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SEKE 2012 Proceedings - Knowledge Systems Institute

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4.4. An Illustrative Example<br />

Now let us look at an illustrative example. Assuming<br />

we have the following KB for classifying animals and plants<br />

that is obtained based on a bias b of three features in à =<br />

{Shape, Cell_Walls, Cell_Functions} where Shape is ab out an<br />

object’s morphology, Cell_Walls pertains to cell walls being<br />

non-rigid or rigid, and Cell_Functions defines if cells break<br />

sugar down to carbon dioxide or turn carbon dioxide into<br />

sugar. We rewrite b = { S, CW, CF} where S stands for<br />

Shape, CW for Cell_Walls, and CF for Cell_Functions.<br />

R1: CucumberShape(x) SeaCucumber(x)<br />

R2: Cucumber(x) CucumberShape(x)<br />

R3: Plant(x) Cucumber(x)<br />

R4: NonRigidCellWalls(x) SeaCucumber(x)<br />

R5: SugarToCarbonDioxide(x) SeaCucumber(x)<br />

R6: Animal(x) NonRigidCellWalls(x)<br />

R7: Animal(x) SugarToCarbonDioxide(x)<br />

R8: Animal(x) RigidCellWalls(x)<br />

R9: Animal(x) CarbonDioxideToSugar(x)<br />

R10: Plant(x) RigidCellWalls(x)<br />

R11: Plant(x) CarbonDioxideToSugar(x)<br />

R12: Plant(x) NonRigidCellWalls(x)<br />

R13: Plant(x) SugarToCarbonDioxide(x)<br />

R14: RigidCellWalls(x) NonRigidCellWalls(x)<br />

R15: CarbonDioxideToSugar(x) SugarToCarbonDioxide(x)<br />

R16: NonRigidCellWalls(x) RigidCellWalls(x)<br />

R17: SugarToCarbonDioxide(x) CarbonDioxideToSugar(x)<br />

Given a seacucumber sc as an input<br />

={SeaCucumber(sc)}, we obtain Plant(sc) from {R1, R2, R3},<br />

and Animal(sc) from {R4, R5, R6, R7}. The given instance of sc<br />

cannot be a plant and an animal at the same time, hence =<br />

{Animal(sc), Plant(sc)} and Animal(sc) Plant(sc). We know<br />

that there is one piece of supportive evidence for Plant(sc)<br />

(via R3 R2 R1) and two pieces of supportive evidence for<br />

Animal(sc) (via R6 R4 and R7 R5). In addition, we can<br />

also obtain two pieces of negative evidence about Plant(sc)<br />

(or two pieces of positive evidence about Plant(sc)) (via<br />

R12 R4 and R13 R5). The issue becomes how to refine b<br />

through minimum shifting to generate a co nsistent bias b.<br />

By calling IDBR with b={S, CW, CF}, the iterative<br />

deepening bias refining process takes place with regard to<br />

the search space in Figure 4.<br />

The minimum shifting process will result in b = {CW,<br />

CF} being returned as a consistent bias. Table 1 shows the<br />

supports for elements in the successor set of b. In addition,<br />

the mKB will be augmented with the following control<br />

information such that next time when an input i includes a<br />

ground atom for SeaCucumber(x), derivations of {R 6 R 4 ,<br />

R 7 R 5 } are preferred and the derivation of {R 3 R 2 R 1 }<br />

will be circumvented.<br />

(): {6 4, 7 5}<br />

{3 2 1}<br />

Figure 4. Search space.<br />

Table 2. Support of {CW, CF} for Plant(sc) and Animal(sc).<br />

CellWalls CellFunction<br />

Plant(SC) 0 0 0<br />

Plant(SC) 0.5 0.5 1.0<br />

Animal(SC) +0.5 +0.5 +1.0<br />

Animal(SC) 0 0 0<br />

5. Conclusion<br />

Total<br />

Support<br />

In this paper, we describe i 2 Learning, a framework for<br />

perpetual learning agents. i 2 Learning allows the learning<br />

episodes of the agent to be initiated by inconsistencies the<br />

agent encounters during its problem-solving episodes.<br />

Learning in the framework amounts to th e continuous<br />

knowledge refinement and/or augmentation in order t o<br />

overcome encountered inconsistencies. An agent’s<br />

performance at tasks can be incrementally improved with<br />

each learning episode. i 2 Learning offers an overarching<br />

structure that accommodates the growth and expansion of<br />

various inconsistency-specific learning strategies. Through<br />

the mutually exclusive inconsistency, we demonstrate<br />

algorithmically how i 2 Learning facilitates learning in terms<br />

of bias shifting.<br />

The main contributions of this research work include<br />

the following. We dem onstrate that learning through<br />

overcoming inconsistency is a viable and useful paradigm.<br />

The i 2 Learning framework accommodates various<br />

inconsistency-specific heuristics to be deployed in the<br />

continuous learning process. Through iterative deepening<br />

bias shifting, an agent’s performance can be incrementally<br />

improved by overcoming instances of mutually exclusive<br />

inconsistency.<br />

Future work can be carried ou t in the following<br />

directions. Experimental work is needed on the iterative<br />

deepening bias shifting process for the mutually exclusive<br />

inconsistency case. Details of other frequently encountered<br />

inconsistencies and their respective learning heuristics still<br />

need to be fleshed out.<br />

Acknowledgements. We express our sincere appreciation<br />

to the anonymous reviewers for their comments that help<br />

improve the content and the presentation of this paper.<br />

254

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