This article considers a critical and experimental approach on the attributive and qualitative AI data modeling and data retrieval in computational probabilistic reasoning. The mathematical correlation of X≈Y in the d=dx/dy differentiations and its point based locations and matrix based predictions in Markov Models, Rete’s Algorithms and Bayesian fields, with the further development of non-linear ‘human-type’ reasoning in AI. The new approach in the ternary system transition (decimal↔binary) of Brusentsov-Bergman principle by its bound allocation in the ‘mirror-based’ system in tn-1… tn+1 powers, and hereon considers its further data retrieval for suitable matching and translation of probabilistic data differentiation. The causation/probability matrix of this paper regards not only bound/free variable in x1,x2,x3, xn variables, but discovers and explains its further subsets in anXqn formula, where the supposition of d=X/Y regarded not as a mathematical placement of the variable X, but as its attributive (a) and qualitative (q) allocation in a certain value/relevance cell of the Probability Triangle of the ternary system. From where the automated differentiation retrieves only the most relevant/objective anXqn data cell, not the closest by the pre-set context, making the AI selections more assertive and preference based than linear.
DOI | 10.11648/j.si.20140204.12 |
Published in | Science Innovation ( Volume 2, Issue 4, August 2014 ) |
Page(s) | 43-62 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Probability, Reasoning, Computational Logic, Abstraction Modeling, Probabilistic Reasoning, AI Reasoning, Automated Differentiations, Probability Calculus
[1] | Audun Jшsang, Artificial Reasoning with Subjective Logic 9,17 (1997) archived at: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.2567 |
[2] | See Stuart C. Shapiro, Knowledge Representation and Reasoning Logics for Artificial Intelligence 186, 632 archived at: www.cse.buffalo.edu/~shapiro/Courses/CSE563/Slides/krrSlides.pdf |
[3] | Fred Kort, Simultaneous Equations and Boolean Algebra in The Analysis of Judicial Decisions, 28 Law & Contemp. Probs. 143-145 (1963), archived at: http://scholarship.law.duke.edu/lcp/vol28/iss1/8 (See more on Kort’s development in automated reasoning in the II part of this research in where we solidify a differential equation of simultaneous reasoning based on its attributive consistency and objective selection of binary programming). |
[4] | See Norm Dingle, Artificial Intelligence: Fuzzy Logic Explained, (11/04/2011) at: http://www.controleng.com/single-article/artificial-intelligence-fuzzy-logic-explained/8f3478c13384a2771ddb7e93a2b6243d.html |
[5] | Yumi Iwasaki, Reasoning with multiple abstraction models in Fourth International Workshop on Qualitative Physics. 186, 194 (1990) archived at: http://www.qrg.northwestern.edu/papers/Files/qr-workshops/QP90/Iwasaki_1990_Reasoning_Multiple_Abstraction_Models.pdf |
[6] | See M. Minea, Comparing Models. Abstraction. Compositional Reasoning, Formal Verification, Lecture 7. 2, 2-32 (2003) archived at:http://bigfoot.cs.upt.ro/~marius/curs/fv/old/lect7_6.pdf |
[7] | Rintanen, Jussi, “Nondeterministic/conditional planning. Motivation” Research Group, Foundations of Artificial Intelligence, University of Freiburg, 12, 30, May 25. 2005. Lecture. at: http://www2.informatik.uni-freiburg.de/~ki/teaching/ss05/aip/ |
[8] | Gunter Neumann, Programming Languages in Artificial Intelligence, DFKI 13, 34 (2014) at: http://www.dfki.de/~neumann/publications/new-ps/ai-pgr.pdf (The principle of doubling argumentation (+ (my-sum x y) (my-sum x y)) (ibid 16) is also explained in d = aXq/aYq in the 3d chapter.) |
[9] | Kreisel G., Models, Translations and Interpretations in Mathematical Interpretation of Formal Systems, 35, 113 ( L.E.J. Brouwer, E.W. Beth, A. Heyting et al. eds., 1955) (Here S1 stands for a formal System by Kreisel, but we use its analog of Interpretation and its application of System 1 transition to System 2 in artificial reasoning levels.) |
[10] | See Daniel L. Schwartz and John B. Black, Shutting Between Depicting Models and Abstract Rules: Induction and Fallback, 20 Cognitive Science no 4 458, Archived at http://onlinelibrary.wiley.com/doi/10.1207/s15516709cog2004_1/pdf (Closed Chain Configuration of abstraction doesn’t necessarily mean sequence of causation and explanation of one conclusion by another as soon as the human thinking is more linear than sporadic. Therefore we presume the open horizontal chain as the most linear chain of basis and its causation probable in human like thinking for AI) |
[11] | See Kewen Wang, Lian Wen, Kedian Mu, Random Logic Programs: Linear Model 4,33 (2014) archived at: http://arxiv.org/abs/1406.6102 |
[12] | See Francis Heylighen, Towards an anticipation control theory of mind, Evolution, Complexity and Cognition group, Vrije Universiteit Brussel. (abstract) 13, 20 at: http://pespmc1.vub.ac.be/Papers/AnticipationControl.pdf (also considers the matching of the conditional probability matrix in the anticipation model. Also matches to conditional sentence as conjunctions of each other, however anticipates time literally.) |
[13] | See Cameron E. Freer, Daniel M. Roy, et al., Towards common-sense reasoning via conditional simulation: legacies of Turing in Artificial Intelligence 12, 51 (December 19, 2012) archived at https://archive.org/details/arxiv-1212.4799 |
[14] | Peter Sunehag; Marcus Hutter, Principles of Solomonoff Induction and AIXI 4, 14 (November 25, 2011) archived at https://archive.org/details/arxiv-1111.6117 (See Section 2.1., “Considers finite and infinite sequences of X”). |
[15] | Martin Gebser, Philipp Obermeier et al, A System for Interactive Query Answering |
[16] | with Answer Set Programming, Proceedings (ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, Turkey, 111,112, 115 archived at: http://arxiv.org/abs/1312.6143 |
[17] | Bruno A. Olshausen, Bayesian theory probability 1, 6 (2004) archive at http://redwood.berkeley.edu/bruno/npb163/bayes.pdf Ibid 4 |
[18] | Raymond J. Mooney, CS 343: Artificial Intelligence Bayesian Networks, at: http://www.cs.utexas.edu/~mooney/cs343/slide-handouts/bayes-nets.pdf |
[19] | See V. Bettadapura, "Face Expression Recognition and Analysis: The State of the Art", Tech Report, arXiv:1203.6722, April 2012 Archived at: http://arxiv.org/ftp/arxiv/papers/1203/1203.6722.pdf pp 11-14, 27. |
[20] | V. Bettadapura, D. R. Sai Sharan, "Pattern Recognition with Localized Gabor Wavelet Grids", IEEE Conference on Computational Intelligence and Multimedia Applications, vol. 2, pp. 517-521, Sivakasi, India, December 2007. 6,19 Archived at http://www.cc.gatech.edu/~vbettada/files/vinay-PR.pdf |
[21] | M. Fisher and M. Wooldridge. Executable Temporal Logic for Distributed AI. In K. Sycara, editor, Proceedings of the Twelfth International Workshop on Distributed Artificial Intelligence |
[22] | See Church Alonzo, Introduction to Mathematical Logic 93, 378 (1996) |
[23] | See Bondarenko A. et al., An abstract, argumentation-theoretic approach to default reasoning 67, 63-101 Artificial Intelligence 93 (1997) archived at http://dx.doi.org/10.1016/S0004-3702(97)00015-5 (Contra-positive equation does a job of a logical sequencer IF and THEN done well, however the degree of provability and validity is too linear and inadequate if explained by such narrow formula) |
[24] | See Carnap Rudolf, Einführung in Die Symbolische Logik 67, 241 (1958). |
[25] | See Quine Willard, Mathematical Logic 29, 346 (1981). |
[26] | See A. Bundy, Discovery and Reasoning in Mathematics in IJCAI _1985-VOLUME 2, 1224, 1221-1230 archived at http://ijcai.org/Past%20Proceedings/IJCAI-85-VOL2/PDF/107.pdf |
[27] | See Brian Guenter, Efficient Symbolic Differentiation for Graphics Applications, Microsoft Research 2, 19 archived at: http://research.microsoft.com/en-us/um/people/bguenter/docs/symbolicdifferentiation.pdf |
[28] | See Griewank, Andreas. "On automatic differentiation." Mathematical Programming: recent developments and applications 6 (1989): 2, 83-107 archived at: http://www.researchgate.net/publication/2703247_On_Automatic_Differentiation/file/9c96052529013aed9e.pdf |
[29] | See Richard D. Neidinger, Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming, SIAM REVIEW Vol. 52, No. 3, pp. 545–563, 547, archived at: http://academics.davidson.edu/math/neidinger/SIAMRev74362.pdf |
[30] | Ibid 546 |
[31] | See Soumya Ray, Mark Craven, Representing Sentence Structure in Hidden Markov Models for Information Extraction in Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI-2001) 4,7 archive at: http://www.biostat.wisc.edu/~craven/papers/ijcai01-hmm.pdf |
[32] | J.D. Pruce, J.K. Reid, AD01, a Fortran 90 code for automatic differentiation 6, 40 Archived at: http://www.numerical.rl.ac.uk/reports/prRAL98057.pdf |
[33] | Carsten Elsner, On Recurrence Formulae For Sums Involving Binomial Coefficients, Dalhousie University, 32, 45 Archived at: http://www.mathstat.dal.ca/FQ/Papers1/43-1/paper43-1-5.pdf |
[34] | See Hassan I. Abdalla, A New Data Re-Allocation Model for Distributed Database Systems, 5 International Journal of Database Theory and Application No.2, 51, 60 (2012) Archived at: http://www.sersc.org/journals/IJDTA/vol5_no2/4.pdf |
[35] | Ibid 50 |
[36] | Andrew Trotman, An Artificial Intelligence Approach To Information Retrieval, University of Otago 3,5 () Archived at: http://www.cs.otago.ac.nz/homepages/andrew/papers/2004-5.pdf |
[37] | See Stakhov, Alexey, Brousentsov's Ternary Principle, Bergman's Number System and Ternary Mirror-symmetrical Arithmetic, Computer Journal, Vol. 45 Issue 2, (2002) Archived at: http://www.ee.bgu.ac.il/~kushnero/ternary/prof%20Stakhov/Ternary%20mirror-symmetrical%20number%20system%20and%20arithmetic.pdf (See Table 2. Of the Abridged location for the variables to binary transition). |
APA Style
Richard Douglas. (2014). The (a, q) Data Modeling in Probabilistic Reasoning. Science Innovation, 2(4), 43-62. https://doi.org/10.11648/j.si.20140204.12
ACS Style
Richard Douglas. The (a, q) Data Modeling in Probabilistic Reasoning. Sci. Innov. 2014, 2(4), 43-62. doi: 10.11648/j.si.20140204.12
AMA Style
Richard Douglas. The (a, q) Data Modeling in Probabilistic Reasoning. Sci Innov. 2014;2(4):43-62. doi: 10.11648/j.si.20140204.12
@article{10.11648/j.si.20140204.12, author = {Richard Douglas}, title = {The (a, q) Data Modeling in Probabilistic Reasoning}, journal = {Science Innovation}, volume = {2}, number = {4}, pages = {43-62}, doi = {10.11648/j.si.20140204.12}, url = {https://doi.org/10.11648/j.si.20140204.12}, eprint = {https://download.sciencepg.com/pdf/10.11648.j.si.20140204.12}, abstract = {This article considers a critical and experimental approach on the attributive and qualitative AI data modeling and data retrieval in computational probabilistic reasoning. The mathematical correlation of X≈Y in the d=dx/dy differentiations and its point based locations and matrix based predictions in Markov Models, Rete’s Algorithms and Bayesian fields, with the further development of non-linear ‘human-type’ reasoning in AI. The new approach in the ternary system transition (decimal↔binary) of Brusentsov-Bergman principle by its bound allocation in the ‘mirror-based’ system in tn-1… tn+1 powers, and hereon considers its further data retrieval for suitable matching and translation of probabilistic data differentiation. The causation/probability matrix of this paper regards not only bound/free variable in x1,x2,x3, xn variables, but discovers and explains its further subsets in anXqn formula, where the supposition of d=X/Y regarded not as a mathematical placement of the variable X, but as its attributive (a) and qualitative (q) allocation in a certain value/relevance cell of the Probability Triangle of the ternary system. From where the automated differentiation retrieves only the most relevant/objective anXqn data cell, not the closest by the pre-set context, making the AI selections more assertive and preference based than linear.}, year = {2014} }
TY - JOUR T1 - The (a, q) Data Modeling in Probabilistic Reasoning AU - Richard Douglas Y1 - 2014/10/30 PY - 2014 N1 - https://doi.org/10.11648/j.si.20140204.12 DO - 10.11648/j.si.20140204.12 T2 - Science Innovation JF - Science Innovation JO - Science Innovation SP - 43 EP - 62 PB - Science Publishing Group SN - 2328-787X UR - https://doi.org/10.11648/j.si.20140204.12 AB - This article considers a critical and experimental approach on the attributive and qualitative AI data modeling and data retrieval in computational probabilistic reasoning. The mathematical correlation of X≈Y in the d=dx/dy differentiations and its point based locations and matrix based predictions in Markov Models, Rete’s Algorithms and Bayesian fields, with the further development of non-linear ‘human-type’ reasoning in AI. The new approach in the ternary system transition (decimal↔binary) of Brusentsov-Bergman principle by its bound allocation in the ‘mirror-based’ system in tn-1… tn+1 powers, and hereon considers its further data retrieval for suitable matching and translation of probabilistic data differentiation. The causation/probability matrix of this paper regards not only bound/free variable in x1,x2,x3, xn variables, but discovers and explains its further subsets in anXqn formula, where the supposition of d=X/Y regarded not as a mathematical placement of the variable X, but as its attributive (a) and qualitative (q) allocation in a certain value/relevance cell of the Probability Triangle of the ternary system. From where the automated differentiation retrieves only the most relevant/objective anXqn data cell, not the closest by the pre-set context, making the AI selections more assertive and preference based than linear. VL - 2 IS - 4 ER -