experience based nonmonotonic reasoning · example wearewaitingforthetram,andit’sasunnyday... ......

Experience Based Nonmonotonic Reasoning

Daniel Borchmann

TU Dresden

2013-09-16

Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 1 / 6

ExampleWe are waiting for the tram, and it’s a sunny day . . .

§ . . . so we expect our tram to be on timeBut then we hear some sirens (may a nearby accident?) . . .

§ . . . so our tram may be late

ObservationNon-monotonic behavior!

How to model?

§ No prior logical knowledge§ Previous experiences

Decide what to expect based on previous experiences in similar situations

ApproachFormalize this situation using formal concept analysis (FCA)



§ . . . so we expect our tram to be on time

But then we hear some sirens (may a nearby accident?) . . .



How to model?









How to model?









How to model?§ No prior logical knowledge

§ Previous experiences








How to model?§ No prior logical knowledge§ Previous experiences




Example

sunny sirens tram on time

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Day 6 ˆ ˆ


Example


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Example


Example


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ExampleOn what days was it sunny and the tram was on time?

t sunny, tram on time u1 = tDay 1,Day 3,Day 4,Day 6 u


Example


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t sunny, tram on time u1

= tDay 1,Day 3,Day 4,Day 6 u


Example


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t sunny, tram on time u1 = tDay 1,Day 3,Day 4,Day 6 u


Example


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Example


Example


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ExampleWhat observations have Day 1 and Day 5 in common?

tDay 1,Day 5 u1 = t sunny u


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tDay 1,Day 5 u1

= t sunny u


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tDay 1,Day 5 u1 = t sunny u


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IdeaIf it is sunny, it normally follows that the tram is on time if this has happenedoften enough in similar situations.

§ True for Day 1, Day 3, Day 4, Day 6§ Not true for Day 5


Example


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§ True for Day 1, Day 3, Day 4, Day 6

§ Not true for Day 5


Example


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§ True for Day 1, Day 3, Day 4, Day 6§ Not true for Day 5


Example


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Example


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ObservationIf is sunny and there are sirens, it is not clear whether the tram will be on time

§ True on Day 4§ Not true on Day 5


Example


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§ True on Day 4

§ Not true on Day 5


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Example


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Not enough evidence!


GoalFormalize notion of “normally follows”

ApproachUse notion of confidence: define for X ,Y sets of attributes

conf(X Ñ Y ) :=

#

1 X 1 = H|(XYY )1|

|X 1|otherwise

as the confidence of X Ñ Y .

Exampleconf(t sunny u Ñ t tram on time u) = 4/5

conf(t sunny, sirens u Ñ t tram on time u) = 1/2

ApproachConsider implications with high confidence as “normally true”



ApproachUse notion of confidence:

define for X ,Y sets of attributes

conf(X Ñ Y ) :=

#

1 X 1 = H|(XYY )1|

|X 1|otherwise







ApproachUse notion of confidence: define for X ,Y sets of attributes

conf(X Ñ Y ) :=

#

1 X 1 = H|(XYY )1|

|X 1|otherwise






So what?

§ Approach does not seem to be new§ Should exist similar approaches, much better investigated

Still interesting!

§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones


So what?§ Approach does not seem to be new

§ Should exist similar approaches, much better investigated

Still interesting!



So what?§ Approach does not seem to be new§ Should exist similar approaches, much better investigated

Still interesting!




Still interesting!§ Shows connection between FCA and NMR

§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones



Still interesting!§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining

§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones



Still interesting!§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data

§ Closer look on connections between this approach and existing ones



Still interesting!§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones


Thank You


experience based nonmonotonic reasoning · example wearewaitingforthetram,andit’sasunnyday... ......

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