On the combination of logical and probabilistic models for information analysis

Applied Intelligence

Volumn 36, Issue 2, 2012, Pages 472-497

  Wang, Jingsong ^a   Byrnes, John ^a   Valtorta, Marco ^a   Huhns, Michael ^b  

^a The Department of Mechanical Engineering   (United States)

^b SRI INTERNATIONAL   (United States)

Author keywords

Bayesian networks; Logic for knowledge representation; Natural deduction proofs; Probabilistic reasoning; Reasoning; Uncertainty

Indexed keywords

AUTOMATICALLY GENERATED; CAUSAL MODEL; DOMAIN SPECIFIC; HORN CLAUSE; LOGICAL SYSTEM; NATURAL DEDUCTION PROOFS; NATURAL DEDUCTION SYSTEMS; NON-STANDARD LOGIC; PRIOR PROBABILITY; PROBABILISTIC MODELS; PROBABILISTIC REASONING; REASONING; UNCERTAINTY;

FORMAL LOGIC; INFORMATION ANALYSIS; KNOWLEDGE REPRESENTATION; LOGIC PROGRAMMING;

BAYESIAN NETWORKS;

EID: 84862141356     PISSN: 0924669X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10489-010-0272-x     Document Type: Article

References (99)

1. Abe J, Akama S (2001) On some aspects of decidability of annotated systems. In: Proceedings of the international conference on artificial intelligence, pp 789-795.
2. Akama S, Abe J (1998) Many-valued and annotated modal logics. In: Proceedings of the 28th international symposium on multiplevalued logic. IEEE Computer Society, Washington, pp 114-119.
3. Bacchus F (1990) Representing and reasoning with probabilistic knowledge: a logical approach to probabilities. MIT Press, Cambridge.
4. Benferhat S, Dubois D, Prade H (2001) Towards a possibilistic logic handling of preferences. Appl Intell 14:303-317. (Pubitemid 32542992)
5. Bertelè U, Brioschi F (1972) Nonserial dynamic programming. Academic Press, New York.
6. Biba M, Ferilli S, Esposito F (2008) Discriminative structure learning of Markov logic networks. In: Proceedings of the 18th international conference on inductive logic programming, ILP '08. Springer, Berlin, pp 59-76.
7. Bundy A (1985) Incidence calculus: a mechanism for probabilistic reasoning. J Autom Reason 1(3):263-283.
8. Byrnes J (1999) Proof search and normal forms in natural deduction. PhD thesis, Department of Philosophy, Carnegie Mellon University.
9. Carbogim DV, da Silva FSC (1998) Annotated logic applications for imperfect information. Appl Intell 9:163-172. (Pubitemid 128513155)
10. Chachoua M, Pacholczyk D (2000) A symbolic approach to uncertainty management. Appl Intell 13:265-283.
11. Cheng J, Emami R, Kerschberg L, Santos JE, Zhao Q, Nguyen H, Wang H, Huhns M, Valtorta M, Dang J, Goradia H, Huang J, Xi S (2005) Omniseer: a cognitive framework for user modeling, reuse of prior and tacit knowledge, and collaborative knowledge services. In: Proceedings of the 38th Hawaii international conference on system sciences (HICSS38), Big Island, HI.
12. Cooper GF (1987) Probabilistic inference using belief networks is np-hard, memo KSL-87-27 (revised July 1988). Tech rep, Medical Computer Science Group, Knowledge Systems Laboratory, Stanford University.
13. Cooper GF (1990) The computational complexity of probabilistic inference using Bayesian belief networks. Artif Intell 42:393-405.
14. Darwiche A (2009) Modeling and reasoning with Bayesian networks. Cambridge University Press, Cambridge.
15. Dekhtyar A, Subrahmanian VS (2000) Hybrid probabilistic programs. J Log Program 43(3):187-250.
16. Dietterich TG, Domingos P, Getoor L, Muggleton S, Tadepalli P (2008) Structured machine learning: the next ten years. Mach Learn 73:3-23.
17. Dubois D, Prade H (1987) Necessity measures and the resolution principle. IEEE Trans Syst Man Cybern 17:474-478.
18. Dubois D, Prade H (1988) Possibility theory. Plenum Press, New York.
19. Dubois D, Prade H (1990) An introduction to possibilistic and fuzzy logics. In: Readings in uncertain reasoning. Morgan Kaufmann Publishers, San Francisco, pp 742-761.
20. Dubois D, Prade H (1994) Can we enforce full compositionality in uncertainty calculi? In: Proc of the 11th nat conf on artificial intelligence (AAAI-94). AAAI Press/MIT Press, Menlo Park/Cambridge, pp 149-154.
21. Dubois D, Prade H (2001) Possibility theory, probability theory and multiple-valued logics: a clarification. Ann Math Artif Intell 32(1-4):35-66.
22. Dubois D, Lang J, Prade H (1987) Theorem proving under uncertainty: a possibility theory-based approach. In: IJCAI'87: proceedings of the 10th international joint conference on artificial intelligence. Morgan Kaufmann Publishers Inc, San Francisco, pp 984-986.
23. Dubois D, Lang J, Prade H (1990) Poslog, an inference system based on possibilistic logic. In: Proc of the North American fuzzy information processing society conference (NAFIPS'90): quarter century of fuzzyness, Toronto, Canada, 06/06/90-08/06/90, pp 177-180.
24. Dubois D, Lang J, Prade H (1994) Automated reasoning using possibilistic logic: semantics, belief revision and variable certainty weights. IEEE Trans Knowl Data Eng 6(1):64-71.
25. Dubois D, Lang J, Prade H (1994) Possibilistic logic. In: Gabbay DM, Hogger CJ, JA Robinson (eds) Handbook of logic in artificial intelligence and logic programming. Nonmonotonic reasoning and uncertain reasoning, vol 3. Oxford University Press, New York, pp 439-513.
26. Fagin R, Halpern JY, Megiddo N (1990) A logic for reasoning about probabilities. Inf Comput 87:78-128.
27. Fierens D, Blockeel H, Bruynooghe M, Ramon J (2005) Logical Bayesian networks and their relation to other probabilistic logical models. In: Proceedings of the 15th international conference on inductive logic programming. Springer, Berlin, pp 121-135. (Pubitemid 41479989)
28. Fierens D, Ramon J, Bruynooghe M, Blockeel H (2008) Learning directed probabilistic logical models: ordering-search versus structure-search. Ann Math Artif Intell 54:99-133.
29. Friedman N, Getoor L, Koller D, Pfeffer A (1999) Learning probabilistic relational models. In: IJCAI. Springer, Berlin, pp 1300- 1309.
30. Getoor L, Taskar B (2007) Introduction to statistical relational learning (adaptive computation and machine learning).MIT Press, Cambridge.
31. Getoor L, Friedman N, Koller D, Taskar B (2001) Learning probabilistic models of relational structure. In: Proceedings of the eighteenth international conference on machine learning. Morgan Kaufmann, San Mateo, pp 170-177.
32. Getoor L, Friedman N, Koller D, Taskar B (2002) Learning probabilistic models of link structure. J Mach Learn Res 3:679-707.
33. Haarslev Pai HI V, Shiri N (2009) A formal framework for description logics with uncertainty. Int J Approx Reason 50(9):1399- 1415.
34. Halpern JY (1990) An analysis of first-order logics of probability. Artif Intell 46:311-350.
35. Halpern JY (2003) Reasoning about uncertainty.MIT Press, Cambridge.
36. Delugach H (ed) (2005) Common logic-a framework for a family of logic-based languages. Tech rep, International Standards Organization: iSO/IEC JTC 1/SC 32N1377, International Standards Organization Final Committee Draft, 2005-12-13, available at http://i-cl.tamu.edu/docs/cl/32N1377T-FCD24707.pdf.
37. Hayes PJ (2006) IKL guide. Tech rep, Florida Institute for Human and Machine Cognition, unpublished memorandum available at http://www.ihmc.us/users/ phayes/IKL/GUIDE/GUIDE.html.
38. Hayes PJ, Menzel C (2006) IKL specification document. Tech rep, Florida Institute for Human and Machine Cognition, unpublished memorandum available at http://www.ihmc.us/users/phayes/IKL/SPEC/SPEC.html.
39. Hollunder B (1995) An alternative proof method for possibilistic logic and its application to terminological logics. Int J Approx Reason 12(2):85-109.
40. Huhns M, Valtorta M, Wang J (2010) Design principles for ontological support of Bayesian evidence management. In: Obrst L, Janssen T, Ceusters W (eds) Semantic technologies, ontologies, and information sharing for intelligence analysis. IOS Press, Amsterdam, pp 163-178.
41. Huynh TN, Mooney RJ (2008) Discriminative structure and parameter learning for Markov logic networks. In: Proceedings of the 25th international conference on machine learning, ICML '08. ACM, New York, pp 416-423.
42. Huynh TN, Mooney RJ (2009) Max-margin weight learning for Markov logic networks. In: Proceedings of the European conference on machine learning and principles and practice of knowledge discovery in databases (ECML/PKDD-09). Bled, pp 248- 263.
43. Jaeger M(1997) Relational Bayesian networks. In: Proceedings of the 13th conference of uncertainty in artificial intelligence (UAI- 13). Morgan Kaufmann, San Mateo, pp 266-273.
44. Jaeger M (2002) Relational Bayesian networks: a survey. Electron Trans Artif Intell 6.
45. Jaeger M (2007) Parameter learning for relational Bayesian networks. In: Proceedings of the international conference in machine Learning.
46. Jensen FV, Nielsen TD (2007) Bayesian networks and decision graphs, 2nd edn. Springer, New York.
47. Johnson DS (1990) A catalog of complexity classes. In: van Leeuwen J (ed) Handbook of theoretical computer science, vol. A: algorithms and complexity. MIT Press, Cambridge, pp 67-161.
48. Kersting K, De Raedt L (2008) Basic principles of learning Bayesian logic programs. In: De Raedt L, Frasconi P, Kersting K, Muggleton S (eds) Probabilistic inductive logic programming. Springer, Berlin, pp 189-221.
49. Kersting K, Raedt LD (2001) Bayesian logic programs. CoRR cs.AI/0111058.
50. Kifer M, Subrahmanian VS (1989) On the expressive power of annotated logic programs. In: Proceedings of the North American conference on logic programming, pp 1069-1089.
51. Kifer M, Subrahmanian VS (1992) Theory of generalized annotated logic programming and its applications. J Log Program 12:335-367.
52. Kim YG, Valtorta M, Vomlel J (2004) A prototypical system for soft evidential update. Appl Intell 21(1):81-97.
53. Kok S, Domingos P (2009) Learning Markov logic network structure via hypergraph lifting. In: Proceedings of the 26th international conference on machine learning (ICML-09).
54. Koller D (1998) Pfeffer a probabilistic frame-based systems. In: Proc AAAI. AAAI Press, Menlo Park, pp 580-587.
55. Laskey KB (2006) First-order Bayesian logic. Technical report C4I06-01. Tech rep, SEOR Department, George Mason University.
56. Laskey KB (2008) MEBN: a language for first-order knowledge bases. Artif Intell 172:140-178. (Pubitemid 350262803)
57. Laskey KB, Mahoney SM (1997) Network fragments: representing knowledge for constructing probabilistic models. In: Proceedings of the thirteenth annual conference on uncertainty in artificial intelligence (UAI-97), Providence, pp 334-341.
58. Liu W, Bundy A (1994) A comprehensive comparison between generalized incidence calculus and the Dempster-Shafer theory of evidence. Int J Hum-Comput Stud 40:1009-1032.
59. Liu W, McBryan D, Bundy A (1998) The method of assigning incidences. Appl Intell 9:139-161. (Pubitemid 128513154)
60. Loveland DW, Stickel M (1976) A hole in goal trees: Some guidance from resolution theory. IEEE Trans Comput 25:335-341.
61. Lowd D, Domingos P (2007) Efficient weight learning forMarkov logic networks. In: Proceedings of the eleventh European conference on principles and practice of knowledge discovery in databases, pp 200-211.
62. Loyer Y, Straccia U (2009) Approximate well-founded semantics, query answering and generalized normal logic programs over lattices. Ann Math Artif Intell 55:389-417.
63. Lu JJ, Murray NV, Rosenthal E (1993) Signed formulas and annotated logics. In: Proceedings of int symposium on multiple-valued logic, pp 48-53. (Pubitemid 23697832)
64. Lukasiewicz T (2007) Probabilistic description logic programs. Int J Approx Reason 45(2):288-307. (Pubitemid 46880199)
65. Lukasiewicz T (2008) Probabilistic description logic programs under inheritance with overriding for the semantic web. Int J Approx Reason 49(1):18-34.
66. Milch B, Russell S (2007) First-order probabilistic languages: Into the unknown. In: Proceedings of the 16th international conference on inductive logic programming, pp 10-24.
67. Muggleton S (1996) Stochastic logic programs. In: Advances in inductive logic programming. IOS Press, Amsterdam, pp 254- 264.
68. Muggleton S (2000) Learning stochastic logic programs. In: Getoor L, Jensen D (eds) Proceedings of the AAAI2000 workshop on learning statistical models from relational data, URL: http://www.doc.ic.ac.uk/~shm/Papers/slplearn. pdf.
69. Neapolitan RE (1990) Probabilistic reasoning in expert systems: theory and algorithms. Wiley, New York.
70. Ng R, Subrahmanian VS (1992) Probabilistic logic programming. Inf Comput 101:150-201.
71. Ngo L, Haddawy P (1996) Answering queries from contextsensitive probabilistic knowledge bases. Theor Comput Sci 171:147-177. (Pubitemid 127452811)
72. Niles I, Pease A (2001) Towards a standard upper ontology. In: Welty C, Smith B (eds) Proceedings of the 2nd international conference on formal ontology in information systems (FOIS-2001), Ogunquit, ME, USA, pp 2-9.
73. Nilsson NJ (1986) Probabilistic logic. Artif Intell 28(1):71-87.
74. Obeid N (2005) A formalism for representing and reasoning with temporal information, event and change. Appl Intell 23:109-119. (Pubitemid 41203110)
75. Orponen P (1990) Dempster's rule of combination is #p-complete. Artif Intell 44:245-253.
76. Paris J (1994) The uncertain reasoner's companion: a mathematical perspective. Cambridge tracts in theoretical computer science, vol 39. Cambridge University Press, Cambridge.
77. Park J (2002) Map complexity results and approximation methods. In: Proceedings of the 18th annual conference on uncertainty in artificial intelligence (UAI-02). Morgan Kaufmann, San Francisco, pp 388-439.
78. Pearl J (2000) Causality: modeling, reasoning, and inference. Cambridge University Press, Cambridge.
79. Peng Y, Reggia JA (1990) Abductive inference models for diagnostic problem solving. Springer, New York.
80. Poole D (2008) The independent choice logic and beyond. In: Probabilistic inductive logic programming: theory and applications. Springer, Berlin, pp 222-243.
81. Qi G, Pan JZ, Ji Q (2007) A possibilistic extension of description logics. In: Proceedings of the international workshop on description logics (DL'07), pp 435-442.
82. Riazanov A, Voronkov A (2002) The design and implementation of Vampire. AI Commun. 15:91-110. (Pubitemid 34838658)
83. Richardson M, Domingos P (2006) Markov logic networks. Mach Learn 62(1-2):107-136. (Pubitemid 43202307)
84. Rose DJ (1972) A graph-theoretic study of the numerical solution of sparse positive definite systems of linear equations. In: Read R (ed) Graph theory and computing. Academic Press, New York, pp 183-217.
85. Roth D (1996) On the hardness of approximate reasoning. Artif Intell 82:273-302. (Pubitemid 126374156)
86. de Salvo Braz R, Amir E, Roth D (2008) A survey of firstorder probabilistic models. In: Holmes D, Jain L (eds) Innovations in Bayesian networks. Springer, Berlin, pp 289-317. URL: http://l2r.cs.uiuc.edu/danr/Papers/ BrazAmRo08.pdf.
87. Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton.
88. Singla P, Domingos P (2005) Discriminative training of Markov logic networks. In: Proc of the natl conf on artificial intelligence.
89. Smets P, Mamdani E, Dubois D, Prade H (eds) (1988) Nonstandard logics for automated reasoning. Academic Press, San Diego.
90. Stoilos G, Stamou G, Pan JZ, Tzouvaras V, Horrocks I (2007) Reasoning with very expressive fuzzy description logics. J Artif Intell Res 273-320.
91. Straccia U (2001) Reasoning within fuzzy description logics. J Artif Intell Res 14:137-166.
92. Straccia U (2006) A fuzzy description logic for the semantic web. In: Sanchez E (ed) Fuzzy logic and the semantic web, capturing intelligence. Elsevier, Amsterdam, pp 73-90. Chap 4.
93. Straccia U (2008) Managing uncertainty and vagueness in description logics, logic programs and description logic programs. In: Baroglio C, Bonatti PA, Maluszýnski J, Marchiori M, Polleres A, Schaffert S (eds) Reasoning web. Springer, Berlin, pp 54-103.
94. Straccia U, Bobillo F (2007) Mixed integer programming, general concept inclusions and fuzzy description logics. In: Proceedings of the 5th conference of the European society for fuzzy logic and technology (EUSFLAT-07), vol 2, University of Ostrava, Ostrava, Czech Republic, pp 213-220.
95. Subrahmanian V (2007) Uncertainty in logic programming: some recollections. Assoc Log Program Newslett 20(2).
96. Subrahmanian VS (1987) On the semantics of quantitative logic programs. In: Proceedings of the 4th IEEE symposium on logic programming, pp 173-182.
97. Valtorta M, Kim YG, Vomlel J (2002) Soft evidential update for probabilistic multiagent systems. Int J Approx Reason 29(1):71-106. (Pubitemid 33060598)
98. Valtorta M, Dang J, Goradia H, Huang J, Huhns M (2005) Extending Heuer's analysis of competing hypotheses method to support complex decision analysis. In: Proceedings of the 2005 international conference on intelligence analysis (IA-05) (CDROM), extended version available at http://www.cse.sc.edu/~mgv/ reports/IA-05.pdf.
99. Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3-28.