Persistent Playgrounds Fall 2011 Managing Software Development 1/27/20161Persistent Playgrounds

Alternative Introduction From an Independence-Friendly Logic website. 1/27/2016Persistent Playgrounds2

Quantifier Game of Lovers 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. 1/27/20163Persistent Playgrounds

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. 1/27/20164Persistent 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. 1/27/20165Persistent Playgrounds

Comparison Persistent Playground tournament second opinion evaluation data mining – strongly defended Isolated Playground tournament nothing data mining – two agree 1/27/20166Persistent Playgrounds

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. 1/27/20167Persistent Playgrounds

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. 1/27/20168Persistent Playgrounds

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. 1/27/20169Persistent Playgrounds

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 1/27/201610Persistent Playgrounds

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 1/27/201611Persistent Playgrounds

Data mining: welfare claims simple 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 1/27/2016Persistent Playgrounds12

Data mining: welfare claims more 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 1/27/2016Persistent Playgrounds13

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 1/27/201614Persistent Playgrounds

Events refute – defender current reputation – opposer current reputation – claim – outcome: refuted/defended 1/27/201615Persistent Playgrounds

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 1/27/201616Persistent Playgrounds

Events agree – reduces to refute and Bob becomes also a proposer of the claim 1/27/201617Persistent Playgrounds

Old 1/27/2016Persistent Playgrounds18

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) 1/27/201619Persistent Playgrounds

Comparison New tournament second opinion evaluation data mining – strongly defended Old tournament nothing data mining – two agree 1/27/201620Persistent Playgrounds

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-y 2 ) maximize k(c): AxEy f(x,y)>=c yes, larger c. skills: calculus, exploring a surface 1/27/201621Persistent Playgrounds