References             Computational epistemology: an overview                                          Danilo DantasCompu...
ReferencesPART I: Which epistemology?Computational epistemology: an overview
ReferencesQuine’s proposal             The stimulation of his sensory receptors is all the evidence             anybody ha...
ReferencesNaturalized versus traditional epistemology                                             Aim        Method       ...
ReferencesThe desirable traits to epistemology        1. To be normative-grounding;        2. To employ non-controversial ...
ReferencesPART II: Computational epistemology (CE)                                  Figure: http://xkcd.com/329/Computatio...
ReferencesApproaches to AI             Thinking Humanly                     Thinking Rationally             “[The automati...
ReferencesEpistemology as the description of the ideal agent      The ideal (but finite) rational agent is a finite rational...
ReferencesThe desirable traits to epistemology        1. To be normative-grounding;        2. To employ non-controversial ...
ReferencesNormative-grounding        S has grounds to believe that p in s           ←→   The ideal agent believes that p  ...
ReferencesPART III: Methods and an exampleComputational epistemology: an overview
ReferencesWhat is 2SAT?      2SAT is the problem of determining whether a given propositional      logic formula in two-co...
ReferencesFormalizing problems      If a problem can be described as a search problem, we may use the      formalization i...
References2SAT as a search problem             The initial state is [x1 , ..., xn ], where x1 = x2 = ... = xn = 1.        ...
References2SAT as a graph                                                       S                                G        ...
ReferencesBuilding agents      The design and test of a putative ideal agent have 3 stages:        1. The choice of a hypo...
ReferencesThe agents for 2SAT             Truth table agent;             Truth line agent;             Simplification agent...
ReferencesAnalyzing the agents 1      In order to be implementable as a model of the ideal agent, an agent      must meet ...
ReferencesAnalyzing the agents 2      In analyzing data, there are 5 important measures:        1. the accuracy rate;     ...
ReferencesTruth table agent: the plots                             Solution cost                                      Time...
ReferencesTruth table agent: solution cost                                                       S                        ...
ReferencesTruth table agent: time and space requirements        Constants            Lines                Time            ...
ReferencesTruth line agent: the plots                             Solution cost                                     Time c...
ReferencesSimplification agent: the plots                             Solution cost                                   Time ...
ReferencesHumans: the plots                             Solution cost                                    Time complexity  ...
ReferencesPART IV: CE and other sciencesComputational epistemology: an overview
ReferencesThe desirable traits to epistemology        1. To be normative-grounding;        2. To employ non-controversial ...
ReferencesIs this still philosophy?Computational epistemology: an overview
ReferencesPART V: The 2nd year paper                                          XComputational epistemology: an overview
ReferencesThe Bayesian agent        1. The Bayesian agent holds degrees of belief in accordance with the           axioms ...
ReferencesThe defeasible agent (Pollock, 1995)        1. The defeasible agent adopts beliefs in response to construing    ...
ReferencesThe Wumpus world                                                       Bree z e    PIT                          ...
ReferencesReferences      Bellman, R. E. (1978). An Inrrocluction to Artificial Intelligence: Can Computer        Think? Bo...
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Epistemologia computacional: intrudução

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Epistemologia computacional: intrudução

  1. 1. References Computational epistemology: an overview Danilo DantasComputational epistemology: an overview
  2. 2. ReferencesPART I: Which epistemology?Computational epistemology: an overview
  3. 3. ReferencesQuine’s proposal The stimulation of his sensory receptors is all the evidence anybody has had to go on, ultimately, in arriving at his picture of the world. Why not just see how this construction really proceeds? Why not settle for psychology? (Quine, 1969, p. 75). Epistemology, or something like it, simply falls into place as a chapter of psychology and hence of natural science. (Quine, 1969, p. 82).Computational epistemology: an overview
  4. 4. ReferencesNaturalized versus traditional epistemology Aim Method Reduction Traditional epistemology normative a priori no Naturalized epistemology descriptive empirical yes∗ Table: The ∗ is true of some naturalized epistemologies (e.g. Quine, 1969), but not of all (e.g. Goldman, 1986).Computational epistemology: an overview
  5. 5. ReferencesThe desirable traits to epistemology 1. To be normative-grounding; 2. To employ non-controversial methods; 3. To be emancipated, but to benefit from empirical data.Computational epistemology: an overview
  6. 6. ReferencesPART II: Computational epistemology (CE) Figure: http://xkcd.com/329/Computational epistemology: an overview
  7. 7. ReferencesApproaches to AI Thinking Humanly Thinking Rationally “[The automation of] activities “The study of the computations that we associate with human that make it possible to perceive, thinking, activities such as reason, and act” (Winston, 1970). decision-making, problem solving, learning (...)” (Bellman, 1978). Acting Humanly Acting Rationally “The creation of machines that “Computational Intelligence is perform functions that require in- the study of the design of intelli- telligence when performed by peo- gent agents” (Poole et al., 1998). ple” (Kurzweil, 1990). Table: Russell and Norvig (2010)Computational epistemology: an overview
  8. 8. ReferencesEpistemology as the description of the ideal agent The ideal (but finite) rational agent is a finite rational agent which acts to achieve the best expected outcome in all possible environments, and which does it using the less possible amount of processing and time.Computational epistemology: an overview
  9. 9. ReferencesThe desirable traits to epistemology 1. To be normative-grounding; 2. To employ non-controversial methods; 3. To be emancipated, but to benefit from empirical data.Computational epistemology: an overview
  10. 10. ReferencesNormative-grounding S has grounds to believe that p in s ←→ The ideal agent believes that p in s S is warranted to believe that p in s S is justified to believe that p in s S has reason to believe that p in s S knows that p in s ←→ S believes that p in s & p is true & The ideal agent believes that p in sComputational epistemology: an overview
  11. 11. ReferencesPART III: Methods and an exampleComputational epistemology: an overview
  12. 12. ReferencesWhat is 2SAT? 2SAT is the problem of determining whether a given propositional logic formula in two-conjunctive normal form (2CNF) is satisfiable of and providing an assignment that satisfies it. E.g. does any assignment satisfies (C ∨ ¬D) ∧ (A ∨ B) ∧ (¬A ∨ ¬C)?Computational epistemology: an overview
  13. 13. ReferencesFormalizing problems If a problem can be described as a search problem, we may use the formalization in proposed by Russell and Norvig (2010, p. 66): The initial state; A function which returns the available actions in a given state; A transition model, which specifies the result of a given action in a given state; The goal test, which determines whether a state is a goal state. A path cost function, which takes a list of pairs state-actions and returns a number.Computational epistemology: an overview
  14. 14. References2SAT as a search problem The initial state is [x1 , ..., xn ], where x1 = x2 = ... = xn = 1. The available actions are to change the value of any number of constants pi from 0 to 1 or from 1 to 0. The transition model returns, for each action, the state with the resulting assignment. The goal test is whether an assignment render the formula true (classical logic rules). The path cost function returns the number of changes in the truth value of constants.Computational epistemology: an overview
  15. 15. References2SAT as a graph S G [1, 1, 1] 3 1 [0, 0, 0] [1, 1, 0] 2 1 [0, 0, 1] [1, 0, 1] 2 2 1 G [0, 1, 0] [1, 0, 0] [0, 1, 1]Computational epistemology: an overview
  16. 16. ReferencesBuilding agents The design and test of a putative ideal agent have 3 stages: 1. The choice of a hypothesis to the ideal agent for a given problem, and the building of a model of the agent based in this hypothesis; 2. The implementation of the model in a computer simulation; 3. The analysis of the data from the simulation.Computational epistemology: an overview
  17. 17. ReferencesThe agents for 2SAT Truth table agent; Truth line agent; Simplification agent.Computational epistemology: an overview
  18. 18. ReferencesAnalyzing the agents 1 In order to be implementable as a model of the ideal agent, an agent must meet some requirements: 1. to have consistent dispositions; 2. to be translatable into a programming language; 3. to be computationally accurate and feasible.Computational epistemology: an overview
  19. 19. ReferencesAnalyzing the agents 2 In analyzing data, there are 5 important measures: 1. the accuracy rate; 2. the solution cost; 3. the time and space requirements; 4. the lower bounds.Computational epistemology: an overview
  20. 20. ReferencesTruth table agent: the plots Solution cost Time complexity Space complexity 400 10000 10000 9000 9000 350 8000 8000 300 7000 7000 Assignments Assignments 250 Path cost 6000 6000 200 5000 5000 4000 4000 150 3000 3000 100 2000 2000 50 1000 1000 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Constants Constants ConstantsComputational epistemology: an overview
  21. 21. ReferencesTruth table agent: solution cost S [1, 1, 1] 1 [0, 0, 0] [1, 1, 0] 1 2 [0, 0, 1] [1, 0, 1] 2 1 [0, 1, 0] [1, 0, 0] 1 [0, 1, 1] 3Computational epistemology: an overview
  22. 22. ReferencesTruth table agent: time and space requirements Constants Lines Time Space 1 2 2 × 10−6 seconds 2 bytes 2 8 4 × 10−6 seconds 8 bytes 5 160 3.2 × 10−5 seconds 160 bytes 10 10240 1 × 10−3 seconds 10 kilobytes 20 4.1942 × 107 1.0486 seconds 20 megabytes 50 2.2518 × 1015 35.7 years 50 petabytes 100 2.5354 × 1032 402 trillions of years 1.1259 × 1017 petabytesComputational epistemology: an overview
  23. 23. ReferencesTruth line agent: the plots Solution cost Time complexity Space complexity 10 400 2000 9 350 1800 1600 8 300 1400 7 Assignments Assignments 250 Path cost 1200 6 200 1000 5 150 800 4 600 100 3 400 50 200 2 1 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Constants Constants ConstantsComputational epistemology: an overview
  24. 24. ReferencesSimplification agent: the plots Solution cost Time complexity Space complexity 4.5 60 30 4 50 25 3.5 40 20 Assignments Assignments 3 Path cost 2.5 30 15 2 20 1.5 10 1 10 5 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Constants Constants ConstantsComputational epistemology: an overview
  25. 25. ReferencesHumans: the plots Solution cost Time complexity Accuracy rate 6 3.5 11000 10000 5 3 9000 2.5 4 Errors (%) Time (ms) 8000 Path cost 2 3 7000 1.5 6000 2 5000 1 1 4000 0.5 3000 0 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Constants Constants ConstantsComputational epistemology: an overview
  26. 26. ReferencesPART IV: CE and other sciencesComputational epistemology: an overview
  27. 27. ReferencesThe desirable traits to epistemology 1. To be normative-grounding; 2. To employ non-controversial methods; 3. To be emancipated, but to benefit from empirical data.Computational epistemology: an overview
  28. 28. ReferencesIs this still philosophy?Computational epistemology: an overview
  29. 29. ReferencesPART V: The 2nd year paper XComputational epistemology: an overview
  30. 30. ReferencesThe Bayesian agent 1. The Bayesian agent holds degrees of belief in accordance with the axioms of the probability calculus; 2. The Bayesian agent employs traditional probability calculus tools to calculate degrees of belief; 2.1 In particular, in acquiring new data, the Bayesian agent updates (some of) its old degrees upon these data using Bayes theorem. ∗ 3. The Bayesian agent holds beliefs in propositions when it degrees of belief in that proposition is higher than a threshold.Computational epistemology: an overview
  31. 31. ReferencesThe defeasible agent (Pollock, 1995) 1. The defeasible agent adopts beliefs in response to construing arguments, provided no defeaters have already been adopted for any step of the argument; 2. The defeasible agent must keep track of the basis upon which its beliefs are held; 3. The defeasible agent must keep track of defeated inferences, and when a defeater is itself retracted, this should reinstate the defeasible inference.Computational epistemology: an overview
  32. 32. ReferencesThe Wumpus world Bree z e PIT 4 Stench Bree z e 3 Stench PIT Bree z e Gold Bree z e 2 Stench Bree z e Bree z e 1 PIT START 1 2 3 4 Figure: Russell and Norvig (2010)Computational epistemology: an overview
  33. 33. ReferencesReferences Bellman, R. E. (1978). An Inrrocluction to Artificial Intelligence: Can Computer Think? Boyd & Fraser Publishing Company, San Francisco. Goldman, A. (1986). Epistemology and Cognition. Cambridge: Harvard University Press. Kurzweil, R. (1990). The Age of Intelligent Machines. MIT Press, Cambridge, Massachusetts. Pollock, J. L. (1995). Cognitive carpentry: a blueprint for how to build a person. The MIT Press. Poole, D., Mackworth, A. K., and Goebel, R. (1998). Computational intelligence: A logical approach. Oxford University Press, Oxford, UK. Quine, W. V. (1969). Ontological Relativity and Other Essays, chapter Epistemology Naturalized, pages 69–90. New York: Columbia UP. Russell, S. and Norvig, P. (2010). Artificial Intelligence: A Modern Approach 3rd Edition. Upper Saddle River,EUA: Prentice-Hall. Winston, P. H. (1970). Learning structural descriptions from examples. technical report mac-tr-76. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cam- bridge, Massachusetts.Computational epistemology: an overview
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