normative multi-agent systems (part i) · w. vasconcelos (univ. of aberdeen, uk) normative mass...

Normative Multi-Agent Systems(Part I)

Wamberto Vasconcelos

Computing Science, University of Aberdeen, [email protected]

Bucharest, Romania – 08 Sep 2014

W. Vasconcelos (Univ. of Aberdeen, UK) Normative MASs ALTiSSimo 2014 1 / 40

Outline

Outline

1 What is this tutorial about?Initial Considerations

Who is this tutorial for/by?

Some initial definitions...MotivationTimeline and Concepts

2 BackgroundPhilosophy of LawDeontic Logics

3 References


What is this tutorial about?

What is this tutorial about?


What is this tutorial about? Initial Considerations

Normative Multi-Agent Systems (NorMAS)

• What are NorMAS?

• What is a “norm”?

• Why NorMAS?

• Timeline of normative research



Who is this tutorial for?

• You!• Erm, but who are you?

I UG/MSc/PhD studentI Post-doctoral researcherI Software developerI AcademicI Other

• What’s your background?I ComputingI MathematicsI LogicsI PhilosophyI Other

• Why are you interested in NorMAS?I It relates to your own researchI You wanted to know what NorMAS were aboutI Other reason(s)



Who is this tutorial by?

• Yours truly...• Erm, but who am I?

I UG/MSc/PhD student (PhD, Univ. of Edinburgh, UK)I Post-doctoral researcher (Univ. of Zurich, Univ. of Edinburgh)I Software developerI Academic (Computing Science Lecturer, University of Aberdeen, UK)I Other?

• What’s my background?I Computing (logic programming, software eng., distributed systems)I MathematicsI Logics (theorem proving, modal logics)I PhilosophyI Other

• Why am I interested in NorMAS?I MAS as means to engineer complex distributed systemsI Norms as a metaphor for software engineeringI It’s exciting, novel (and old!), appealing, promising, etc.


What is this tutorial about? Some initial definitions...

What are NorMAS?

They are a sub-class of MAS whereby

• Norms affect/impact behaviour of components (and overall system)

• Norms are explicitly represented and processed (e.g., design)

• Agents explicitly process norms

From the literature:

• “systems in the behavior of which norms play a role and which neednormative concepts in order to be described or specified” [MW93]

• “a (MAS) together with normative systems in which agents on theone hand can decide whether to follow the explicitly representednorms, and on the other the normative systems specify how and [to]which extent the agents can modify norms” [BTV06]

• “systems where individual and collective behaviour are affected bynorms” [AGNvdT13]



What are norms?

Chambers Dictionary (http://www.chambers.co.uk):

• “an accepted standard of behaviour within a society”

Merriam-Webster Dictionary (http://www.merriam-webster.com):

• a principle of right action binding upon the members of a group andserving to guide, control, or regulate proper and acceptable behavior

• a pattern or trait taken to be typical in the behavior of a social group


http://www.chambers.co.uk

http://www.merriam-webster.com


What are norms? (cont’d)

• Means to specify individual/collective behaviour within societiesI Hence, there is no need for norms if a) you live in an island; or b) you

cannot move/act (e.g., you are book or a computer (?!))

• What one must, may and should not do in which circumstances

• Examples:I You must remain silent during the presentationI We may chat during the coffee breakI We should not remain in this room after 7PM

• Other aspects in norms:I Who created the norm (and which authority they have)I Who is policing/enforcing the normI What punishment for violating the normI What reward for complying with the normI More on these later...



What are norms? (cont’d)

Very important

• Norms describe ideal behaviours

• They are not hard constraints

• We choose to comply with or violate norms

• This is autonomy, an essential property of software agents

• Norms provide means to regulate societies, but still allowing autonomy

• Beauty/challenge: FindI The minimal set ofI Most general norms whichI Give most choices of norm-compliant behaviour



Norm vs Law vs Policy vs Rule

Norms = laws?

• Yes: they have the same components and serve similar purposes.

• No: the laws of physics are never violated (or are they?)

Norms = policies?

• Policies in computer science:I UNIX/Linux file access policiesI Database access rightsI Java sandboxing

• Policies stipulate permissions and prohibitions, not obligations

• However, recent need: “Web service X must carry out transaction”

Norms = rules?

• Yes: norms are neatly represented as rules

• No: rules are always applicable

N.B.: In common parlance, these terms become blurred



Why NorMAS?

A personal (albeit rational!) view:

• Influence/pressure from technology:I Networking ubiquituous, easy to connect disparate componentsI Software becoming more and more sophisticatedI Web-services, cloud computing, all require communicationI IT solutions now comprise 1000s of sub-components interacting

• Influence/pressure from new uses of ICT:I Computers help people communicate (e.g., Facebook)I More autonomy of software (e.g., pictures uploaded onto Instagram)

• Large collections of autonomous components interacting

• How to manage these?

• Answer: just like in societies, let’s use norms!



Why NorMAS? (Cont’d)

• So, we have systems consisting of 1000s of autonomous &heterogeneous components

I Autonomous – components have choices on how to behaveI Heterogeneous – different vendors, technologies, attitudes

• We must provide guarantees to solutionsI Graceful degradationI Minimal quality of serviceI Essential functionalities always delivered

• Norms provide means to regulate components and, hence, the system

• However:I What kinds of norms and how to represent them?I How to use norms (as a component, as a designer)?I How to connect norms with standard software engineering

processes/products?I More questions (and some answers!) in the rest of the tutorial!



Timeline of normative research


Background

Background


Background Philosophy of Law

Philosophy of Law

• Norms as laws, hence this part of tutorial

• Intersection of philosophy and jurisprudenceI Initially studied by (religious/mystic) philosophersI In older civilisations (e.g., Mayans) law stemmed from religion

• Some questions [Wac06, Wik13]:I “What is law?”I “How do law and morality relate?”I “Does law have a purpose? (e.g., promote social justice/welfare)I “What moral or political theories provide a foundation for the law?”

• Utilitarianism: laws should produce best consequences

• Deontology: laws should protect individual autonomy, liberty or rights

• Virtue jurisprudence: law should promote virtue among citizens



Philosophy of Law (Cont’d)

• Moral and ethical issues of law-making

• Aristotle (384-322 BCE), Cicero (106-43 BCE), Thomas Aquinas(1225-74)

• Hobbes (1588-1679), Locke (1632-1704), Rousseau (1712-78), Hume(1711-76)

• Are there “natural laws” which are “in agreement with nature”?

• U.S. Declaration of Independence: right to life, liberty and pursuit ofhappiness

• French declaration of human rights

• Different theories, approaches and attitudes to law:I Racial discrimination was legal in apartheid South AfricaI Why do we now think this is absurd?I The South African law makers/enforcers thought these were normal

• End of slavery, women’s right, etc.: a changing landscape



Philosophy of Law (Cont’d)

Fuller’s (1902-78) 8 principles [Mur05]:

1 Laws must be general (not ad-hoc)

2 Laws must be promulgated (made public)

3 Laws must not be retroactive

4 Laws must be clear

5 Laws must not be contradictory

6 Laws must be possible to be complied with

7 Laws must be constant

8 There must be congruence between law and official action

These impact on NorMAS, as we shall see


Background Deontic Logics

Deontic Logics: Origins

• Normative multi-agent systems borrow much from deontic logics

• Deontic: from the Greek δεoν (“that which is binding”)

• Concerned with normative conceptsI Obligation, prohibition, permission, power, etc.

• Mally (1926) – first formal system of deontic logic [Mal71]1

• von Wright (1951) – deontic logic as a branch of logic [vW51]

• McNamara (2006) – account of deontic logic developments [McN06]

• Many formulations (syntax, semantics, and axiomatisation)

• Let’s look at a simple version to ground our discussion

1See also http://plato.stanford.edu/entries/mally-deontic/.W. Vasconcelos (Univ. of Aberdeen, UK) Normative MASs ALTiSSimo 2014 20 / 40

http://plato.stanford.edu/entries/mally-deontic/


Standard Deontic Logic (SDL): Preliminaries

• Most cited/studied system

• Based on propositional logic (no variables, no quantification)

• A modal logic (it has a special modal operator)

• Monadic modal operators (one-place operator)

• Deontic modal operators:I O – “obliged”I F – “forbidden”I P – “permitted”



Standard Deontic Logic (SDL): Syntax

Building blocks• P = {p1, p2, . . .}, a countably infinite set of proposition variables• Logical operators ¬,∧,∨,→ (with usual meanings)• Modal operator O (unary, prefixed to formulae)• “`” (logical consequence) and “|=” (semantic entailment)

SDL: Syntax

The set of well-formed deontic formulae DW is defined as

1 P ⊂ DW2 If φ, ϕ ∈ DW then ¬φ, φ ∧ ϕ, φ ∨ ϕ and φ→ ϕ are all in DW3 If φ ∈ DW then Oφ ∈ DW

Abbreviations

• Fφdef= O¬φ (prohibition)

• Pφdef= ¬O¬φ (permission)



Standard Deontic Logic (SDL): Axiomatisation

We axiomatise SDL as follows [McN06]:

SDL: Axioms

A1 All tautologies ` ϕ in W (TAUT)A2 O(φ→ ϕ)→ (Oφ→ Oϕ) (O-K)A3 Oφ→ ¬O¬φ (O-D)MP If ` φ and ` φ→ ϕ then ` ϕ (MP)R2 If ` φ then ` Oφ (O-NEC)



Standard Deontic Logic (SDL): Theorems

Some SDL theorems

O> (O-N)¬O⊥ (O-OD)O(φ ∧ ϕ)→ (Oφ ∧Oϕ) (O-OD)Oφ ∨ Fφ ∨ Pφ (O-Exhaustion)Oφ→ ¬O¬φ (O-NC)



Standard Deontic Logic (SDL): Semantics

• Semantics: mathematical model to capture “meaning”

• Modal logics: Kripke (possible-worlds) semanticsI States (of the world) in which propositions hold or notI Accessibility relation among these states

Kripke Model

A Kripke model is a tuple M = 〈S ,R,V 〉 where

• S = {s1, s2, . . .} is a non-empty set of states of the world

• R ⊆ S × S is an accessibility relation among states

• V : S 7→ 2P is a valuation function mapping states to propositions

R is serial: for every si ∈ S , there is a sj ∈ S , (si , sj) ∈ R.



SDL: problems & paradoxes

• In spite of its classic syntax and semantics, SDL has many open issues[MDW94, Han06, Bv12]

• Paradoxes: formulae which are valid, but are counter-intuitiveI Usefulness of a logic inversely proportional to amount/extent of its

paradoxes

• Some paradoxes:

1 Ross’s paradox2 “No free choice” paradox3 Penitent’s paradox4 Contrary-to-duty imperatives



SDL: Paradoxes

Ross’s Paradox

• Oφ→ O(φ ∨ ϕ) is valid

• However, suppose the following subformulae:I φ stands for “post a letter”I ϕ stands for “burn a letter”

• Oφ→ O(φ ∨ ϕ) stands for

“if one is obliged to post a letter thenone is obliged to post a letter or burn it”

• This is counter-intuitive in ordinary language use



SDL: Paradoxes (Cont’d)

“No free choice” Paradox

• (Pφ ∨ Pϕ)→ P(φ ∨ ϕ) is valid

• If ¬Pφ is the case (φ is not permitted), we can still infer P(φ ∨ ϕ) (φor ϕ are permitted)

• This is counter-intuitive since “φ or ϕ are permitted” suggests thatone is free to choose to either do φ or ϕ, but φ is not permitted!




Penitent’s Paradox

• Fφ→ F(φ ∨ ϕ) is valid

• However, suppose the following subformulae:I φ stands for “comit a crime”I ϕ stands for “do penitence”

• Fφ→ F(φ ∨ ϕ) stands for

“if one is forbidden to commit a crime thenone is forbidden to commit a crime or do penitence”

• This is counter-intuitive in ordinary language use




Contrary-to-duty imperatives [Chi63]

• Consider the scenario:

1 You are obliged to go to the party2 It is obligatory that if you go to the party, you tell that you are coming3 If you don’t go to the party, you are obliged to tell you are not coming4 You don’t go to the party

• Statements sensible, (seemingly) consistent, and none is redundant

• However, if we try to represent this in SDL we run into trouble:

1 Op2 O(p → q)3 ¬p → O¬q4 ¬p

In SDL this formalisation allows us to inferI Oq (from O(φ→ ϕ)→ (Oφ→ Oϕ), O(p → q) and Op)I O¬q (from ¬p → O¬q and ¬p)

• The scenario is inconsistent!



Problems with deontic logic

• SDL has other problems important to Computer Science

• Let’s look at some of them (from [Bv12]):

1 Do norms have a truth value?2 Are permissions really needed?3 Are norms over actions or states?4 How do we check norm compliance?



Problems with deontic logic (Cont’d)

Problem 1: Norms do not have a truth value.

• “it is raining” – is either true or false

• ObeQuiet – is this true/false?

• If norms do not have truth-values, then we cannot reason with them

• What computations can we carry out with norms, then?




Problem 2: What are permissions for? Are they really needed?

• Idea: what is not explicitly permitted is prohibited

• Idea: if a higher authority permits something, a lower authoritycannot forbid it

• Idea: permissions are exceptions to obligations (in legal theory)

• Are permissions the same as rights?




Problem 3: Are norms over actions or states?

• FbeHere vs. OshutDoor

• Sometimes we need both, but there are technical issues

• Actions are important in computing (commands, functionalities)

• States are important for analysis and verification




Problem 4: How do we check norm compliance?

• Violations: when an agentI Didn’t perform an obliged action (but it might still do it!)I Performed a forbidden actionI Didn’t perform a permission (!?)

• Compliance: when an agentI Performed an obliged actionI Didn’t perform a forbidden action (but it might still do it!)

Related to this problem:How do we enforce norm compliance while preserving autonomy?



Deontic reasoning

• In spite of problem 1, there are “mechanisms” for SDL reasoning

• Reasoning: given a set of axioms Ψ, infer ϕ

• Formally: Ψ ` ϕ?

• Not a trivial problemI Axiom R2 stipulates that “if ` φ then ` Oϕ”I Suppose p ∈ ΨI We can infer Ψ ` Op, Ψ ` OOp, Ψ ` OOOp and so on

• Deontic/modal reasoning [Li08] has a high computational complexity

• Theorem proving for full SDL is not always feasible

• What parts/fragments of SDL can we make use of for NorMAS?


References

References I

Giulia Andrighetto, Guido Governatori, Pablo Noriega, and LeendertW. N. van der Torre (eds.), Normative multi-agent systems,Dagstuhl Follow-Ups, vol. 4, Schloss Dagstuhl–Leibniz-Zentrum fuerInformatik, Dagstuhl, Germany, 2013.

Guido Boella, Leendert Torre, and Harko Verhagen, Introduction tonormative multiagent systems, Computational & MathematicalOrganization Theory 12 (2006), no. 2-3.

Jan Broersen and Leendert van der Torre, Ten problems of deonticlogic and normative reasoning in computer science, LNCS, vol.7388, Springer, 2012.

Roderick M. Chisholm, Contrary-to-duty imperatives and deonticlogic, Analysis 24 (1963), no. 2.


References

References II

Jorg Hansen, The paradoxes of deontic logic: Alive and kicking,Theoria: A Swedish Journal of Philosophy 72 (2006), no. 3.

Zhen Li, Efficient and generic reasoning for modal logics, Ph.D.thesis, The University of Manchester, United Kingdom, 2008.

Ernst Mally, Grundgesetze des sollens, Logische Schriften, SyntheseHistorical Library, vol. 3, Springer, 1971.

Paul McNamara, Deontic logic, Logic and the Modalities in theTwentieth Century, vol. 7, North-Holland, 2006.

J. J. C. Meyer, F. P. M. Dignum, and R. J. Wieringa, The paradoxesof deontic logic revisited: a computer science perspective,Technical Report UU-CS-1994-38, University of Utrecht, Utrecht,1994.


References

References III

Colleen Murphy, Lon Fuller and the moral value of the rule oflaw, Law & Philosophy 24 (2005), no. 3.

J.-J.Ch. Meyer and R.J. Wieringa, Applications of deontic logic incomputer science: A concise overview, Deontic Logic in ComputerScience: Normative System Specification, John Wiley & Sons, 1993.

G. H. von Wright, Deontic logic, Mind 60 (1951), no. 237.

Raymond Wacks, Philosophy of law: A very short introduction,Very Short Introductions, Oxford University Press, Oxford, UK, 2006.

Wikipedia, Philosophy of law — Wikipedia, the freeencyclopedia, 2013, [Online; accessed 29-May-2013].


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