib048 10.1016/j.artint.2008.03.003_bib006 Beeri (10.1016/j.artint.2008.03.003_bib004) 1981 10.1016/j.artint.2008.03.003_bib007 10.1016/j.artint.2008.03.003_bib043 Bistarelli (10.1016/j.artint.2008.03.003_bib008) 1997; 44 Haenni (10.1016/j.artint.2008.03.003_bib027) 2000 Kask (10.1016/j.artint.2008.03.003_bib032) 2005; 166 Bistarelli (10.1016/j.artint.2008.03.003_bib009) 1999; 4 10.1016/j.artint.2008.03.003_bib030 10.1016/j.artint.2008.03.003_bib031 Shenoy (10.1016/j.artint.2008.03.003_bib056) 1992 Dechter (10.1016/j.artint.2008.03.003_bib024) 2003; 50 Schiex (10.1016/j.artint.2008.03.003_bib049) 1992 Shenoy (10.1016/j.artint.2008.03.003_bib058) 1997; 17 |
| References_xml | – volume: 29 start-page: 33 year: 1986 end-page: 61 ident: bib019 article-title: Theories of causal ordering publication-title: Artif. Intell. – reference: S. Bistarelli, S.K.L. Fung, J.H.M. Lee, H. Leung, A local search framework for semiring-based constraint satisfaction problems, in: Proc. CP2003 Workshop on Soft Constraints (Soft-2003), 2003 – volume: 159 start-page: 1 year: 2004 end-page: 26 ident: bib039 article-title: Solving weighted CSP by maintaining arc consistency publication-title: Artif. Intell. – volume: 154 start-page: 199 year: 2004 end-page: 227 ident: bib016 article-title: Arc consistency for soft constraints publication-title: Artif. Intell. – start-page: 259 year: 1996 end-page: 275 ident: bib057 article-title: Axioms for dynamic programming publication-title: Computational Learning and Probabilistic Reasoning – start-page: 105 year: 1988 end-page: 134 ident: bib060 article-title: Ordinal conditional functions: A dynamic theory of epistemic states publication-title: Causation in Decision, Belief Change, and Statistics, vol. 2 – volume: vol. 9 start-page: 169 year: 1990 end-page: 198 ident: bib059 article-title: Axioms for probability and belief-function propagation publication-title: Uncertainty in Artificial Intelligence 4 – volume: 17 start-page: 239 year: 1997 end-page: 263 ident: bib058 article-title: Binary join trees for computing marginals in the Shenoy–Shafer architecture publication-title: Internat. J. Approx. Reason. – volume: 50 start-page: 157 year: 1988 end-page: 224 ident: bib041 article-title: Local computations with probabilities on graphical structures and their application to expert systems publication-title: J. Royal Stat. Soc. – reference: E. Amir, Efficient approximation for triangulation of minimum treewidth, in: Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence, 2001, pp. 7–15 – volume: vol. 67 year: 1996 ident: bib054 article-title: Probabilistic Expert Systems publication-title: CBMS-NSF Regional Conference Series in Applied Mathematics – year: 2004 ident: bib035 article-title: Valuation algebras induced by semirings. Tech. Rep. 04-03, Department of Informatics, University of Fribourg – year: 1967 ident: bib015 article-title: Algebraic Theory of Semigroups. American Mathematical Society – volume: 37 start-page: 1 year: 2004 end-page: 41 ident: bib026 article-title: Ordered valuation algebras: A generic framework for approximating inference publication-title: Internat. J. Approx. Reason. – volume: 166 start-page: 165 year: 2005 end-page: 193 ident: bib032 article-title: Unifying cluster-tree decompositions for reasoning in graphical models publication-title: Artif. Intell. – start-page: 386 year: 1999 end-page: 396 ident: bib045 article-title: Logical deduction using the local computation framework publication-title: European Conf. ECSQARU'99 – reference: N. Wilson, Bounds and pre-processing for local computation of semiring valuations, in: J. Kohlas, J. Mengin, N. Wilson (Eds.), ECAI'2004, Workshop 22: Local Computation for Logics and Uncertainty, 2004, pp. 53–56 – start-page: 83 year: 1992 end-page: 104 ident: bib056 article-title: Valuation-based systems: A framework for managing uncertainty in expert systems publication-title: Fuzzy Logic for the Management of Uncertainty – year: 2004 ident: bib005 article-title: Soft constraint propagation and solving in constraint handling rules publication-title: Comput. Intell. – reference: L. Chang, A.K. Mackworth, Generalized constraint-based inference, Tech. Rep. TR-2005-10, Dept. of Computer Science, Univ. of British Columbia, 2005 – reference: Schiex, T., Fargier, H., Verfaillie, G., Valued constraint satisfaction problems: Hard and easy problems, in: Proc. IJCAI-95, 1995, pp. 631–637 – reference: V. Gogate, R. Dechter, A complete anytime algorithm for treewidth, in: Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence UAI-04, 2004, pp. 201–208 – volume: 34 start-page: 1 year: 1987 end-page: 38 ident: bib023 article-title: Network-based heuristics for constraint satisfaction problems publication-title: Artif. Intell. – volume: 10 start-page: 313 year: 1960 end-page: 334 ident: bib052 article-title: Statistical metric spaces publication-title: Pacific J. Math. – year: 2000 ident: bib033 article-title: Triangular Norms publication-title: Trends in Logic – reference: M. Pouly, J. Kohlas, Minimizing communication costs of distributed local computation, Tech. rep., Department of Informatics, University of Fribourg, 2005 – volume: 83 start-page: 70 year: 1956 end-page: 97 ident: bib028 article-title: The l1-algebra of a commutative semigroup publication-title: Trans. Amer. Math. Soc. – start-page: 5 year: 2000 end-page: 40 ident: bib037 article-title: Computation in valuation algebras publication-title: Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 5: Algorithms for Uncertainty and Defeasible Reasoning – volume: 21 start-page: 51 year: 1997 end-page: 70 ident: bib040 article-title: Local computation with valuations from a commutative semigroup publication-title: Ann. Math. Artif. Intell. – volume: 28 start-page: 535 year: 1942 end-page: 537 ident: bib044 article-title: Statistical metrics publication-title: Proc. Nat. Acad. Sci. – volume: 79 start-page: 361 year: 1953 end-page: 379 ident: bib017 article-title: Demi-groupes inversifs et demi-groupes réunions de demi-groupes simples publication-title: Ann. Sci. Ecole Norm. Sup. – reference: K. Kask, R. Dechter, Mini-bucket heuristics for improved search, in: Proc. UAI99, 1999, pp. 314–323 – volume: 46 start-page: 325 year: 2000 end-page: 343 ident: bib001 article-title: The generalized distributive law publication-title: IEEE Trans. Inform. Theory – year: 2003 ident: bib034 article-title: Information Algebras: Generic Structures for Inference – reference: M. Pouly, Nenok 1.1 user guide, Tech. Rep. 06-02, Department of Informatics, University of Fribourg, 2006 – start-page: 109 year: 1954 end-page: 112 ident: bib061 article-title: On decompositions of a commutative semigroup publication-title: Kodai Math. Sem. Rep. – year: 1997 ident: bib038 article-title: Idempotent Analysis and its Applications – reference: S. Bistarelli, F. Gadducci, Enhancing constraints manipulation in semiring-based formalisms, in: Proc. 17th European Conference on Artificial Intelligence (ECAI 2006), 2006, pp. 63–67 – volume: 113 start-page: 41 year: 1999 end-page: 85 ident: bib021 article-title: Bucket elimination: A unifying framework for reasoning publication-title: Artif. Intell. – reference: K. Kask, R. Dechter, Branch and bound with mini-bucket heuristics, in: Proc. International Joint Conference on Artificial Intelligence (IJCAI99), 1999, pp. 426–433 – volume: 9 start-page: 651 year: 1999 end-page: 681 ident: bib036 article-title: Propositional information systems publication-title: J. Logic Comput. – start-page: 221 year: 2000 end-page: 287 ident: bib027 article-title: Probabilistic argumentation systems publication-title: Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 5: Algorithms for Uncertainty and Defeasible Reasoning – start-page: 268 year: 1992 end-page: 275 ident: bib049 article-title: Possibilistic constraint satisfaction problems or “how to handle soft constraints?” publication-title: Uncertainty in Artificial Intelligence: Proc. of the Eighth Conference – volume: 11 start-page: 1 year: 1993 end-page: 22 ident: bib010 article-title: A tourist guide through treewidth publication-title: Acta Cybern. – volume: vol. 4271 start-page: 1 year: 2006 end-page: 14 ident: bib011 article-title: Treewidth: Characterizations, applications, and computations publication-title: WG – reference: R. Dechter, Mini-buckets: A general scheme for generating approximations in automated reasoning, in: Proc. Fifteenth International Joint Conference of Artificial Intelligence (IJCAI97), 1997, pp. 1297–1303 – reference: R. Mateescu, R. Dechter, K. Kask, Tree approximation for belief updating, in: Proc. AAAI-2002, 2002, pp. 553–559 – reference: L. Chang, Semiring-based unifying framework for constraint-based inference, Master's thesis, University of British Columbia, 2005 – volume: 77 start-page: 337 year: 1996 end-page: 348 ident: bib012 article-title: Linear independence in bottleneck algebras publication-title: Fuzzy Sets Syst. – year: 1992 ident: bib003 article-title: Synchronization and Linearity: An Algebra for Discrete Event Systems – reference: J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., 1988 – volume: 4 start-page: 269 year: 1990 end-page: 282 ident: bib029 article-title: Bayesian updating in causal probabilistic networks by local computations publication-title: Comp. Stat. Q. – volume: 4 year: 1999 ident: bib009 article-title: Semiring-based CSPs and valued CSPs: Frameworks, properties and comparison publication-title: CONSTRAINTS: An International Journal – volume: 118 start-page: 00 year: 1996 ident: bib018 article-title: Idempotent uninorms publication-title: European J. Op. Res. – reference: G. Shafer, P. Shenoy, Local computation in hypertrees, Tech. Rep. 201, School of Business, University of Kansas, Lawrence, 1988 – reference: R. Dechter, K. Kask, J. Larrosa, A general scheme for multiple lower bound computation in constraint optimization, in: Proc. CP2001, 2001, pp. 346–360 – volume: 50 start-page: 107 year: 2003 end-page: 153 ident: bib024 article-title: Mini-buckets: A general scheme for bounded inference publication-title: J. ACM – volume: 80 start-page: 111 year: 1996 end-page: 120 ident: bib063 article-title: Uninorm aggregation operators publication-title: Fuzzy Sets Syst. – year: 2004 ident: bib051 article-title: Local computation in covering join trees, Tech. Rep. 04-16, Department of Informatics, University of Fribourg – volume: 44 start-page: 201 year: 1997 end-page: 236 ident: bib008 article-title: Semiring-based constraint satisfaction and optimization optimisation publication-title: J. ACM – year: 1983 ident: bib042 article-title: The Theory of Relational Databases – reference: G. Shafer, An axiomatic study of computation in hypertrees, Working Paper 232, School of Business, University of Kansas, 1991 – start-page: 355 year: 1981 end-page: 362 ident: bib004 article-title: Properties of acyclic database schemes publication-title: ACM Symposium on Theory of Computing – start-page: 259 year: 1996 ident: 10.1016/j.artint.2008.03.003_bib057 article-title: Axioms for dynamic programming – ident: 10.1016/j.artint.2008.03.003_bib013 – volume: 44 start-page: 201 year: 1997 ident: 10.1016/j.artint.2008.03.003_bib008 article-title: Semiring-based constraint satisfaction and optimization optimisation publication-title: J. ACM doi: 10.1145/256303.256306 – year: 2003 ident: 10.1016/j.artint.2008.03.003_bib034 – volume: 28 start-page: 535 year: 1942 ident: 10.1016/j.artint.2008.03.003_bib044 article-title: Statistical metrics publication-title: Proc. Nat. Acad. Sci. doi: 10.1073/pnas.28.12.535 – ident: 10.1016/j.artint.2008.03.003_bib055 – volume: 83 start-page: 70 year: 1956 ident: 10.1016/j.artint.2008.03.003_bib028 article-title: The l1-algebra of a commutative semigroup publication-title: Trans. Amer. Math. Soc. – volume: 9 start-page: 651 issue: 5 year: 1999 ident: 10.1016/j.artint.2008.03.003_bib036 article-title: Propositional information systems publication-title: J. Logic Comput. doi: 10.1093/logcom/9.5.651 – volume: vol. 4271 start-page: 1 year: 2006 ident: 10.1016/j.artint.2008.03.003_bib011 article-title: Treewidth: Characterizations, applications, and computations – ident: 10.1016/j.artint.2008.03.003_bib051 – volume: 46 start-page: 325 issue: 2 year: 2000 ident: 10.1016/j.artint.2008.03.003_bib001 article-title: The generalized distributive law publication-title: IEEE Trans. Inform. Theory doi: 10.1109/18.825794 – ident: 10.1016/j.artint.2008.03.003_bib014 – ident: 10.1016/j.artint.2008.03.003_bib020 – start-page: 355 year: 1981 ident: 10.1016/j.artint.2008.03.003_bib004 article-title: Properties of acyclic database schemes – volume: 10 start-page: 313 year: 1960 ident: 10.1016/j.artint.2008.03.003_bib052 article-title: Statistical metric spaces publication-title: Pacific J. Math. doi: 10.2140/pjm.1960.10.313 – volume: 50 start-page: 157 issue: 2 year: 1988 ident: 10.1016/j.artint.2008.03.003_bib041 article-title: Local computations with probabilities on graphical structures and their application to expert systems publication-title: J. Royal Stat. Soc. doi: 10.1111/j.2517-6161.1988.tb01721.x – start-page: 386 year: 1999 ident: 10.1016/j.artint.2008.03.003_bib045 article-title: Logical deduction using the local computation framework – volume: vol. 67 year: 1996 ident: 10.1016/j.artint.2008.03.003_bib054 article-title: Probabilistic Expert Systems – year: 1992 ident: 10.1016/j.artint.2008.03.003_bib003 – ident: 10.1016/j.artint.2008.03.003_bib035 – volume: 11 start-page: 1 issue: 1–2 year: 1993 ident: 10.1016/j.artint.2008.03.003_bib010 article-title: A tourist guide through treewidth publication-title: Acta Cybern. – volume: 154 start-page: 199 issue: 1–2 year: 2004 ident: 10.1016/j.artint.2008.03.003_bib016 article-title: Arc consistency for soft constraints publication-title: Artif. Intell. doi: 10.1016/j.artint.2003.09.002 – ident: 10.1016/j.artint.2008.03.003_bib031 – year: 1983 ident: 10.1016/j.artint.2008.03.003_bib042 – ident: 10.1016/j.artint.2008.03.003_bib007 – start-page: 5 year: 2000 ident: 10.1016/j.artint.2008.03.003_bib037 article-title: Computation in valuation algebras – volume: 77 start-page: 337 issue: 3 year: 1996 ident: 10.1016/j.artint.2008.03.003_bib012 article-title: Linear independence in bottleneck algebras publication-title: Fuzzy Sets Syst. doi: 10.1016/0165-0114(95)00052-6 – ident: 10.1016/j.artint.2008.03.003_bib062 – volume: 17 start-page: 239 year: 1997 ident: 10.1016/j.artint.2008.03.003_bib058 article-title: Binary join trees for computing marginals in the Shenoy–Shafer architecture publication-title: Internat. J. Approx. Reason. doi: 10.1016/S0888-613X(97)89135-9 – year: 1967 ident: 10.1016/j.artint.2008.03.003_bib015 – start-page: 109 year: 1954 ident: 10.1016/j.artint.2008.03.003_bib061 article-title: On decompositions of a commutative semigroup publication-title: Kodai Math. Sem. Rep. doi: 10.2996/kmj/1138843534 – start-page: 105 year: 1988 ident: 10.1016/j.artint.2008.03.003_bib060 article-title: Ordinal conditional functions: A dynamic theory of epistemic states – volume: 34 start-page: 1 issue: 1 year: 1987 ident: 10.1016/j.artint.2008.03.003_bib023 article-title: Network-based heuristics for constraint satisfaction problems publication-title: Artif. Intell. doi: 10.1016/0004-3702(87)90002-6 – year: 2004 ident: 10.1016/j.artint.2008.03.003_bib005 article-title: Soft constraint propagation and solving in constraint handling rules publication-title: Comput. Intell. doi: 10.1111/j.0824-7935.2004.00239.x – ident: 10.1016/j.artint.2008.03.003_bib050 – ident: 10.1016/j.artint.2008.03.003_bib030 – volume: 113 start-page: 41 issue: 1–2 year: 1999 ident: 10.1016/j.artint.2008.03.003_bib021 article-title: Bucket elimination: A unifying framework for reasoning publication-title: Artif. Intell. doi: 10.1016/S0004-3702(99)00059-4 – ident: 10.1016/j.artint.2008.03.003_bib053 – ident: 10.1016/j.artint.2008.03.003_bib006 – ident: 10.1016/j.artint.2008.03.003_bib002 – start-page: 268 year: 1992 ident: 10.1016/j.artint.2008.03.003_bib049 article-title: Possibilistic constraint satisfaction problems or “how to handle soft constraints?” – start-page: 221 year: 2000 ident: 10.1016/j.artint.2008.03.003_bib027 article-title: Probabilistic argumentation systems – ident: 10.1016/j.artint.2008.03.003_bib025 – volume: 80 start-page: 111 year: 1996 ident: 10.1016/j.artint.2008.03.003_bib063 article-title: Uninorm aggregation operators publication-title: Fuzzy Sets Syst. doi: 10.1016/0165-0114(95)00133-6 – ident: 10.1016/j.artint.2008.03.003_bib046 doi: 10.1016/B978-0-08-051489-5.50008-4 – ident: 10.1016/j.artint.2008.03.003_bib048 – ident: 10.1016/j.artint.2008.03.003_bib043 – volume: 21 start-page: 51 issue: 1 year: 1997 ident: 10.1016/j.artint.2008.03.003_bib040 article-title: Local computation with valuations from a commutative semigroup publication-title: Ann. Math. Artif. Intell. doi: 10.1023/A:1018953016172 – volume: 79 start-page: 361 issue: 3 year: 1953 ident: 10.1016/j.artint.2008.03.003_bib017 article-title: Demi-groupes inversifs et demi-groupes réunions de demi-groupes simples publication-title: Ann. Sci. Ecole Norm. Sup. doi: 10.24033/asens.1015 – start-page: 83 year: 1992 ident: 10.1016/j.artint.2008.03.003_bib056 article-title: Valuation-based systems: A framework for managing uncertainty in expert systems – volume: 50 start-page: 107 issue: 2 year: 2003 ident: 10.1016/j.artint.2008.03.003_bib024 article-title: Mini-buckets: A general scheme for bounded inference publication-title: J. ACM doi: 10.1145/636865.636866 – volume: 37 start-page: 1 issue: 1 year: 2004 ident: 10.1016/j.artint.2008.03.003_bib026 article-title: Ordered valuation algebras: A generic framework for approximating inference publication-title: Internat. J. Approx. Reason. doi: 10.1016/j.ijar.2003.10.009 – ident: 10.1016/j.artint.2008.03.003_bib022 doi: 10.1007/3-540-45578-7_24 – volume: 166 start-page: 165 issue: 1–2 year: 2005 ident: 10.1016/j.artint.2008.03.003_bib032 article-title: Unifying cluster-tree decompositions for reasoning in graphical models publication-title: Artif. Intell. doi: 10.1016/j.artint.2005.04.004 – volume: 159 start-page: 1 year: 2004 ident: 10.1016/j.artint.2008.03.003_bib039 article-title: Solving weighted CSP by maintaining arc consistency publication-title: Artif. Intell. doi: 10.1016/j.artint.2004.05.004 – ident: 10.1016/j.artint.2008.03.003_bib047 – volume: 29 start-page: 33 year: 1986 ident: 10.1016/j.artint.2008.03.003_bib019 article-title: Theories of causal ordering publication-title: Artif. Intell. doi: 10.1016/0004-3702(86)90090-1 – volume: vol. 9 start-page: 169 year: 1990 ident: 10.1016/j.artint.2008.03.003_bib059 article-title: Axioms for probability and belief-function propagation – volume: 4 issue: 3 year: 1999 ident: 10.1016/j.artint.2008.03.003_bib009 article-title: Semiring-based CSPs and valued CSPs: Frameworks, properties and comparison publication-title: CONSTRAINTS: An International Journal doi: 10.1023/A:1026441215081 – volume: 4 start-page: 269 year: 1990 ident: 10.1016/j.artint.2008.03.003_bib029 article-title: Bayesian updating in causal probabilistic networks by local computations publication-title: Comp. Stat. Q. – volume: 118 start-page: 00 issue: 631-642 year: 1996 ident: 10.1016/j.artint.2008.03.003_bib018 article-title: Idempotent uninorms publication-title: European J. Op. Res. – year: 1997 ident: 10.1016/j.artint.2008.03.003_bib038 – year: 2000 ident: 10.1016/j.artint.2008.03.003_bib033 article-title: Triangular Norms doi: 10.1007/978-94-015-9540-7 |
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| SubjectTerms | Applied sciences Artificial intelligence Combinatorics Combinatorics. Ordered structures Computer science; control theory; systems Exact sciences and technology Graph theory Information retrieval. Graph Join tree decompositions Learning and adaptive systems Local computation Mathematics Sciences and techniques of general use Semirings Soft constraints Theoretical computing Uncertainty Valuation algebras Valuation networks |
| Title | Semiring induced valuation algebras: Exact and approximate local computation algorithms |
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