Epistemologia computacional: intrudução

References

Computational epistemology: an overview

Danilo Dantas


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PART I: Which epistemology?


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Quine’s proposal

The stimulation of his sensory receptors is all the evidenceanybody has had to go on, ultimately, in arriving at hispicture of the world. Why not just see how this constructionreally proceeds? Why not settle for psychology?(Quine, 1969, p. 75).

Epistemology, or something like it, simply falls into place asa chapter of psychology and hence of natural science.(Quine, 1969, p. 82).


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Naturalized versus traditional epistemology

Aim Method ReductionTraditional epistemology normative a priori noNaturalized epistemology descriptive empirical yes∗

Table: The ∗ is true of some naturalized epistemologies (e.g. Quine, 1969),but not of all (e.g. Goldman, 1986).


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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.


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PART II: Computational epistemology (CE)

Figure: http://xkcd.com/329/


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Approaches to AI

Thinking Humanly Thinking Rationally“[The automation of] activitiesthat we associate with humanthinking, activities such asdecision-making, problem solving,learning (...)” (Bellman, 1978).

“The study of the computationsthat make it possible to perceive,reason, and act” (Winston, 1970).

Acting Humanly Acting Rationally“The creation of machines thatperform functions that require in-telligence when performed by peo-ple” (Kurzweil, 1990).

“Computational Intelligence isthe study of the design of intelli-gent agents” (Poole et al., 1998).

Table: Russell and Norvig (2010)


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Epistemology as the description of the ideal agent

The ideal (but finite) rational agent is a finite rational agentwhich acts to achieve the best expected outcome in all possibleenvironments, and which does it using the less possible amount ofprocessing and time.


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Normative-grounding

S has grounds to believe that p in s ←→ The ideal agent believes that pin s

S is warranted to believe that p in sS is justified to believe that p in sS 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 thatp in s


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PART III: Methods and an example


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What is 2SAT?

2SAT is the problem of determining whether a given propositionallogic formula in two-conjunctive normal form (2CNF) is satisfiable ofand providing an assignment that satisfies it.

E.g. does any assignment satisfies (C ∨ ¬D) ∧ (A ∨B) ∧ (¬A ∨ ¬C)?


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Formalizing problems

If a problem can be described as a search problem, we may use theformalization in proposed by Russell and Norvig (2010, p. 66):

I The initial state;

I A function which returns the available actions in a given state;

I A transition model, which specifies the result of a given actionin a given state;

I The goal test, which determines whether a state is a goal state.

I A path cost function, which takes a list of pairs state-actionsand returns a number.


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2SAT as a search problem

I The initial state is [x1, ..., xn], where x1 = x2 = ... = xn = 1.

I The available actions are to change the value of any number ofconstants pi from 0 to 1 or from 1 to 0.

I The transition model returns, for each action, the state withthe resulting assignment.

I The goal test is whether an assignment render the formula true(classical logic rules).

I The path cost function returns the number of changes in thetruth value of constants.


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2SAT as a graph

[1, 1, 1]

S

[1, 1, 0]

[1, 0, 1]

[1, 0, 0]

[0, 1, 1]

[0, 1, 0]G

[0, 0, 1]

[0, 0, 0]

G1

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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.


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The agents for 2SAT

I Truth table agent;

I Truth line agent;

I Simplification agent.


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Analyzing the agents 1

In order to be implementable as a model of the ideal agent, an agentmust meet some requirements:

1. to have consistent dispositions;

2. to be translatable into a programming language;

3. to be computationally accurate and feasible.


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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.


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Truth table agent: the plots

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Solution cost

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Truth table agent: solution cost

[1, 1, 1]

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[1, 1, 0]

[1, 0, 1]

[1, 0, 0]

[0, 1, 1]

[0, 1, 0]

[0, 0, 1]

[0, 0, 0]

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Truth table agent: time and space requirements

Constants Lines Time Space1 2 2× 10−6 seconds 2 bytes2 8 4× 10−6 seconds 8 bytes5 160 3.2× 10−5 seconds 160 bytes10 10240 1× 10−3 seconds 10 kilobytes20 4.1942× 107 1.0486 seconds 20 megabytes50 2.2518× 1015 35.7 years 50 petabytes100 2.5354× 1032 402 trillions of years 1.1259× 1017 petabytes


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Truth line agent: the plots

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Simplification agent: the plots

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cost

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Humans: the plots

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PART IV: CE and other sciences


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Is this still philosophy?


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PART V: The 2nd year paper

X


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The Bayesian agent

1. The Bayesian agent holds degrees of belief in accordance with theaxioms of the probability calculus;

2. The Bayesian agent employs traditional probability calculus toolsto 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 itdegrees of belief in that proposition is higher than a threshold.


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The defeasible agent (Pollock, 1995)

1. The defeasible agent adopts beliefs in response to construingarguments, provided no defeaters have already been adopted forany step of the argument;

2. The defeasible agent must keep track of the basis upon which itsbeliefs are held;

3. The defeasible agent must keep track of defeated inferences, andwhen a defeater is itself retracted, this should reinstate thedefeasible inference.


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The Wumpus world

PIT

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Stench

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Gold

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Figure: Russell and Norvig (2010)


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References

Bellman, R. E. (1978). An Inrrocluction to Artificial Intelligence: Can ComputerThink? Boyd & Fraser Publishing Company, San Francisco.

Goldman, A. (1986). Epistemology and Cognition. Cambridge: Harvard UniversityPress.

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. TheMIT Press.

Poole, D., Mackworth, A. K., and Goebel, R. (1998). Computational intelligence: Alogical approach. Oxford University Press, Oxford, UK.

Quine, W. V. (1969). Ontological Relativity and Other Essays, chapter EpistemologyNaturalized, pages 69–90. New York: Columbia UP.

Russell, S. and Norvig, P. (2010). Artificial Intelligence: A Modern Approach 3rdEdition. Upper Saddle River,EUA: Prentice-Hall.

Winston, P. H. (1970). Learning structural descriptions from examples. technical reportmac-tr-76. Department of Electrical Engineering and Computer Science,Massachusetts Institute of Technology, Cam- bridge, Massachusetts.


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Epistemologia computacional: intrudução