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Introduction Norms Heuristics for Normative Conflict Resolution

An Argumentation Inspired Heuristic for Resolving Normative Conflict

Nir Oren, Michael Luck, Simon Miles, Timothy J. Norman nir.oren, michael.luck, simon.miles@kcl.ac.uk, t.j.norman@abdn.ac.uk

King’s College London, University of Aberdeen

12 May 2008

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution

Introduction

Alice promised Bob that she would go to the theatre with him. Alice promised her sick mother that she would visit her in hospital. Alice must cook dinner for her friends. Alice must write a paper for her boss. Alice can’t go to the hospital and theatre simultaneously, and cooking dinner does not leave enough time to write the paper. What should Alice do?

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution

Introduction

Alice’s promises, as well as what she should, must, or is allowed to do, can be represented as a set of norms imposed on her. In computational settings, particularly within the agent paradigm, norms are useful for many reasons, including:

Norms are declarative. Decisions on whether to comply with norms are decentralised. By reasoning about other’s norms, one may make assumptions about their behaviour. These assumptions may lead to computational savings.

Weaknesses of the normative approach includes the problem of resolving normative conflict.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution

Overview

We examine how an agent may reason about, and resolve normative conflict. The result of such reasoning is a set of norms that the agent will attempt to honour, it will drop, or ignore, norms

• utside this set.

We propose some heuristics, based on argumentation theory, allowing an agent to decide which norms it should comply with. Our focus is on the heuristic, rather than having a complex model of norms.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

A Model of Norms

Obob(theatre) A norm has a type (obligation, permission, prohibition). A norm is imposed on the agent by some social entity. We refer to this as the norm’s social context. Agents handle norms with different social contexts in very different ways. A norm has a normative goal. We consider norms already adopted by the agent, and thus do not specify a “norm target”.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

A Model of Norms

We ignore

Conditional norms. Discharge of norms. Temporal effects. Distinctions between actions and states.

We assume

Norms are all or nothing, if an agent decides to ignore a norm once, they will always ignore the norm.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

Agents and the Environment

Agents have a set of norms, and are aware of the social contexts associated with the norms. They have preferences (i.e. a partial ordering) over the social contexts. Agents operate within an environment containing the various social contexts, and a set of “states of affairs”, representing the agent’s effects on the environment. Certain states of affairs may be mutually exclusive, capturing the notion that certain norms may not be complied with simultaneously.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

Formalisation

Norm = Nc(g) where N ∈ {O, P, F} Environment = S, C Normative Agent = (Norms, ≤) mutuallyExclusive : S × S

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

Normative Conflict Graph

By using its norms and the mutuallyExclusive relation, an agent may generate a normative conflict graph (NCG). A NCG captures those norms that the agent is unable to simultaneously satisfy. The edges of the NCG are directed based on the types of norms. The problem the agent faces may now be seen as selecting a subset of nodes (norms) from the NCG that have no edges between them.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

Example

(a) Obob(theatre) (b) OsickMother(hospital) (c) Ofriends(cooking) (d) Oboss(paper) (e) Psuperior(delayPaper) (theatre, hospital) (hospital, theatre) (cooking, paper) (paper, delay) (cooking, theatre) (paper, cooking) (hospital, paper) (theatre, cooking) (delay, paper) (paper, hospital)

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

Example

a c d b e

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

Pruning

Agents may prune edges from the NCG based on social context preferences (more important social contexts take precedence over less important social contexts). Some agents, referred to as extended normative agents, may have a strict partial ordering over norm types. EA = (Norms, ≤, ≺) These agents prefer to honour one type of norm over another.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

Example

(a) Obob(theatre) (b) OsickMother(hospital) (c) Ofriends(cooking) (d) Oboss(paper) (e) Psuperior(delayPaper) friends < bob bob < boss sickMother < boss friends < boss (theatre, hospital) (hospital, theatre) (cooking, paper) (paper, delay) (cooking, theatre) (paper, cooking) (hospital, paper) (theatre, cooking) (delay, paper) (paper, hospital) O ≺ P

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

Example

a c d b e

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

Example

a c d b e

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution The Model Normative Conflict Graph Example

Example

a c d b e

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

The Heuristics

Our approach:

1

Construct NCG

2

Prune the NCG

3

If edges remain in the graph, use a heuristic to select norms to honour

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

The Random Drop Heuristic

Given a normative conflict graph, select an edge (i.e. a normative conflict) at random. If this edge is labelled (n, m), node m (and all edges containing it) are removed from the graph. This process is repeated until no edges remain in the graph.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

a c b

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

c b

(b, a)

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

c

(b, a), (c, b)

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

a c b

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

a c

(c, b)

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Argumentation

Similarities exist between NCGs and abstract argumentation frameworks. An abstract argumentation framework is a graph of arguments, and attacks between arguments. Argumentation researchers look for sets of “consistent” arguments. One requirement for such a consistent set is that it be conflict free. A set of arguments S is conflict free iff ∄A, B ∈ S such that attacks(A, B).

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Maximal Conflict-free Set Heuristic

Select the norms found in the maximal (with respect to number

• f norms) conflict free set, as computed from the normative

conflict graph. If multiple such sets exist, select one at random.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Maximal Conflict-free Set Heuristic

a c d b e

{a}, {b}, {c}, {d}, {e}, {a, d}, {a, e}, {b, e}, {c, b}, {c, e}, {b, c, e}

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

a c d b

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

a c d b

{a, c}, {b, d}

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

a c d b

{a,c}, {b, d}

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Argumentation

Conflict free is a necessary, but not sufficient condition for a set of arguments to be acceptable. An argument A ∈ AR is acceptable with respect to a set of arguments S iff for every argument B ∈ AR, such that attacks(B, A), there is a C ∈ S such that attacks(C, B). Then we may define a conflict free set of arguments S as admissible iff each argument in S is acceptable with respect to S.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Preferred Extension Heuristic

A preferred extension of an argument system AR is a maximal (with respect to set inclusion) admissible set of AR.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Preferred Extension Heuristic

A preferred extension of an argument system AR is a maximal (with respect to set inclusion) admissible set of AR. Given a normative conflict graph, choose those norms present in the maximal (with respect to set size) preferred extension, and drop all other norms.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Preferred Extension Heuristic

Multiple preferred extensions may exist. All contain “most important” norms. If conflicts between highest priority norms exist, they will appear in different extensions. A rational agent may select any preferred extension (at random).

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

a c d b e

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

a c d b e

{a}, {e}, {a, e}, {b, e}, {b, c, e}

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

a c d b e

{b, c, e}

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Example

a c d b e

{b, c, e} Paper writing (d) is always ignored as Alice prefers permissions over obligations.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Evaluation

We evaluated how many norms each heuristic was able to keep in the conflict free NCG. During each run, a random NCG was generated. 16 norms. 0-241 conflicts. For each distinct number of conflicts, results were averaged over 10 simulations.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Results

2 4 6 8 10 12 14 16 50 100 150 200 250 Preferred Extension Conflict Free Random Drop

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Results

As expected, fewer norms are retained as conflicts increase. The conflict free heuristic, by definition contains the maximal number of norms that may be retained. Preferred extension outperforms random drop. Convergence occurs when the system is highly, or minimally constrained.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Odd length loops

a c b

Odd length loops cause problems for the preferred extension heuristic.

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Future Work

Dealing with odd length loops. Heuristics based on different argumentation semantics (e.g. sceptical semantics are useful when reasoning about another’s norms). Accrual of social contexts (are two promises to friends more important than a promise to the boss?) Introduction of utility Support between norms (representing groups of norms that may have to be honoured or dropped together). A more realistic normative model

Nir Oren et al. Heuristics for Normative Conflict

Introduction Norms Heuristics for Normative Conflict Resolution Random Drop Maximal Conflict-free Set Heuristic Preferred Extension Based Heuristic Evaluation

Conclusions

An agent may have to decide which norms to honour, and which to ignore when the effects of some of its norms are mutually exclusive. This results in a graph structure of interactions between norms. We introduced three heuristics to make use of this graph structure, allowing an agent to decide which norms to retain. The heuristics based on results from argumentation theory

• utperformed the simplest random drop heuristic.

Nir Oren et al. Heuristics for Normative Conflict