Belief Augmented Frames for Knowledge Representation

1. Belief Augmented Frames for Knowledge Representation Colin Tan, Department of Computer Science, School of Computing, National University of Singapore.

2. Belief Augmented FramesMotivation • Frames • Flexible, intuitive way of representing knowledge. • Frames represent an entity or a concept • Frames consist of slots with values • Represents relations between current frame and other frames. • Slots have events attached to them • Can invoke procedures (“daemons”) whenever a slot’s value is changed, removed etc.

3. Belief Augmented FramesMotivation • In the original definition of frames, slot-value pairs are “definite”. • One improvement is to introduce uncertainties into these relations.

4. Belief Augmented FramesMotivation • Statistical representations are not always ideal: • If we are p% certain that a fact is true, this doesn’t mean that we are 1-p% certain that it is false. • Various uncertainty reasoning methods introduced to address this: • Dempster-Schafer Theory • Transferrable Belief Model • Probabilistic Argumentation Systems

5. Belief Augmented FramesMotivation • By combining uncertainty measures with frames: • Uncertainties in slot-value pair assignments provide frames with greater expressiveness and reasoning ability. • Frames offer a neat intuitive structure for reasoning uncertain relations.

6. Modeling Uncertainty in Belief Augmented Frames • Uncertainty not only on slot-value pair assignments, but also on the existence of the concept/object represented by the frame. • The belief mass Tfis called the “Supporting Mass”, and it is the degree of support that the fact f is true. • Likewise Ffis the Refuting Mass, and it is the degree of support that the fact f is false.

7. Modeling Uncertainty in Belief Augmented Frames • In general: • 0  Tf , Ff 1 • Tfis fully independent of Ff • Tf + Ff  1 • The Degree of Inclination Difis defined as: • Dif = Tf - Ff • The Plausibility plf is defined as: • Plf = 1 - Ff

8. Combining Belief Masses • Fuzzy-logic style min-max functions are used to combine belief masses from different facts. • Given two facts P and Q: • Conjunctions • TPQ = min(TP, TQ) • FPQ = max(FP, FQ)

9. Combining Belief Masses • Given two facts P and Q: • Disjunctions • TPQ = max(TP, TQ) • FP  Q = min(FP, FQ) • Negation • TP = FP • FP = TP

10. Reasoning Example • Suppose we have the following facts: • P:-A   B, P:-A  C  B, P:-A  B • Supose also that A, B and C are three facts defined as follows (Fact, Tfact, Ffact) • (A, 0.3, 0.4), (B, 0.9, 0.2), (C, 0.8, 0.3) • Then to evalute P: • P =((A   B)  (A  C  B))  (A  B) • P = ((A   B)  (A  C  B))  (A  B) = ((A  B)  (A  C  B))  (A  B)

11. Reasoning Example • P =((A   B)  (A  C  B))  (A  B) • TP = min(max(min(TA, FB), min(FA, TC, FB)), max(FA, TB)) = min(max(min(0.3, 0.2), min(0.4, 0.8, 0.2)), max(0.4, 0.9)) = min(max(0.2, 0.2), max(0.4, 0.9)) = min(0.2, 0.9) = 0.2

12. Reasoning Example • P = ((A  B)  (A  C  B))  (A  B) FP = max(min(max(FA, TB), max(TA, FC, TB)), min(TA, TB)) = max(min(max(0.4, 0.9), max(0.3, 0.3, 0.9)), min(0.3, 0.9)) = max(min(0.9, 0.9), min(0.3, 0.9)) = 0.9 DIP = 0.2 – 0.9 = -0.7 PlsP = 1 – 0.9 = 0.1

13. Major BAF Operations • add_concept(con, ex_t, ex_f) • Creates a new frame named “con” representing a concept or an object. ex_t and ex_f are respectively the supporting and refuting masses for the existence of “con”. • add_concept_inh(con, par, ex_t, ex_f, in_t, in_f) • Creates a new frame “con” inheriting all the slot-value assignments of a parent frame “par”. • Sets up “isChild” and “isParent” relations between the new and parent frames. in_t and in_f are respectively the supporting and refuting masses for these relations.

14. Major BAF Operations • add_rel(frame, slot, value, r_t, r_f) • Adds a new relationship between current frame “frame” and another frame “value”, with the relation given in “slot” r_t and r_f are respectively the supporting and refuting masses for this relation. • abstract(frame, frame_set) • Creates a new frame “frame” consisting of slot-value assignments found in every frame in the given set “frame_set”. • The new frame will thus contain all the slot-value assignments common to every frame in the set.

15. Daemons • Daemons, or event handlers, may be attached to slots to respond to any of the following events. • NewValue:A new value is being added to a slot. • DelValue: An existing value is being deleted. • UpdValue: The belief masses for an existing value is being updated. • NeedValue: An empty slot needs a value.

16. Daemons • Demons respond with: • dm_Ignore: No action to be taken • dm_Rule: Execute a returned rule set • dm_Assign: Assign a returned value to the slot • dm_Delete: Remove existing value from slot • dm_Rule can be returned together with dm_Assign, dm_Delete and dm_Ignore. • dm_Assign has two modes: • Exclusive: All previous slot assignments are removed • Inclusive: Returned value is attached to previous values.

17. Rules • Rules may be attached to modify the existence or relation belief values. E.g. • rel(a, rel1, b) :- rel(c,rel2,d), rel(c,rel3,e) • The Supporting and Refuting belief masses for a rel1 b will depend on the Supporting and Refuting belief masses for the right hand side. • Rules are “Prolog-like”, everything on RHS is taken to be a conjunction. • Identical named rules are taken to be conjunctions, and the final belief values are evaluated as in the earlier example.

18. Application • Text Classification • Compute term frequency ftfrom all documents in a class. • Let fti be the term frequency of term t in document i in class c. Let ftk be the term frequency of term t in document k of class c’, where c’  c • cT= mini(fti) • cF = maxk(ftk)

19. Application • Text Classification • For an unseen document dm, extract all terms tm. • Compute: • Tc = min(TCt) • Fc = max(FCt) • Here TCt, FCt= Support and Refuting mass for term t in class C, as computed earlier. • Compute DIC = TCt  FCt • The document is classified as class cmax = argmaxC(DIC)

20. Application • Text Classification • Trained on 400 news articles broken into 5 categories. • Tested on training set (inside test) and unseen set of 100 articles. • Evaluation of BAF vs. Naïve Bayes

21. Results – Inside Test

22. Results – Outside Test

23. Results - Analysis • BAF outperforms Naïve Bayes for all outside tests. • BAF performs slightly less well than Naïve Bayes without smoothing or with Jeffreys-Perks smoothing for inside tests • Results are promising – Use thesaurus to improve results?

24. Difficulties • Semantics of slots is ill-defined • There is no fixed way to use the slots to represent relations between frames. • This complicates the modeling of real-world English sentences. E.g. • The black cat stole the purse. • Should this be modeled as stole(subject: cat, object: purse), cat(action:stole, object:purse), purse(action:stolenby, subject:cat)?

25. Difficulties • Many ways to derive a-priori Supporting and Refuting masses. • Some ways might be better than others. • Separation of Supporting and Refuting masses introduces additional problems that can make modeling awkward and counter-intuitive: • E.g. plsf < Tf, when Tf , Ff> 0.5

26. Difficulties • The range for the sum of Tf ,andFf falls in [0, 2] instead of [0, 1]. This is again counter-intuitive.

27. Future Work • A model for measuring the quality of the knowledge in the BAF knowledge base should be developed. • To apply BAF to more problems to study its behavior, especially against established methods.