persistent playgrounds fall 2011 managing software development 1/27/20161persistent playgrounds

Persistent Playgrounds

Fall 2011Managing Software Development

05/03/23 1Persistent Playgrounds

Alternative Introduction

• From an Independence-Friendly Logic website.

05/03/23 Persistent Playgrounds 2

Quantifier Game of Lovers• http://mtl.uta.fi/logic-group/iflogic.html• Bob and Alice are two lovers who can never seem to

agree about anything. Whenever Alice makes a claim, Bob immediately tries to refute it. If Alice makes an existential claim, Bob demands that she identify an individual satisfying it. When Alice asserts a negated formula the lovers switch roles: Bob attempts to defend the claim, whilst Alice tries to refute it.

• When Alice asserts an ordinary first-order claim, the ensuing dispute is a game of perfect information. If the claim is true, Alice will always win. If it is false, Bob will always win.


http://mtl.uta.fi/logic-group/iflogic.html

Proofs / Winning Strategies

• Skolemization is the process of eliminating the existential quantifiers from a formula by introducing fresh function symbols.

• A Skolem function produces a witness for an existential claim. Taken together, a set of Skolem functions for a claim can be seen as encoding a strategy for Alice in the associated semantic game. If the claim is true, the Skolem functions can be assumed to encode a winning strategy.


Persistent Playgrounds

Persistent Playground• Tracks the evolution of

solution techniques in a domain over several years.

• Compares old approaches with new ones. The new approaches should succeed over all old ones.

• Builds incrementally a knowledge base through a sequence of tournaments. Develops the techniques to defend the claims in knowledge base.

Isolated Playground• Persistent playground with

only one tournament.


Comparison

Persistent Playground• tournament• second opinion evaluation• data mining

– strongly defended

Isolated Playground• tournament• nothing• data mining

– two agree


Second Opinion• After a tournament is complete we have:– welfare set from previous tournament– strongly defended claims -> might be true– strongly refuted claims -> might be false

• Apply data mining step. • Many of the strongly defended or refuted claims

have not been seen by many avatars.• All avatars must give their decision (refute,

strengthen or agree) on each strongly defended or refuted claim as well as on the old welfare claims.


Second Opinion

• The second opinion evaluation will change the set of strongly defended and refuted claims.

• The second opinion evaluation is like a tournament but without proposing claims. Instead claims come from data mining.

• Apply data mining step again.


SCG

• Tournament– list of claims with statistics

• Datamining Results of Tournament– WelfareClaims• strongly defended claims

– DemocraticCleanup• claims are even more strongly defended or they are

less strongly defended and dropped from the welfare set. All vote with justification.


Statistics collected for claim

• list of proposers• for each claim and proposer– how often defended• reputation of defender at time of defense

– how often refuted• reputation of refuters at time of refutation


Statistics collected for claim

• for each claim– how often defended• average reputation of defender at time of defense

– how often refuted• average reputation of refuters at time of refutation


Data mining: welfare claimssimple

• C : d: defended r: refuted• d: how often defended• r: how often refuted• Keep it simple– d/(d+r) > 0.99: true welfare claims– r/(d+r) > 0.99: false welfare claims


Data mining: welfare claimsmore complex

• C : d: defended (ard) r: refuted (arr)• d: how often defended• r: how often refuted• More complex:– d*ard/(d*ard+r*arr) > 0.99: true welfare claims– r*arr/(d*ard+r*arr) > 0.99: false welfare claims

• ard: average reputation of defender• arr: average reputation of refuter


Why reputation

• if r1>r2: – claim C is defended against an opposer with

reputation r1 counts more than – claim C is defended against an opposer with

reputation r2


Events

• refute– defender• current reputation

– opposer• current reputation

– claim– outcome: refuted/defended


Events

• strengthen– reduces to refute and the strengthened claim has

Bob as defender– if strengthening not successful we have a

successful defense of the original claim• defender• opposer• claim• defended


Events

• agree– reduces to refute and Bob becomes also a

proposer of the claim


Old


Why reputation

• if r1>r2: – claim C is defended by a proposer with against an

opposer with reputation r1 counts more than – claim C is defended against an opposer with

reputation r2 – difference reputation(proposer)-

reputation(opposer)


Comparison

New• tournament• second opinion evaluation• data mining

– strongly defended

Old• tournament• nothing• data mining

– two agree


Playground Comparisons

HSR• Kind: ForAllExists• Instance: (n,k)• InstanceSet: singleton• Solution: decision tree• quality: depth of tree• solve: minimize• claim: HSR(n,k)<=q• strengthen: yes, smaller q.• skills needed: Pascal’s triangle,

memoization

MMG• ForAllExists• x• [0,1]• y • f(x,y)=xy+(1-x)(1-y2)• maximize• k(c): AxEy f(x,y)>=c• yes, larger c.• skills: calculus, exploring a

surface


persistent playgrounds fall 2011 managing software development 1/27/20161persistent playgrounds

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