Inconsistency Management for Traffic Regulations Harald Beck - - PowerPoint PPT Presentation

Inconsistency Management for Traffic Regulations

Harald Beck

Supervisors: Thomas Eiter & Thomas Krennwallner

November 18, 2013

Introduction Goals Formal Model Reasoning Tasks Summary

Inconsistency Management for Traffic Regulations

◮ Traffic regulation order: 30 km/h speed limit along the blue line

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 1 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Inconsistency Management for Traffic Regulations

◮ Traffic regulation order: 30 km/h speed limit along the blue line ◮ Traffic measure: legal information (intention)

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 1 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Inconsistency Management for Traffic Regulations

◮ Traffic regulation order: 30 km/h speed limit along the blue line ◮ Traffic measure: legal information (intention) ◮ Q: Which traffic signs are required to announce this measure?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 1 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Inconsistency Management for Traffic Regulations

◮ Traffic regulation order: 30 km/h speed limit along the blue line ◮ Traffic measure: legal information (intention) ◮ Q: Which traffic signs are required to announce this measure?

30

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 1 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Inconsistency Management for Traffic Regulations

◮ Traffic regulation order: 30 km/h speed limit along the blue line ◮ Traffic measure: legal information (intention) ◮ Q: Which traffic signs are required to announce this measure?

30 30

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 1 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Inconsistency Management for Traffic Regulations

◮ Traffic regulation order: 30 km/h speed limit along the blue line ◮ Traffic measure: legal information (intention) ◮ Q: Which traffic signs are required to announce this measure?

30 30

?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 1 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Inconsistency Management for Traffic Regulations

◮ Traffic regulation order: 30 km/h speed limit along the blue line ◮ Traffic measure: legal information (intention) ◮ Q: Which traffic signs are required to announce this measure?

30 30 30

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 1 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Inconsistency Management for Traffic Regulations

◮ Traffic regulation order: 30 km/h speed limit along the blue line ◮ No need for repeated start sign in this case

30 30

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 6 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Inconsistency Management for Traffic Regulations

◮ Traffic regulation order: 30 km/h speed limit along the blue line ◮ Updates may have side effects

30 30

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 6 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Data Management Goals (Use Cases)

◮ Consistency: Given a set of measures and/or signs on a street,

are they consistent (w.r.t. the traffic regulation)?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 8 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Data Management Goals (Use Cases)

◮ Consistency: Given a set of measures and/or signs on a street,

are they consistent (w.r.t. the traffic regulation)?

◮ Correspondence: Do measures and signs express the same

“effects,” i.e., are there no unannounced measures or unjustified traffic signs?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 8 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Data Management Goals (Use Cases)

◮ Consistency: Given a set of measures and/or signs on a street,

are they consistent (w.r.t. the traffic regulation)?

◮ Correspondence: Do measures and signs express the same

“effects,” i.e., are there no unannounced measures or unjustified traffic signs?

◮ Diagnosis: Which minimal set of measures/signs explain

inconsistency or non-correspondence?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 8 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Data Management Goals (Use Cases)

◮ Consistency: Given a set of measures and/or signs on a street,

are they consistent (w.r.t. the traffic regulation)?

◮ Correspondence: Do measures and signs express the same

“effects,” i.e., are there no unannounced measures or unjustified traffic signs?

◮ Diagnosis: Which minimal set of measures/signs explain

inconsistency or non-correspondence?

◮ Repair: Which minimal changes to the scenario can resolve these

problems?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 8 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Data Management Goals (Use Cases)

◮ Consistency: Given a set of measures and/or signs on a street,

are they consistent (w.r.t. the traffic regulation)?

◮ Correspondence: Do measures and signs express the same

“effects,” i.e., are there no unannounced measures or unjustified traffic signs?

◮ Diagnosis: Which minimal set of measures/signs explain

inconsistency or non-correspondence?

◮ Repair: Which minimal changes to the scenario can resolve these

problems?

◮ Strict repair: Repair measure & sign data at the same time

◮ Practical use cases obtained as special cases

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 8 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

High-level approach (overview)

◮ Street maps: labelled, directed graphs

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 9 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

High-level approach (overview)

◮ Street maps: labelled, directed graphs ◮ Logic-based approach. Edges and labels reflected as atoms

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 9 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

High-level approach (overview)

◮ Street maps: labelled, directed graphs ◮ Logic-based approach. Edges and labels reflected as atoms ◮ Represent measures and signs by edge/node labels

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 9 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

High-level approach (overview)

◮ Street maps: labelled, directed graphs ◮ Logic-based approach. Edges and labels reflected as atoms ◮ Represent measures and signs by edge/node labels ◮ Traffic regulation: 2-stage evaluation approach by logical formulas

◮ Translate into “effect” labels (i.e., a common language) by an effect

mapping

◮ Evaluate effects by a conflict specification, potentially creating

“conflict” labels

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 9 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

High-level approach (overview)

◮ Street maps: labelled, directed graphs ◮ Logic-based approach. Edges and labels reflected as atoms ◮ Represent measures and signs by edge/node labels ◮ Traffic regulation: 2-stage evaluation approach by logical formulas

◮ Translate into “effect” labels (i.e., a common language) by an effect

mapping

◮ Evaluate effects by a conflict specification, potentially creating

“conflict” labels

◮ Inconsistency, if a conflict can be derived

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 9 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

High-level approach (overview)

◮ Street maps: labelled, directed graphs ◮ Logic-based approach. Edges and labels reflected as atoms ◮ Represent measures and signs by edge/node labels ◮ Traffic regulation: 2-stage evaluation approach by logical formulas

◮ Translate into “effect” labels (i.e., a common language) by an effect

mapping

◮ Evaluate effects by a conflict specification, potentially creating

“conflict” labels

◮ Inconsistency, if a conflict can be derived ◮ Leave open which predicate logic is used

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 9 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Scenario

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3

◮ Labelled street graph G. Sets of edge atoms

{. . . , e(lane, v2, v3), e(straight, v3, y1), e(right, x2, y1), . . . }

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 10 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Scenario

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3

◮ Labelled street graph G. Sets of edge atoms

{. . . , e(lane, v2, v3), e(straight, v3, y1), e(right, x2, y1), . . . }

◮ Traffic measures M (edge labels

), e.g.: (spl=speed limit) {m(spl(30), v2, v3), m(spl(30), v3, y1), m(spl(30), y1, y2)}

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 10 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Scenario

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 30 30

◮ Labelled street graph G. Sets of edge atoms

{. . . , e(lane, v2, v3), e(straight, v3, y1), e(right, x2, y1), . . . }

◮ Traffic measures M (edge labels

), e.g.: (spl=speed limit) {m(spl(30), v2, v3), m(spl(30), v3, y1), m(spl(30), y1, y2)}

◮ Traffic signs S (node labels), e.g.:

{s(start(spl(30)), v2), s(start(spl(30)), y1), s(end(spl(30)), y2)}

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 10 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Effects

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◮ Effects (edge labels

): common language to define meaning of both measures and signs, e.g.: (maxsp = maximum speed) {f(maxsp(30), v2, v3), f(maxsp(30), v3, y1)}

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 11 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Effects

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30

◮ Effects (edge labels

): common language to define meaning of both measures and signs, e.g.: (maxsp = maximum speed) {f(maxsp(30), v2, v3), f(maxsp(30), v3, y1)}

◮ Effect mapping P: formulas to obtain effect labels in 1st mapping

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 11 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Effects

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30

◮ Effects (edge labels

): common language to define meaning of both measures and signs, e.g.: (maxsp = maximum speed) {f(maxsp(30), v2, v3), f(maxsp(30), v3, y1)}

◮ Effect mapping P: formulas to obtain effect labels in 1st mapping ◮ FP G(I): effects of (measure and sign) input I on graph G due to P

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 11 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Conflicts

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◮ Conflicts (node labels)

c(bad-end(maxsp(30)), y1)

◮ Conflict specification Sp: formulas to obtain conflict labels in 2nd

mapping due to effects

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 12 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Conflicts

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Conflicts (node labels)

c(ambig-spl, y1)

◮ Conflict specification Sp: formulas to obtain conflict labels in 2nd

mapping due to effects

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 12 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Conflicts

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Conflicts (node labels)

c(ambig-spl, y1)

◮ Conflict specification Sp: formulas to obtain conflict labels in 2nd

mapping due to effects

◮ CP,Sp G

(I): conflicts of input I on graph G due to Sp and (effects

• btained by) P
• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 12 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

ASP mapping examples

◮ Effect mapping P

f(maxsp(K), V, W) ← m(spl(K), V, W)

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 13 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

ASP mapping examples

◮ Effect mapping P

f(maxsp(K), V, W) ← m(spl(K), V, W) f(maxsp(K), V, W) ← s(start(spl(K)), V), e(lane, V, W) f(maxsp(K), V, W) ← s(start(spl(K)), V), e(straight, V, W)

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 13 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

ASP mapping examples

◮ Effect mapping P

f(maxsp(K), V, W) ← m(spl(K), V, W) f(maxsp(K), V, W) ← s(start(spl(K)), V), e(lane, V, W) f(maxsp(K), V, W) ← s(start(spl(K)), V), e(straight, V, W) f(maxsp(K), V, W) ← f(maxsp(K), U, V), in-dir(U, V), in-dir(V, W), not block-prop(maxsp(K), V)

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 13 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

ASP mapping examples

◮ Effect mapping P

f(maxsp(K), V, W) ← m(spl(K), V, W) f(maxsp(K), V, W) ← s(start(spl(K)), V), e(lane, V, W) f(maxsp(K), V, W) ← s(start(spl(K)), V), e(straight, V, W) f(maxsp(K), V, W) ← f(maxsp(K), U, V), in-dir(U, V), in-dir(V, W), not block-prop(maxsp(K), V) block-prop(maxsp(K), V) ← s(end(spl(K)), V) . . .

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 13 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

ASP mapping examples

◮ Effect mapping P

f(maxsp(K), V, W) ← m(spl(K), V, W) f(maxsp(K), V, W) ← s(start(spl(K)), V), e(lane, V, W) f(maxsp(K), V, W) ← s(start(spl(K)), V), e(straight, V, W) f(maxsp(K), V, W) ← f(maxsp(K), U, V), in-dir(U, V), in-dir(V, W), not block-prop(maxsp(K), V) block-prop(maxsp(K), V) ← s(end(spl(K)), V) . . .

◮ Conflict specification Sp

c(ambig-spl, V) ← f(maxsp(K), V, W), f(maxsp(L), V, W), K = L.

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 13 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Consistency

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Given a set of measures and/or signs on a street, are they

consistent (w.r.t. the traffic regulation)?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 14 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Consistency

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Given a set of measures and/or signs on a street, are they

consistent (w.r.t. the traffic regulation)?

◮ CP,Sp G

(I) = ∅?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 14 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Consistency

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Given a set of measures and/or signs on a street, are they

consistent (w.r.t. the traffic regulation)?

◮ CP,Sp G

(I) = ∅?

◮ Example. CP,Sp G

(I) = {c(ambig-spl, y1)}

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 14 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Correspondence

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Do measures and signs express the same effects, i.e., are there

no unannounced measures or unjustified traffic signs?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 15 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Correspondence

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Do measures and signs express the same effects, i.e., are there

no unannounced measures or unjustified traffic signs?

◮ FP G(M) = FP G(S)?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 15 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Correspondence

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Do measures and signs express the same effects, i.e., are there

no unannounced measures or unjustified traffic signs?

◮ FP G(M) = FP G(S)? ◮ Example.

◮ f(maxsp(30), y1, y2) ∈ FP

G(M) unannounced: not in FP G(S)

◮ f(maxsp(40), y1, y2) ∈ FP

G(S) unjustified: not in FP G(M)

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 15 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Diagnosis

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Which minimal set of measures/signs explain a set of conflicts?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 16 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Diagnosis

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Which minimal set of measures/signs explain a set of conflicts? ◮ Given C ⊆ CP,Sp G

(I), find min. J ⊆ I s.t. C ⊆ CP,Sp

G

(J)

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 16 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Diagnosis

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◮ Which minimal set of measures/signs explain a set of conflicts? ◮ Given C ⊆ CP,Sp G

(I), find min. J ⊆ I s.t. C ⊆ CP,Sp

G

(J)

◮ Example. C = {c(ambig-spl, y1)}.

J = {m(spl(30), y1, y2), s(start(spl(40)), y1)}

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 16 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Repair & Strict repair

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◮ Which minimal changes to the scenario can resolve the conflicts?

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 17 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Repair & Strict repair

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Which minimal changes to the scenario can resolve the conflicts? ◮ Find “good” deletions I− ⊆ I and additions I+ ⊆ IG \ I

s.t. CP,Sp

G

(I′) = ∅, where I′ = (I \ I−) ∪ I+

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 17 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Repair & Strict repair

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Which minimal changes to the scenario can resolve the conflicts? ◮ Find “good” deletions I− ⊆ I and additions I+ ⊆ IG \ I

s.t. CP,Sp

G

(I′) = ∅, where I′ = (I \ I−) ∪ I+

◮ Strict repair: ... and FP G(I′ ∩ MG) = FP G(I′ ∩ SG)

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 17 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Strict repair example

◮ Conflicts C = {c(ambig-spl, y1)}

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 18 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Strict repair example

◮ Conflicts C = {c(ambig-spl, y1)} ◮ Repair 1. Preference: Minimal number of changes.

I− = {m(spl(30), y1, y2)}, I+ = {m(spl(40), y1, y2)} v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 18 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Strict repair example

◮ Conflicts C = {c(ambig-spl, y1)} ◮ Repair 2. Prefer sign changes over measures changes.

I− = {s(start(spl(40)), y1), s(end(spl(40)), y2)} I+ = {s(start(spl(30)), y1)), s(end(spl(30)), y2).} v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 30 30

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 18 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Summary /1

◮ Domain analysis

◮ No scientific literature was available ◮ Meaning of traffic measures & signs ◮ Problems which may occur (conflicts) ◮ Identification of use cases ◮ Challenges & technical approach

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 19 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Summary /1

◮ Domain analysis

◮ No scientific literature was available ◮ Meaning of traffic measures & signs ◮ Problems which may occur (conflicts) ◮ Identification of use cases ◮ Challenges & technical approach

◮ Formal model for traffic regulations

◮ Street graph, traffic measures & signs ◮ Effects & conflicts ◮ Logic-based traffic regulation / specification

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 19 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Summary /2

◮ Reasoning tasks

◮ Consistency evaluation ◮ Correspondence ◮ Diagnosis ◮ Independence / context of conflicts ◮ Repair ◮ Relations between diagnoses and repairs ◮ Strict repair ◮ Adjustment, Generation

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 20 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Summary /2

◮ Reasoning tasks

◮ Consistency evaluation ◮ Correspondence ◮ Diagnosis ◮ Independence / context of conflicts ◮ Repair ◮ Relations between diagnoses and repairs ◮ Strict repair ◮ Adjustment, Generation

◮ Complexity results for different logics (FOL + 3 ASPs)

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 20 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Summary /2

◮ Reasoning tasks

◮ Consistency evaluation ◮ Correspondence ◮ Diagnosis ◮ Independence / context of conflicts ◮ Repair ◮ Relations between diagnoses and repairs ◮ Strict repair ◮ Adjustment, Generation

◮ Complexity results for different logics (FOL + 3 ASPs) ◮ Implementation prototype with Answer Set Programming

◮ uniform encoding and specification for all use cases ◮ core program + simple extensions ◮ highly modular due to formal model & sets of rules

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 20 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

C’est c ¸a

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 21 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

C’est c ¸a

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 21 / 22

Introduction Goals Formal Model Reasoning Tasks Summary

Thank you!

Thomas Eiter Thomas Krennwallner Stefan Kollarits Torsten Sch¨

• nberg

Marlene Handschuh Christoph Hillinger Roman Steiner

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 22 / 22

Appendix

Traffic Regulation Problem

◮ Scenario Sc = (G, M, S)

◮ Street graph G ◮ Traffic measures M ◮ Traffic signs S ◮ ground atoms of form e(t, v, w), m(t, v, w), s(t, v)

◮ Traffic regulation Π = (P, Sp) in a predicate logic L

◮ Effect mapping P: M, S effects FP

G(M ∪ S)

◮ Conflict specification Sp: FP

G(M ∪ S) conflicts CP,Sp G

(M ∪ S)

◮ Traffic Regulation Problem T = (Sc, Π)

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 23 / 22

Appendix

2-stage Mapping

◮ Closed world operator:

X = X ∪ {¬x | x ∈ Y \ X}, Y implicit

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 24 / 22

Appendix

2-stage Mapping

◮ Closed world operator:

X = X ∪ {¬x | x ∈ Y \ X}, Y implicit

◮ Theory T, atom sets X (input), Y (base set), graph G

CnG(T, X, Y) = { y ∈ Y | T ∪ G ∪ X | = y }

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 24 / 22

Appendix

2-stage Mapping

◮ Closed world operator:

X = X ∪ {¬x | x ∈ Y \ X}, Y implicit

◮ Theory T, atom sets X (input), Y (base set), graph G

CnG(T, X, Y) = { y ∈ Y | T ∪ G ∪ X | = y }

◮ Base sets MG/SG/FG/CG: measures/signs/effects/conflicts on G

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 24 / 22

Appendix

2-stage Mapping

◮ Closed world operator:

X = X ∪ {¬x | x ∈ Y \ X}, Y implicit

◮ Theory T, atom sets X (input), Y (base set), graph G

CnG(T, X, Y) = { y ∈ Y | T ∪ G ∪ X | = y }

◮ Base sets MG/SG/FG/CG: measures/signs/effects/conflicts on G ◮ 2 stages: Effect mapping P, Conflict specification Sp

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 24 / 22

Appendix

2-stage Mapping

◮ Closed world operator:

X = X ∪ {¬x | x ∈ Y \ X}, Y implicit

◮ Theory P, atom sets I (input), FG (base set: effects), graph G

CnG(P, I, FG) = { f(t, v, w) ∈ FG | P ∪ G ∪ I | = f(t, v, w) }

◮ Base sets MG/SG/FG/CG: measures/signs/effects/conflicts on G ◮ 2 stages: Effect mapping P, Conflict specification Sp

I MG ∪ SG

• perator

labels base set CnG(P, I, FG) FP

G(I)

FG CnG(Sp, FP

G(I), CG)

CP,Sp

G

(I) CG

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 24 / 22

Appendix

2-stage Mapping

◮ Closed world operator:

X = X ∪ {¬x | x ∈ Y \ X}, Y implicit

◮ Theory Sp, atom sets FP G(I) (input), CG (base set: conflicts), graph G

CnG(Sp, FP

G(I), CG) = { c(t, v) ∈ CG | Sp ∪

G ∪ FP

G(I) |

= c(t, v) }

◮ Base sets MG/SG/FG/CG: measures/signs/effects/conflicts on G ◮ 2 stages: Effect mapping P, Conflict specification Sp

I MG ∪ SG

• perator

labels base set CnG(P, I, FG) FP

G(I)

FG CnG(Sp, FP

G(I), CG)

CP,Sp

G

(I) CG

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 24 / 22

Appendix

Answer Set Programming prototype

◮ Experiments with clingo and dlv ◮ Uniform approach towards all reasoning tasks. Idea:

◮ Repair will potential require new atoms ◮ Input atoms form initial pool ◮ Each measure/sign from the pool can either be used or not ◮ Only the effects of used measures & signs are computed ◮ View reasoning tasks as constraints on this usage

◮ Measure & signs: function symbols x ∈ { m, s }:

input(x(. . . )). measure/sign is given as input pool(x(. . . )). measure/sign is in pool (for guessing) use(x(. . . )). measure/sign is used

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 25 / 22

Appendix

ASP Implementation Prototype

◮ guess: Π ∪ G ∪ I ∪ Pool

◮ Π: traffic regulation / specification ◮ G: street graph ◮ I: input (measures & signs); initial pool ◮ Pool: use(X) v -use(X) :- pool(X).

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 26 / 22

Appendix

ASP Implementation Prototype

◮ guess: Π ∪ G ∪ I ∪ Pool

◮ Π: traffic regulation / specification ◮ G: street graph ◮ I: input (measures & signs); initial pool ◮ Pool: use(X) v -use(X) :- pool(X).

◮ check: additional constraints based on reasoning task

◮ Eval: use(X) :- input(X) ◮ Diagnosis: :- not c(t,v) for resp. conflicts c(t,v) ◮ Repair: :- c(t,v) for resp. conflicts c(t,v)

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 26 / 22

Appendix

Implementation of conflict evaluation (consistency)

◮ Compute CP,Sp G

(I), i.e., the set of conflicts derivable from the input I ⊆ MG ∪ SG whether T is consistent

◮ Approach: Use entire input. Add rule to effect mapping:

use(x(. . . )) :- input(x(. . . )).

◮ T is consistent iff answer set does not contain a conflict atom.

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 27 / 22

Appendix

Implementation of conflict evaluation (consistency)

◮ Compute CP,Sp G

(I), i.e., the set of conflicts derivable from the input I ⊆ MG ∪ SG whether T is consistent

◮ Approach: Use entire input. Add rule to effect mapping:

use(x(. . . )) :- input(x(. . . )).

◮ T is consistent iff answer set does not contain a conflict atom. ◮ Example.

input(m(spl(30),v2,v3)). input(m(spl(30),v3,y1)). input(m(spl(30),y1,y2)). in effect mapping: f(maxsp(K),V,W) :- e(T,V,W), #int(K), use(m(spl(K),V,W)).

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 27 / 22

Appendix

Flexible modifications to the input

Let x ∈ {m, s}.

◮ Input is initial pool, which may be used or not.

pool(x(. . . )) :- input(x(. . . )). use(x(. . . )) v -use(x(. . . )) :- pool(x(. . . )).

◮ General modifications possible:

keep(x(. . . )) :- use(x(. . . )), input(x(. . . )). del(x(. . . )) :- -use(x(. . . )), input(x(. . . )). add(x(. . . )) :- use(x(. . . )), not input(x(. . . )).

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 28 / 22

Appendix

Diagnosis implementation

◮ Approach: Given a set of conflicts C to be diagnosed, add to

conflict specification for each c(t,v) ∈ C a rule :- not c(t,v).

◮ Diagnosis: Keep as few input atoms J ⊆ I as possible such that

C ⊆ CP,Sp

G

(J), and do not allow additions. :- add(x(. . . )).

% adding not allowed

:∼ keep(x(. . . )).

% keep as few as possible

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 29 / 22

Appendix

Diagnosis example

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Evaluation: {c(ambig-spl,y1).} ◮ Add to conflict specification

:- not c(ambig-spl,y1) :- add(m(T,X,V)). :- add(s(T,V)). :∼ keep(m(T,X,V)). :∼ keep(s(T,V)).

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 30 / 22

Appendix

Diagnosis example /2

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 40

◮ Result:

{ keep(m(spl(30),y1,y2)). keep(s(start(spl(30)),y1)). }

◮ Add to conflict specification

:- not c(ambig-spl,y1) :- add(m(T,X,V)). :- add(s(T,V)). :∼ keep(m(T,X,V)). :∼ keep(s(T,V)).

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 31 / 22

Appendix

Repair implementation

◮ Must add new measures/signs to the pool based on domain

knowledge, e.g.,

◮ If there is a measure m(T,X,Y) in the pool, add a start sign at X

and an end sign at Y to the pool. pool(s(start(T),X)) :- pool(m(T,X,Y)). pool(s(end(T),Y)) :- pool(m(T,X,Y)).

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 32 / 22

Appendix

Repair implementation

◮ Must add new measures/signs to the pool based on domain

knowledge, e.g.,

◮ If there is a measure m(T,X,Y) in the pool, add a start sign at X

and an end sign at Y to the pool. pool(s(start(T),X)) :- pool(m(T,X,Y)). pool(s(end(T),Y)) :- pool(m(T,X,Y)).

◮ Approach: Add/delete as little as possible such that no conflict is

derived :- c(T,V).

% forbid any conflict

:∼ del(s(T,X)). :∼ add(s(T,X)). :∼ del(m(T,X,Y)). :∼ add(m(T,X,Y)).

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 32 / 22

Appendix

Repair implementation

◮ Must add new measures/signs to the pool based on domain

knowledge, e.g.,

◮ If there is a measure m(T,X,Y) in the pool, add a start sign at X

and an end sign at Y to the pool. pool(s(start(T),X)) :- pool(m(T,X,Y)). pool(s(end(T),Y)) :- pool(m(T,X,Y)).

◮ Approach: Add/delete as little as possible such that no conflict is

derived :- c(T,V).

% forbid any conflict

:∼ del(s(T,X)). [1:1] % prefer changes of signs [:1] :∼ add(s(T,X)). [2:1] % over measures [:2], :∼ del(m(T,X,Y)). [1:2] % then deletions [1:] :∼ add(m(T,X,Y)). [2:2] % over additions [2:].

◮ dlv optimizes hierarchically: :∼ <body>. [Weight:Level]

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 32 / 22

Appendix

Strict repair example

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 40 40

◮ Add to conflict specification (rules shown before and)

:- c(ambig-spl,y1)

◮ Result (without preferences)

{ del(m(spl(30),y1,y2)). add(m(spl(40),y1,y2)). }

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 33 / 22

Appendix

Strict repair example /2

v1 v2 v3 w2 w1 x1 x2 y1 y2 y3 u1 u2 u3 z1 z2 z3 30 30 30

◮ Add to conflict specification (rules shown before and)

:- c(ambig-spl,y1)

◮ Result with preference to change signs

{ del(s(start(spl(40)),y1)). del(s(end(spl(40)),y2)). add(s(start(spl(30)),y1)). add(s(end(spl(30)),y2)). }

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 34 / 22

Appendix

Adjustment & Generation

◮ Restricted scenarios / restricting repairs lead to special cases,

relevant for data imports and merging.

◮ Adjustment of signs, s.t. they correspond with measures.

Amounts to finding a repair consisting exclusively of traffic signs. (Recall 30 km/h example.)

◮ Generation of signs from scratch, s.t. they correspond with

• measures. Corresponds to a repair (∅, I+) on scenario (G, M, ∅),

where I+ consists exclusively of signs.

Example (encoding of special domain knowledge)

◮ Favor changes in signs over changes in measures ◮ Favor deletions of linear measures over zones ◮ Never delete a residential area ◮ . . .

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 35 / 22

Appendix

Reasoning Tasks: Theory

◮ Def. Set of conflicts C is independent of Y ⊆ I if for each

diagnosis J for C and each Y′ ⊆ Y, J \ Y′ is also a diagnosis for C.

◮ Def. A context for C is a set X ⊆ I s.t. i) C is independent of I \ X

and ii) C is not independent of any non-empty X′ ⊆ X

◮ Prop. Context of each C is unique ◮ Prop. All ⊆-minimal diagnoses are in the context ◮ Thm. The context is the union of minimal elements of maximal

convex subsets of the set of diagnoses

◮ Def. Collection of sets S convex if it has no ‘holes’, i.e., the property

that S ⊆ S′′ ⊆ S′ and S, S′ ∈ S implies S′′ ∈ S

◮ Cor. If set of diagnoses is convex, then context equals union of

⊆-minimal diagnoses

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 36 / 22

Appendix

Reasoning Tasks: Theory /2

◮ Def. DT (C): set of diagnoses for conflicts C ◮ Def. H ⊆ n i=1 Xi hitting set for S = {X1, . . . , Xn}

if H ∩ X = ∅ for all X ∈ S

◮ Def. T [I−, I+] updated T due to (I−, I+) ◮ Prop. If J ⊆ I is a hitting set for DT (C), then C ⊆ C(T [J, ∅]) ◮ Due to potential side effects C ∩ C(T [J, ∅]) = ∅ is not guaranteed ◮ Consequence: In general, it does not suffice to delete a minimal

hitting set for all (⊆-minimal) diagnoses

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 37 / 22

Appendix

Reasoning Tasks: Decision problems

Let I ⊆ MG ∪ SG be a set of measures and/or signs on a graph G

◮ CONS: decide CP,Sp G

(I) = ∅, i.e., whether T is consistent

◮ UMINDIAG: decide, whether a unique ⊆-minimal diagnosis exists,

i.e., for given C ⊆ CP,Sp

G

(I) a set J ⊆ I, s.t. C ⊆ CP,Sp

G

(J)

◮ CORR: decide M and S correspond, i.e., FP G(M) = FP G(S) ◮ REPAIR: decide whether an admissible repair exists, i.e., deleting

some I− ⊆ I and adding new measures and signs I+ s.t. modification is consistent

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 38 / 22

Appendix

Complexity of Reasoning Tasks

Logic L IMPL CONS CORR UMINDIAG REPAIR general FO+DCA co-NExp PNExp

• PNExp

ASP¬s Exp Exp Exp ASP¬ co-NExp PNExp

• PNExp

ASP∨,¬ co-NExpNP PNExpNP

• PNExpNP

BPA FO+DCA PSpace PSpace PSpace ASP¬s PNP PNP in P

Σp

2

, Πp 2-hard

Σp

2

ASP¬ Πp

2

P

Σp

2

• in P

Σp

3

, Πp 3-hard

Σp

3

ASP∨,¬ Πp

3

P

Σp

3

• in P

Σp

4

, Πp 4-hard

Σp

4

Legend: general case / bounded predicate arities (completeness results unless stated otherwise) ◮ FO+DCA: first-order logic with domain closure assumption ◮ ASP¬s, ASP¬, ASP∨,¬: stratified, normal, disjunctive answer set programs ◮ IMPL: Known logical entailment complexities ◮ PO

: restricted PO s.t. all queries for O are evaluable in parallel

• H. Beck (TU Vienna)

Inconsistency Mgmt. for Traffic Regulations 39 / 22

Appendix

Example: Loop

Scenario: Four mandatory left turns cause a loop

a1 a2 a3 a4 a5 a6 a7 a8 b1 b2 b3 b4 b5 b6 b7 b8 c1 c2 c3 c4 c5 c6 c7 c8 d1 d2 d3 d4 d5 d6 d7 d8

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Inconsistency Mgmt. for Traffic Regulations 40 / 22