On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set...
Transcript of On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set...
![Page 1: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/1.jpg)
On the Use of Epistemic Ordering Functionsas Decision Criteria
for Automated and Assisted Belief Revision in SNePS(Preliminary Report)
Ari I. Fogel and Stuart C. Shapiro
Department of Computer Science and EngineeringUniversity at Buffalo, Buffalo, NY 14260
{arifogel,shapiro}@buffalo.edu
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 1 / 19
![Page 2: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/2.jpg)
Outline
1 Introduction
2 Using Epistemic Ordering Functions
3 Demonstrations
4 Conclusions
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 2 / 19
![Page 3: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/3.jpg)
Introduction
Goal
Algorithms for using a user-supplied epistemic ordering relation
for automated or user-assisted belief revision
with a miminal burden on the user.
Generalizes previous workon use of epistemic ordering for BR in SNePS.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 3 / 19
![Page 4: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/4.jpg)
Introduction
Setting, Representation
SNePS Knowledge Representation and Reasoning System.
Implemented.
First-Order Logic.
Finite Belief Base (Knowledge Base, KB).
Every belief either hypothesis (hyp) or derived (der).(Could be both.)
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 4 / 19
![Page 5: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/5.jpg)
Introduction
Setting, Representation
SNePS Knowledge Representation and Reasoning System.
Implemented.
First-Order Logic.
Finite Belief Base (Knowledge Base, KB).
Every belief either hypothesis (hyp) or derived (der).(Could be both.)
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 4 / 19
![Page 6: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/6.jpg)
Introduction
Setting, Representation
SNePS Knowledge Representation and Reasoning System.
Implemented.
First-Order Logic.
Finite Belief Base (Knowledge Base, KB).
Every belief either hypothesis (hyp) or derived (der).(Could be both.)
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 4 / 19
![Page 7: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/7.jpg)
Introduction
Setting, Representation
SNePS Knowledge Representation and Reasoning System.
Implemented.
First-Order Logic.
Finite Belief Base (Knowledge Base, KB).
Every belief either hypothesis (hyp) or derived (der).(Could be both.)
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 4 / 19
![Page 8: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/8.jpg)
Introduction
Setting, Representation
SNePS Knowledge Representation and Reasoning System.
Implemented.
First-Order Logic.
Finite Belief Base (Knowledge Base, KB).
Every belief either hypothesis (hyp) or derived (der).(Could be both.)
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 4 / 19
![Page 9: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/9.jpg)
Introduction
Setting, Inference
Forward, backward, and bi-directional inference.
Uses Relevance Logic (R, paraconsistent).
Every belief has a set of origin sets (OSs).
One OS for each way it has been derived so far.
OS = set of hyps actually used for the derivation.
Computed by rules of inference.If p is a hyp, {p} ∈ os(p).
Context = a set of hyps.
Current Context (CC) = a set of hyps currently believed.
Proposition p is asserted (believed)iff ∃s[s ∈ os(p) ∧ s ⊆ CC ].
[Martins & Shapiro, AIJ, 1988]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 5 / 19
![Page 10: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/10.jpg)
Introduction
Setting, Inference
Forward, backward, and bi-directional inference.
Uses Relevance Logic (R, paraconsistent).
Every belief has a set of origin sets (OSs).
One OS for each way it has been derived so far.
OS = set of hyps actually used for the derivation.
Computed by rules of inference.If p is a hyp, {p} ∈ os(p).
Context = a set of hyps.
Current Context (CC) = a set of hyps currently believed.
Proposition p is asserted (believed)iff ∃s[s ∈ os(p) ∧ s ⊆ CC ].
[Martins & Shapiro, AIJ, 1988]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 5 / 19
![Page 11: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/11.jpg)
Introduction
Setting, Inference
Forward, backward, and bi-directional inference.
Uses Relevance Logic (R, paraconsistent).
Every belief has a set of origin sets (OSs).
One OS for each way it has been derived so far.
OS = set of hyps actually used for the derivation.
Computed by rules of inference.If p is a hyp, {p} ∈ os(p).
Context = a set of hyps.
Current Context (CC) = a set of hyps currently believed.
Proposition p is asserted (believed)iff ∃s[s ∈ os(p) ∧ s ⊆ CC ].
[Martins & Shapiro, AIJ, 1988]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 5 / 19
![Page 12: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/12.jpg)
Introduction
Setting, Inference
Forward, backward, and bi-directional inference.
Uses Relevance Logic (R, paraconsistent).
Every belief has a set of origin sets (OSs).
One OS for each way it has been derived so far.
OS = set of hyps actually used for the derivation.
Computed by rules of inference.If p is a hyp, {p} ∈ os(p).
Context = a set of hyps.
Current Context (CC) = a set of hyps currently believed.
Proposition p is asserted (believed)iff ∃s[s ∈ os(p) ∧ s ⊆ CC ].
[Martins & Shapiro, AIJ, 1988]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 5 / 19
![Page 13: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/13.jpg)
Introduction
Setting, Inference
Forward, backward, and bi-directional inference.
Uses Relevance Logic (R, paraconsistent).
Every belief has a set of origin sets (OSs).
One OS for each way it has been derived so far.
OS = set of hyps actually used for the derivation.
Computed by rules of inference.If p is a hyp, {p} ∈ os(p).
Context = a set of hyps.
Current Context (CC) = a set of hyps currently believed.
Proposition p is asserted (believed)iff ∃s[s ∈ os(p) ∧ s ⊆ CC ].
[Martins & Shapiro, AIJ, 1988]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 5 / 19
![Page 14: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/14.jpg)
Introduction
Setting, Inference
Forward, backward, and bi-directional inference.
Uses Relevance Logic (R, paraconsistent).
Every belief has a set of origin sets (OSs).
One OS for each way it has been derived so far.
OS = set of hyps actually used for the derivation.
Computed by rules of inference.If p is a hyp, {p} ∈ os(p).
Context = a set of hyps.
Current Context (CC) = a set of hyps currently believed.
Proposition p is asserted (believed)iff ∃s[s ∈ os(p) ∧ s ⊆ CC ].
[Martins & Shapiro, AIJ, 1988]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 5 / 19
![Page 15: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/15.jpg)
Introduction
Setting, Inference
Forward, backward, and bi-directional inference.
Uses Relevance Logic (R, paraconsistent).
Every belief has a set of origin sets (OSs).
One OS for each way it has been derived so far.
OS = set of hyps actually used for the derivation.
Computed by rules of inference.If p is a hyp, {p} ∈ os(p).
Context = a set of hyps.
Current Context (CC) = a set of hyps currently believed.
Proposition p is asserted (believed)iff ∃s[s ∈ os(p) ∧ s ⊆ CC ].
[Martins & Shapiro, AIJ, 1988]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 5 / 19
![Page 16: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/16.jpg)
Introduction
SNeBR
Contradiction recognizedwhen both some p and ¬p become asserted (believed).
Same data object used for p in both wffs.Second one (call it ¬p) could have been
a hyp just added to the KB;derived by forward inference from a hyp just added to the KB;derived by backward inferencefrom some hyps not previously realized to be inconsistent with p.
Each of p, ¬p could be a hypothesis or derived.
Nogood = s1 ∪ s2 s.t. s1 ∈ os(p) ∧ s2 ∈ os(¬p)a minimally inconsistent set of hyps.
To restore KB to state of not being known to be inconsistent,must remove one hyp in each nogood from CC.Guaranteed to be sufficient.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 6 / 19
![Page 17: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/17.jpg)
Introduction
SNeBR
Contradiction recognizedwhen both some p and ¬p become asserted (believed).
Same data object used for p in both wffs.Second one (call it ¬p) could have been
a hyp just added to the KB;derived by forward inference from a hyp just added to the KB;derived by backward inferencefrom some hyps not previously realized to be inconsistent with p.
Each of p, ¬p could be a hypothesis or derived.
Nogood = s1 ∪ s2 s.t. s1 ∈ os(p) ∧ s2 ∈ os(¬p)a minimally inconsistent set of hyps.
To restore KB to state of not being known to be inconsistent,must remove one hyp in each nogood from CC.Guaranteed to be sufficient.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 6 / 19
![Page 18: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/18.jpg)
Introduction
SNeBR
Contradiction recognizedwhen both some p and ¬p become asserted (believed).
Same data object used for p in both wffs.Second one (call it ¬p) could have been
a hyp just added to the KB;derived by forward inference from a hyp just added to the KB;derived by backward inferencefrom some hyps not previously realized to be inconsistent with p.
Each of p, ¬p could be a hypothesis or derived.
Nogood = s1 ∪ s2 s.t. s1 ∈ os(p) ∧ s2 ∈ os(¬p)a minimally inconsistent set of hyps.
To restore KB to state of not being known to be inconsistent,must remove one hyp in each nogood from CC.Guaranteed to be sufficient.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 6 / 19
![Page 19: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/19.jpg)
Introduction
SNeBR
Contradiction recognizedwhen both some p and ¬p become asserted (believed).
Same data object used for p in both wffs.Second one (call it ¬p) could have been
a hyp just added to the KB;derived by forward inference from a hyp just added to the KB;derived by backward inferencefrom some hyps not previously realized to be inconsistent with p.
Each of p, ¬p could be a hypothesis or derived.
Nogood = s1 ∪ s2 s.t. s1 ∈ os(p) ∧ s2 ∈ os(¬p)a minimally inconsistent set of hyps.
To restore KB to state of not being known to be inconsistent,must remove one hyp in each nogood from CC.Guaranteed to be sufficient.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 6 / 19
![Page 20: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/20.jpg)
Introduction
SNeBR
Contradiction recognizedwhen both some p and ¬p become asserted (believed).
Same data object used for p in both wffs.Second one (call it ¬p) could have been
a hyp just added to the KB;derived by forward inference from a hyp just added to the KB;derived by backward inferencefrom some hyps not previously realized to be inconsistent with p.
Each of p, ¬p could be a hypothesis or derived.
Nogood = s1 ∪ s2 s.t. s1 ∈ os(p) ∧ s2 ∈ os(¬p)a minimally inconsistent set of hyps.
To restore KB to state of not being known to be inconsistent,must remove one hyp in each nogood from CC.Guaranteed to be sufficient.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 6 / 19
![Page 21: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/21.jpg)
Introduction
SNeBR
Contradiction recognizedwhen both some p and ¬p become asserted (believed).
Same data object used for p in both wffs.Second one (call it ¬p) could have been
a hyp just added to the KB;derived by forward inference from a hyp just added to the KB;derived by backward inferencefrom some hyps not previously realized to be inconsistent with p.
Each of p, ¬p could be a hypothesis or derived.
Nogood = s1 ∪ s2 s.t. s1 ∈ os(p) ∧ s2 ∈ os(¬p)a minimally inconsistent set of hyps.
To restore KB to state of not being known to be inconsistent,must remove one hyp in each nogood from CC.Guaranteed to be sufficient.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 6 / 19
![Page 22: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/22.jpg)
Introduction
SNeBR
Contradiction recognizedwhen both some p and ¬p become asserted (believed).
Same data object used for p in both wffs.Second one (call it ¬p) could have been
a hyp just added to the KB;derived by forward inference from a hyp just added to the KB;derived by backward inferencefrom some hyps not previously realized to be inconsistent with p.
Each of p, ¬p could be a hypothesis or derived.
Nogood = s1 ∪ s2 s.t. s1 ∈ os(p) ∧ s2 ∈ os(¬p)a minimally inconsistent set of hyps.
To restore KB to state of not being known to be inconsistent,must remove one hyp in each nogood from CC.Guaranteed to be sufficient.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 6 / 19
![Page 23: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/23.jpg)
Introduction
SNeBR
Contradiction recognizedwhen both some p and ¬p become asserted (believed).
Same data object used for p in both wffs.Second one (call it ¬p) could have been
a hyp just added to the KB;derived by forward inference from a hyp just added to the KB;derived by backward inferencefrom some hyps not previously realized to be inconsistent with p.
Each of p, ¬p could be a hypothesis or derived.
Nogood = s1 ∪ s2 s.t. s1 ∈ os(p) ∧ s2 ∈ os(¬p)a minimally inconsistent set of hyps.
To restore KB to state of not being known to be inconsistent,must remove one hyp in each nogood from CC.Guaranteed to be sufficient.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 6 / 19
![Page 24: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/24.jpg)
Introduction
Assisted Belief Revision in SNeBR
Present each nogood to user.
Ask user to choose at least one hyp per nogood for removal from CC.
Is non-prioritized belief revision.(Not predetermined whether p or ¬p survives.)
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 7 / 19
![Page 25: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/25.jpg)
Introduction
Assisted Belief Revision in SNeBR
Present each nogood to user.
Ask user to choose at least one hyp per nogood for removal from CC.
Is non-prioritized belief revision.(Not predetermined whether p or ¬p survives.)
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 7 / 19
![Page 26: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/26.jpg)
Introduction
Assisted Belief Revision in SNeBR
Present each nogood to user.
Ask user to choose at least one hyp per nogood for removal from CC.
Is non-prioritized belief revision.(Not predetermined whether p or ¬p survives.)
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 7 / 19
![Page 27: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/27.jpg)
Introduction
Previous Restricted Prioritized BR in SNeBR
In context of SNePS-based agents acting on-line.
Assumes all beliefs are about the current state of the world.
Agent performs believe(p)but currently believes ~p.
If nor{p, ...} is believed as hyp, it is removed from CC.If xor{p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.If andor(0,1){p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.Else do assisted BR.
“State Constraints”
[Shapiro & Kandefer, NRAC-2005]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 8 / 19
![Page 28: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/28.jpg)
Introduction
Previous Restricted Prioritized BR in SNeBR
In context of SNePS-based agents acting on-line.
Assumes all beliefs are about the current state of the world.
Agent performs believe(p)but currently believes ~p.
If nor{p, ...} is believed as hyp, it is removed from CC.If xor{p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.If andor(0,1){p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.Else do assisted BR.
“State Constraints”
[Shapiro & Kandefer, NRAC-2005]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 8 / 19
![Page 29: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/29.jpg)
Introduction
Previous Restricted Prioritized BR in SNeBR
In context of SNePS-based agents acting on-line.
Assumes all beliefs are about the current state of the world.
Agent performs believe(p)but currently believes ~p.
If nor{p, ...} is believed as hyp, it is removed from CC.If xor{p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.If andor(0,1){p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.Else do assisted BR.
“State Constraints”
[Shapiro & Kandefer, NRAC-2005]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 8 / 19
![Page 30: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/30.jpg)
Introduction
Previous Restricted Prioritized BR in SNeBR
In context of SNePS-based agents acting on-line.
Assumes all beliefs are about the current state of the world.
Agent performs believe(p)but currently believes ~p.
If nor{p, ...} is believed as hyp, it is removed from CC.If xor{p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.If andor(0,1){p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.Else do assisted BR.
“State Constraints”
[Shapiro & Kandefer, NRAC-2005]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 8 / 19
![Page 31: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/31.jpg)
Introduction
Previous Restricted Prioritized BR in SNeBR
In context of SNePS-based agents acting on-line.
Assumes all beliefs are about the current state of the world.
Agent performs believe(p)but currently believes ~p.
If nor{p, ...} is believed as hyp, it is removed from CC.If xor{p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.If andor(0,1){p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.Else do assisted BR.
“State Constraints”
[Shapiro & Kandefer, NRAC-2005]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 8 / 19
![Page 32: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/32.jpg)
Introduction
Previous Restricted Prioritized BR in SNeBR
In context of SNePS-based agents acting on-line.
Assumes all beliefs are about the current state of the world.
Agent performs believe(p)but currently believes ~p.
If nor{p, ...} is believed as hyp, it is removed from CC.If xor{p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.If andor(0,1){p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.Else do assisted BR.
“State Constraints”
[Shapiro & Kandefer, NRAC-2005]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 8 / 19
![Page 33: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/33.jpg)
Introduction
Previous Restricted Prioritized BR in SNeBR
In context of SNePS-based agents acting on-line.
Assumes all beliefs are about the current state of the world.
Agent performs believe(p)but currently believes ~p.
If nor{p, ...} is believed as hyp, it is removed from CC.If xor{p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.If andor(0,1){p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.Else do assisted BR.
“State Constraints”
[Shapiro & Kandefer, NRAC-2005]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 8 / 19
![Page 34: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/34.jpg)
Introduction
Previous Restricted Prioritized BR in SNeBR
In context of SNePS-based agents acting on-line.
Assumes all beliefs are about the current state of the world.
Agent performs believe(p)but currently believes ~p.
If nor{p, ...} is believed as hyp, it is removed from CC.If xor{p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.If andor(0,1){p, q, ...} is believed,and q is believed as a hyp,q is removed from CC.Else do assisted BR.
“State Constraints”
[Shapiro & Kandefer, NRAC-2005]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 8 / 19
![Page 35: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/35.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 36: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/36.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 37: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/37.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 38: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/38.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 39: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/39.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 40: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/40.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 41: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/41.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 42: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/42.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 43: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/43.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 44: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/44.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 45: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/45.jpg)
Using Epistemic Ordering Functions
Problem Statement
Have
A set of nogoods, Σ = {σ1, ..., σn}.A set of prioritized beliefs, P, possibly empty.total preorder, ≤, over hyps.
∀h1, h2 ∈ hyps, h1 ≤ h2 ∨ h2 ≤ h1.transitive.∀h1, h2[h1 ∈ P ∧ h2 6∈ P → h1 > h2]
Assume only moderate burden on user to specify ≤.
Want
A set T of hyps to retract.Retract at least one hyp from each nogood.∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ∩ σ)]Don’t retract w if could have chosen τ and w > τ .∀τ [τ ∈ T → ∃σ[σ ∈ Σ ∧ τ ∈ σ ∧ ∀w [w ∈ σ → τ ≤ w ]]]Retract as few hyps as necessary.∀T ′[T ′ ⊂ T → ¬∀σ[σ ∈ Σ→ ∃τ [τ ∈ (T ′ ∩ σ)]]]
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 9 / 19
![Page 46: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/46.jpg)
Using Epistemic Ordering Functions
In Case of Ties
If need to decide whether h1 or h2 goes into Tand h1 ≤ h2 ∧ h2 ≤ h1,we have a tie that needs breaking.
3 Possibilities:
1 ≤ is a well preorder, and above doesn’t occur.
2 Use t≤, a subset of ≤ that is a well preorder.
3 Ask the user, but as little as possible.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 10 / 19
![Page 47: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/47.jpg)
Using Epistemic Ordering Functions
Algorithm 1 Using Well Preorder (Sketch)
Put minimally entrenched hyp first in every σOrder Σ in descending order of first hyps of σswhile (Σ 6= ∅) do
Add first hyp of first σ to TDelete from Σ every σ that contains that hyp
end while
Algorithm 1 is correct.
Space complexity: O(|Σ|) memory units.
Time complexity: O(|Σ|2 · |σ|max)
See paper for proofs.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 11 / 19
![Page 48: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/48.jpg)
Using Epistemic Ordering Functions
Algorithm 2 Using Total Preorder (Sketch)
loopfor all σi ∈ Σ s.t. σi has exactly one minimally entrenched hyp, p,AND the other hyps in σi are not minimally entrenched in any otherσ do
Add p to T , and delete from Σ every σ that contains pif Σ = ∅ then return T end if
end forfor some σ ∈ Σ that has multiple minimally entrenched hyps do
Query User which minimally entrenched hyp is least desiredModify ≤ accordingly
end forend loop
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 12 / 19
![Page 49: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/49.jpg)
Using Epistemic Ordering Functions
Algorithm 2 Analysis
Algorithm 2 is correct.
Space complexity: O(|Σ|2 · |σ|2max) memory units.
Time complexity: O(|Σ|2 · |σ|2max)
See paper for proofs.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 13 / 19
![Page 50: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/50.jpg)
Demonstrations
Epistemic Ordering by Source Credibility
Idea:Rank hypotheses by relative credibility of their sources.
Based on:
Johnson & Shapiro, “Says Who?,” UB TR 99-08Shapiro & Johnson, “Automatic BR in SNePS,” NMR-2000.
Uses object-language meta-knowledge [Shapiro, et al., AI Magazine, 2007]:
HasSource(p, s): Belief p’s source is s.IsBetterSource(s1, s2): Source s1 is more credible than source s2.
≤:
An unsourced belief is more entrenched than a sourced belief.Two sourced beliefs are ordered based on the order of their sources.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 14 / 19
![Page 51: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/51.jpg)
Demonstrations
Says Who KB
IsBetterSource(holybook, prof).
IsBetterSource(prof, nerd).
IsBetterSource(fran, nerd).
IsBetterSource(nerd, sexist).
HasSource(all(x)(old(x)=>smart(x)), holybook).
HasSource(all(x)(grad(x)=>smart(x)), prof).
HasSource(all(x)(jock(x)=>~smart(x)), nerd).
HasSource(all(x)(female(x)=>~smart(x)), sexist).
HasSource(and{old(fran),grad(fran),jock(fran),female(fran)},fran).
: smart(fran)?
wff24!: smart(fran)
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 15 / 19
![Page 52: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/52.jpg)
Demonstrations
Lifting Restriction of Prioritized BR in SNeBR
Revision of approach of SNePS Wumpus World Agent[Shapiro & Kandefer, NRAC-2005].
Instead of state constraints being more entrenched,fluents are less entrenched.
Uses meta-linguistic list of propositional fluent symbols.
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 16 / 19
![Page 53: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/53.jpg)
Demonstrations
Example of Using Fluents
: ^(setf *fluents* ’(Facing))
(snepslog::Facing)
: xor{Facing(north),Facing(south),Facing(east),Facing(west)}.
wff5!: xor{Facing(west),Facing(east),Facing(south),Facing(north)}
: perform believe(Facing(west))
: Facing(?d)?
wff9!: ~Facing(north)
wff8!: ~Facing(south)
wff7!: ~Facing(east)
wff4!: Facing(west)
: perform believe(Facing(east))
: Facing(?d)?
wff11!: ~Facing(west)
wff9!: ~Facing(north)
wff8!: ~Facing(south)
wff3!: Facing(east)
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 17 / 19
![Page 54: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/54.jpg)
Conclusions
Conclusions
In setting of
Finite belief base
Hypotheses identified
Derived beliefs have (possibly multiple) origin sets
Not all derivable beliefs have been derived
Concern with known inconsistency (explicit contradiction)
Showed how to do
Automatic prioritized or non-prioritized Belief Revisionwith a well preorder among hypotheses
Minimally assisted prioritized or non-prioritized Belief Revisionwith a total preorder among hypotheses
Generalized several previous ad hoc techniques
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 18 / 19
![Page 55: On the Use of Epistemic Ordering Functions as Decision ...shapiro/Talks/fogsha11a.pdf · OS = set of hyps actually used for the derivation. Computed by rules of inference. If p is](https://reader034.fdocuments.in/reader034/viewer/2022051923/6011090ea0a61d2a1b278b5a/html5/thumbnails/55.jpg)
Conclusions
For More Information
Paper in the proceedings
Ari’s MS thesis:http://www.cse.buffalo.edu/sneps/Bibliography/fogelThesis.pdf
A. I. Fogel & S. C. Shapiro (UB) NRAC 2011 19 / 19