Probabilistic Logic Programming

• narrow down network of interaction
• build knowledge base based on automatically learned facts
• video recognition

In prolog, world is modelled with facts and relations In problog, there is a probability associated with the facts to get a distribution over possible worlds.

Distribution Semantics [Sato, ICLP 95]: probabilistic choices + logic program = distribution over possible worlds

e.g.

PRISM

multi-valued switches

ICL

probabilistic alternative

ProbLog

Probabilistic facts + annotated disjunctions

LPADs

annotated disjunctions

CP-Logic

causal probabilistic laws

• basic is discrete RVs
• continuous RVs
• decision theory
• special ways to handle time & dynamics
• integrating PLP with deep learning => Neural Predicates

A bit of gambling

Probabilistic Choices:

• toss (biased) coin & draw ball from each urn
  • 30% balls are red, 70% are blue in one urn
  • 20%,30% and 50% red, green, blue balls resp. in another urn

Consequences:

• win if (heads and a red ball) or (two balls of same color)

0.4 :: heads 

0.3 :: col(1,red); 0.7 :: col(1,blue). 
0.2 :: col(2, red); 0.3 :: col(2,gree); 0.5 :: col(2,blue). 

win :- heads, col(_, red). 
win :- col(1,C), col(2,C).

• First 3 statements are probabilistic choices.
• Last 2 lines are the consequences.

now we can ask probabilistic questions. e.g.

• probability of win?
• probability of win given some constraints.
• MPE - Most Probabilistic World .

0.5 :: weather(sun,0); 0.5::weather(rain,0). 
0.6 :: weather(sun,T); 0.4:weather(rain,T) :- T>0, Tprev is T-1, weather(sun,Tprev). 
0.2 :: weather(sum,T); 0.8::weather(rain,T) :- T>0, Tpreve is T-1, weater(rain,Tprev).

Last two lines are probabilities of weather based on the condtion of previous day's weather.

There are infinitely many possible worlds but for probabilistic queries finitely many possible world suffice to answer any ground query (e.g. weather of day 2).