Apresentação do capítulo 0 de minha dissertação, bem como a explicação de como será o capítulo 1 (no final).

1. References
Computational epistemology: an overview
Danilo Dantas
Computational epistemology: an overview

2. References
PART I: Which epistemology?
Computational epistemology: an overview

3. References
Quine’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. References
Naturalized 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. References
The 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. References
PART II: Computational epistemology (CE)
Figure: http://xkcd.com/329/
Computational epistemology: an overview

7. References
Approaches 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. References
Epistemology 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. References
The 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. References
Normative-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 s
Computational epistemology: an overview

11. References
PART III: Methods and an example
Computational epistemology: an overview

12. References
What 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. References
Formalizing 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. References
2SAT 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. References
2SAT 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. References
Building 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. References
The agents for 2SAT
Truth table agent;
Truth line agent;
Simplification agent.
Computational epistemology: an overview

18. References
Analyzing 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. References
Analyzing 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. References
Truth 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 Constants
Computational epistemology: an overview

21. References
Truth 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] 3
Computational epistemology: an overview

22. References
Truth 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 petabytes
Computational epistemology: an overview

23. References
Truth 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 Constants
Computational epistemology: an overview

24. References
Simplification 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 Constants
Computational epistemology: an overview

25. References
Humans: 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 Constants
Computational epistemology: an overview

26. References
PART IV: CE and other sciences
Computational epistemology: an overview

27. References
The 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. References
Is this still philosophy?
Computational epistemology: an overview

29. References
PART V: The 2nd year paper
X
Computational epistemology: an overview

30. References
The 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. References
The 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. References
The 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. References
References
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