Ten Problems of Deontic Logic in Computer Science

Transcription

1 Ten Problems of Deontic Logic in Computer Science 1 University of Utrecht 2 Individual and Collective Reasoning Group Computer Science and Communication University of Luxembourg ESSLLI 2010 (Copenhagen) August 2010

2 Motivation 1 Computer systems become ever more sophisticated, distributed and autonomous. As a consequence, there is a growing interest in describing and controlling these systems on the more general level of their rules and modes of interaction. 2 Recently, the important role of normative reasoning is recognized within the community working on social software, but a clear understanding of the work on norms and deontic logic that is done over the last 60 years is lacking in this area. 3 In the years to come, the Handbook of Deontic Logic will appear. Its aims are to give an historical overview, to present the promising approaches so far, and to point to the deontic logic challenges of the future.

3 Introduction There is no recent text book on deontic logic Deontic logicians distinguish good from bad (and in between) GQ = Good Questions: questions one should study BQ = Bad Questions: questions which have become irrelevant Personal view, but also lessons from working on the handbook Foundational: we use propositional logic only But we make some references to more advanced systems Interrupt if something is unclear - let s make it interactive Most of the ten problems are self-contained Acknowledgement: Hansen, Pigozzi & van der Torre, Ten philosophical problems in deontic logic, 2007

4 1 Problem 1 - In what sense are obligations different from norms? 2 Problem 2 - How to reason about contrary to duty norms? 3 Problem 3 - How do norms change? 4 Problem 4 - What is the role of time in deontic reasoning? 5 Problem 5 - How to relate various kinds of permissions? 6 Problem 6 - What is the role of action in deontic reasoning? 7 Problem 7 - What is the role of constitutive norms? 8 Problem 8 - How do norms influence, solve, or control games?

5 In what sense are obligations different from norms? BQ Can norms have truth values? (Jorgensen, 1938) Imperatives, promises, legal statutes, and moral standards are usually not viewed as being true or false. E.g.: John, leave the room! BQ Is a logic of norms possible? Without truth, norms cannot: be premise or conclusion in an inference, be termed consistent or contradictory, or be compounded by truth-functional operators. BQ Can deontic logic be built on descriptive obligations only? (Makinson, 1998) turns the Bad Questions into a Good Question: Problem 1. How can deontic logic be reconstructed in accord with the philosophical position that norms are neither true nor false? Explained in following slides in three steps.

6 Step 1: Traditional Deontic Logic, axiomatic (1951) In what sense are obligations different from norms? SDL = normal modal logic of type KD (advanced) extends the propositional tautologies with the axioms K : O(x y) (Ox Oy) and D : (Ox O x), closed under modus ponens x, x y/y and Necessitation x/ox Prohibition & permission defined Fx = O x and Px = O x. BQ Which representation for conditional norms O(x a)? O(x a) = O(a x), or O(x a) = a Ox, or something else BQ Factual or deontic detachment? Factual detachment: (O(x a) a) Ox Deontic detachment: (O(x a) Oa) Ox

7 Step 2: Traditional Deontic Logic, possible worlds (1969) In what sense are obligations different from norms? DSDL3 = dyadic modal logic (advanced) Kripke models W, where is total pre-order O(x a) iff x holds in all the most preferred a worlds Axiomatized by Lewis (counterfactuals, 1973) and Spohn BQ Which representation for conditional norms O(x a)? BQ Which logical relations hold among conditional norms? BQ Factual or deontic detachment? Factual detachment: (O(x a) a) Ox Deontic detachment: (O(x a) Oa) Ox BQ How are logical relations and detachment related? For example, transitivity and deontic detachment

8 Step 3: Modern Deontic Logic, iterative (1998) In what sense are obligations different from norms? Makinson s iterative detachment approach Normative code N is pairs of propositional formulas (a, x) Gross output: out(n, A) = apply N as rules on A E.g., E 0 =,E n+1 = {x (a, x) N, E n A implies a} Net output: consistency constraint for output E.g., E n+1 = {x (a, x) N, E n implies a} if consistent, E n otherwise BQ Which representation for conditional norms O(x a)? GQ How to detach obligations from conditional norms? Factual detachment: ((a, x) a) Ox Deontic detachment: ((a, x) Oa) Ox BQ How are logical relations and detachment related?

9 Norms CTD Change Time Permission Action Institution Games Candidates for a New Standard Makinson s iterative detachment approach GQ Which approaches do not fit into this general framework? GQ What are the alternatives to this iterative framework? Algebraic Programming Non-Monotonic a:b/oc Reactive Diagnostic q /\ V(n) p Labeled Op!p,Oq!q ² O(p/\q)!p,!q Iterative a in out(c,b) Imperativistic!p,!q ² O(p/\q) Dynamic Input/Output K Jan Broersen1 and Leon van der Torre2 O

10 Problem 1 - Some Good Questions Makinson s iterative detachment approach GQ When is a normative system coherent? GQ When is a norm redundant? GQ When are two normative systems equivalent? GQ How are the three questions above related? GQ Which meta-logical properties can or should hold? Law2case principle Strong case2law principle GQ How to prevent the pragmatic oddity without creating the drowning problem?

11 Problem 2 - How to reason about contrary to duty norms?

12 Problem 3 - How do norms change?

13 Problem 3 - How do norms change? Problem 1 - In what sense are obligations different from norms? GQ How is obligation change different from norm change? How to formalize the relation between them? Obligations can change while normative system remains same Detachment of obligation, delegation, etc A relatively clear and well studied subject (in 70s and 80s) Norm change: the new challenge (workshops 2007, 2010) Norm revision and contraction, e.g. change of legal code Norm evolution, e.g. change of social norms Merging normative systems, e.g. merger of companies

14 Problem 3 - How do norms change? Problem 3.1. How to revise a set of norms? Alchóurron & Makinson [1981] study changes of legal code: addition amendment: revision derogation: contraction Legal code is a non-empty and finite set of propositions. Starting point of belief revision (with Gärdenfors), a.k.a. AGM AGM 1985: minimality represented by recovery postulate More advanced variants, e.g. for iterated belief revision Also some issues with prioritized norms we do not consider Defeasible deontic logic derived from non-monotonic logic

15 AGM 85 C. E. Alchourrón, P. Gärdenfors, and D. Makinson. On the logic of theory change: Partial meet contraction Jan Broersen and revision 1 and Leon functions. van der J. Torre Symb. 2 Log., Ten50(2): , Problems of Deontic Logic in Computer Science

16 AGM 85

17 Problem How to revise a set of norms? BQ Do the AGM postulates hold for norm revision? E.g., success postulate criticized in belief revision GQ Does AGM offer a satisfactory framework for norm revision? Role of minimal change in norm change Revision of conditional norms Example If we have {(, a), (a, b)} and we have that c is an exception to the obligation to do b, then we need to have b out(n, c). Two solutions seem to be {( c, a), (a, b)} or {(, a), (a c, b)}. GQ What triggers the change of a norm? AGM says a new or removed norm GQ Do general patterns in the revision of norms exist? If so, how to formalize them? GQ Derogation is contraction? How about annulment?

18 Problem 3 - How do norms change? GQ How to formalize the evolution of (social) norms? E.g., norm about phone calls during meetings No persons who change the norm like in legal code Change of social norm triggered by norm violations Social delegation cycle: relates agent desires and social goals GQ How to merge sets of norms? Problem only recently addressed in the literature. GQ What is norm merging? 1 Merging norms that belong to the same normative system 2 Merging norms that belong to different systems

19 Merging norms: same normative system Example (Cholvy & Cuppens 1999) An organization that works with secret documents has two rules. R 1 = It is obligatory that any document containing some secret information is kept in a safe, when nobody is using this document. R 2 = If nobody has used a given document for five years, then it is obligatory to destroy this document by burning it. To derive a contradiction we need to add an IC that keeping a document and destroying it are contradictory actions The notion of coherence between norms can involve information other than norms. Is this a genuine problem of merging norms?

20 Merging norms: different systems Example (Grégoire, 2004) The Belgian-French bilateral agreement preventing double taxation: Resident in B France State Worker Taxable in B Resident in B Work in France Taxable in B Belief merging would simply give a set containing the two initial rules. But if someone is not a State worker in France (but works in France), we would get contradictory requirements from the Belgium and the France parties.

21 Problem How to merge sets of norms? Belief merging (a.k.a. belief fusion) is a generalization of belief revision. Belief merging dedicated to the combination of information coming from different (conflicting) sources. GQ Can belief merging offer a satisfactory framework for norms? GQ Do distinctions in belief merging correspond to something? Belief merging distinguishes majoritarian and egalitarian operators. They try to capture the intuitions that often guide the aggregation of individual preferences into a social one. These intuitions seem to have nothing to say when we try to model the merging of sets of norms. GQ What are alternative frameworks for norm merging?

22 Problem 4 - What is the role of time in deontic reasoning?

23 Problem 5 - Permissive norms BQ How to solve the following problem with permissions: Example (Ross paradox) Px implies P(x y), e.g., if a person is permitted to smoke, he is also permitted to smoke or kill. BQ How to formalize free choice permissions: Example (Free choice permission) P(x y) implies Px Py, e.g., You may either sleep on the sofa-bed or sleep on the guest room bed implies You may sleep on the sofa-bed and you may sleep on the guest room bed.

24 Problem 5 - Permissive norms BQ Is permission unilateral (Op Pp) or bilateral (Pp Op)? BQ What is difference between weak (negative, tacit) and strong (positive, implicit and explicit) permission? von Wright (1951): Permission is dual of obligation Px = def O x (weak permission) Negative permission defined without permissive norms Px = def x out(n, A) (weak permission) BQ Are permissive norms necessary for normative systems? Example (Bulygin 1986) Permissive norms are needed when there multiple authorities. If a higher authority permits you, a lower authority cannot prohibit it.

25 Problem 5 - Permissive norms BQ What is the difference between permission and authorization? Example (Makinson1986) A priest may be authorized to marry people, in the sense that his actions may have that effect, without being permitted to do so. GQ What is a right? Example If you have the right to enter, then a guard must let you in. Concept of permission is multi-faceted. Problem 5. How to relate various kinds of permissions and relate them to obligations?

26 Problem 5 - Permissive norms Problem 1 - In what sense are obligations different from norms? Problem 3 - How is obligation change different from norm change? GQ How are permissions different from permissive norms? One of three reasons for Makinson s iterated approach GQ How do permissive norms influence obligations? Obligations imply permissions, but how about the other way? GQ How to formalize relation permissions and permissive norms? Something is positively permitted iff the code explicitly presents it. However, permissions follow from explicit ones.

27 Problem 5 - Permissive norms Example Consider a set G consisting of the norm (work, tax), and a set P consisting of (18y, vote). Does it follow from our mini-code that voting is permitted on condition of being employed? In one sense yes: there is nothing in the code that forbids it (negative permission). In another sense no: a person may be employed at the age of 17 and not covered by the explicit permission (positive static permission). But in another sense, yes again. For if we were to forbid a person to vote on the condition of being employed we would be creating an incoherence in the code, in its application to people who are both employed and 18 or over (dynamic positive permission).

28 Problem 5 - Permissive norms Kinds of permissions used in different circumstances: Negative permissions seem to answer to the needs of the citizen, who needs to now that his action is not forbidden. Since it s difficult to establish these kinds of permissions (also because of ambiguities in the code), positive static permissions seem to suit better the need to know what is explicitly permitted. Lastly, dynamic permissions are the answers to the need of the legislator, who need to anticipate the effect of changing an existing corpus of norms by adding a prohibition.

29 Problem 6 -

30 Problem 7 - What is the role of constitutive norms? Normative system contains definitions, expressions of purposes, conceptual rules, etc.: we call them constitutive norms. Example An act of theft is punished by a prison sentence not exceeding 5 years or a fine. GQ What is the role of constitutive norms? (What can t we do if we have only regulative and permissive norms) Meaning postulates and intermediate concepts Creation of social reality, counts-as conditionals Legal and institutional powers of agents Defining the way normative systems can change Interpretation issues...

31 Example meaning postulates and intermediate concepts An act of theft is punished by a prison sentence not exceeding 5 years or a fine. Someone commits an act of theft if that person has taken a movable object from the possession of another person into his own possession with the intention to own it, and if the act occurred without the consent of the other person or some other legal authorization. A person in the sense of the law is a human being that has been born. A movable object is any physical object that is not a person or a piece of land. A movable object is in the possession of a person if that person is able to control its uses and location. The owner of an object is within the limits of the law entitled to do with it whatever he wants, namely keep it, use it, transfer possession or ownership of the object to another person, and destroy or abandon it.

32 Meaning postulates and intermediate concepts Intermediate concepts link legal terms to terms that describe natural facts. GQ Why are there intermediate concepts? Wedberg & Ross (1950s): a legal term like ownership (x is the owner of y at time t) serves the purpose of economy of expression of a set of legal rules. To regulate normative change and legal interpretation by judge To resolve conflicts

33 Problem 7 - Meaning postulates and intermediate concepts Example (Intermediates to resolve conflicts) Suppose that (, dog) forbids dogs on the premises There is also a higher order principle that no blind person may be required to give up her guide dog. The judge cannot change the statute. What he can do is to conclude that the statute does not apply to guide dogs. So the statute must be re-interpreted as reading (, tdog) with the additional intermediate (dog guidedog, tdog) T, and thus no conflict arises for the case of blind persons that want to keep their guide dog. GQ What is the exact process of creating and modifying theoretical terms in order to resolve conflicts?

34 Problem 7 - Meaning postulates and intermediate concepts GQ How can meaning postulates and intermediate terms be incorporated into semantics for deontic logic reasoning? Problem 1 - In what sense are obligations different from norms? Problem 3 - How is obligation change different from norm change? Problem 5 - How are permissions different from permissive norms? GQ How are intermediate concepts different from meaning postulates? GQ How are institutional facts different from constitutive norms? M = set of intermediates of the form (a, x) Out(G, A, M) = out(g, A out(m, A))

35 Problem 7 - Constitutive norms GQ How do regulative, permissive and constitutive norms interact?

36 Problem 7 - Constitutive norms There is no consensus on the logic of counts-as conditionals, probably due to the fact that the concept is not studied in depth yet. For example, the adoption of the transitivity rule T for Jones & Sergot s logic is criticized by Artosi, Rotolo & Vida: They claim that non-monotonicity is a crucial feature of count-as conditionals: Example: Suppose that in an auction if the agent x raises one hand, this may count as making a bid. It is clear that this does not hold if x raises one hand and scratches his own head.

37 Problem 8 -