the right direction - Semantic Scholar

Download PDF
2 downloads 996 Views 103KB Size Report
Comment
Research group on Information Technology and Administrative Systems,. University of Oslo. Department of Philosophy, University of Oslo. In this paper we ... x has a liberty in face of y to perform some action iff x has no obligation to y to refrain.
THE R IGHT D IRECTION Henning Herrestad & Christen Krogh1 Norwegian Research Centre for Computers and Law, Research group on Information Technology and Administrative Systems, University of Oslo Department of Philosophy, University of Oslo. In this paper we propose an approach to the formalisation of rights building on the attempts of David Makinson and Lars Lindahl at improving Stig Kanger's formalisation of W.N. Hohfeld's theory. We are developing the suggestion of using indexes on modal operators to express that rights have direction. 1.

I NTRODUCTION

If, by developing formal theories of rights, we could get a clear hold on what we mean by saying that someone has a certain right, then moral and legal discourse might become less vague and confused. Furthermore, a formal theory of rights would be an important contribution to the construction of computer programs to aid in systems specification and legal drafting (Jones & Sergot (1992)). As noted by Makinson (1986) W.N. Hohfeld's theory of rights (1913) has offered a standing challenge to logicians because of its "abstract and systematizing character". The best known proposal of a formalisation of Hohfeld's theory has been presented by Stig Kanger (1971,1972) (and with Helle Kanger (1966)). This attempt has been further developed by Lindahl (1977, 1991) and Makinson (1986), to which the present paper is a response. They hold that what may be termed 'the counterparty problem', and the expression of rights without a counterparty are two central problems for Kanger's proposal. In order to present these problems, we shall give a brief introduction to Kanger's formalisation. 2.

K ANGER 'S F ORMAL V ERSION OF H OHFELD 'S T HEORY

Hohfeld's theory of 'right' may be summarised in the following biconditional sentences: i)

x has a claim against y with respect to some action iff y has a obligation to x to perform that action.

ii)

x has a liberty in face of y to perform some action iff x has no obligation to y to refrain from doing that action.

iii)

x has a legal power over y with respect to some legal relation iff x is able to perform some action that changes this legal relation of y in some way.

iv)

x has a legal immunity from y with respect to some legal relation iff y is unable to perform any action that would change this legal relation of x.

We may accordingly talk about four kinds of rights; claim-rights, liberty-rights, power-rights and immunity-rights. Each right is perceived as a normative relation between two individuals.

1

This research has been kindly funded by NAVF project #469.92.008, to contribute to the Esprit project MEDLAR II. Christen Krogh is on permitted leave from Department of Knowledge Based Systems at SINTEF-SI.

Herrestad & Krogh

The Right Direction

Stig Kanger2 proposed the following formal version of Hohfeld's theory: (1) (2) (3) (4)

Claim (x,y,A) Liberty(x,y,A) Power (x,y,A) Immunity(x,y,A)

≡ ≡ ≡ ≡

OE(y,A) ¬OE(x,¬A) ¬O¬E(x,A) O¬E(y,¬A)

(5) (6) (7) (8)

Counter-Claim(x,y,A) Counter-Liberty(x,y,A) Counter-Power (x,y,A) Counter-Immunity(x,y,A)

≡ ≡ ≡ ≡

OE(y,¬A) ¬OE(x,A) ¬O¬E(x,¬A) O¬E(y,A)

Kanger termed these relations 'simple types of right'. 'O' is the obligation operator of standard deontic logic (SDL), and 'E' is an abstract action operator following the modal logic ET (Chellas 1980 notation).'E(x,A)' reads 'x sees to it that A is the case', and 'O E(x,A)' reads 'It is obliged that x sees to it that A is the case'3. Here all the relations are expressed from the viewpoint of the bearer of the right 'x'. 'x' is what Jeremy Bentham termed 'the party favoured by law'. (1) to (4) are easily recognisable as explications of i) to iv), while (5) to (8) simply are the result of substituting '¬A' for 'A' and replacing '¬¬A' by 'A'. 3.

T HE C OUNTERPARTY P ROBLEM

Hansson (1970) made the observation that while deontic logicians seemed fixed on discussing the structure of obligations pertaining to one individual or group, Hohfeld and his followers were more interested in the normative relations between parties. Kanger, being a deontic logician, explicated Hohfeld's normative relations in terms of single agent obligations or permissions – without making the relations explicit. The explicans divides the rights in two sets; {(1),(4),(5),(8)} conferring obligations on the counterparty of the right-relation (hence termed O-rights), and {(2),(3),(6),(7)} conferring permissions4 on the bearer of the right (hence termed P-rights). In both cases reference to the other party of the right-relation is missing. As pointed out by Lindahl (1991) this is problematic. For instance the explication of 'Claim(x,y,A)' leads us to assume that whenever there is an obligation on an individual 'y' to see to the existence of some state of affairs 'A', it implicitly exists another individual 'x' who bears a right of having 'A' brought about. Re-working one of Lindahl's examples, we may also illustrate the opposite problem: Suppose that 'x' has a house in a suburban area. We may plausibly assume: 'x has no right that y does not walk around in the garden of x's neighbour z' (y's walking in z's garden is no concern of x's)'. In Kanger's language 'x's situation is described as: 'not Counter-Immunity(x,y,A)', where 'A' expresses that 'y walks in z´s garden'. In Kanger's formalisation this is expressed as '¬(O¬E(y,A))', which is equivalent to a general permission of 'y' to walk in 'z's garden. This is problematic, as we may well suppose that 'z' himself has forbidden 'y' to walk in 'z's garden – a situation which can not be consistently expressed within Kanger's system5. Apparently Kanger saw this problem. As a response he generated the set of maximally consistent conjunctions (the maxi-conjunctions) of affirmed or negated conjunctions of (1) to (8). By maximal we mean that if any further conjunct (taken from 1 - 8) is added to a conjunction, then this new conjunction is either inconsistent or redundant. Hence every conjunction makes a complete specification of the relative freedom of two parties 'x' and 'y'. Due to the logics of 'O' and 'E' Kanger got 26 maxi-conjunctions, which he termed 'atomic types of right' (numbered {K1-K26}). As every conjunction is a consistent combination of Orights and P-rights with respect to the same state of affairs, we tend to assume that in every conjunct expressing a simple type where 'x' is the bearer, 'y' is the implicit counterparty, and 2 3 4 5

See Kanger & Kanger [1966], Kanger [1972]. See sections 5 & 6 for axiomatisations of SDL and the action logic. Assuming the standard interdefinability of 'O' and 'P' (P =def ¬O¬). Since '¬(O¬E(y,A)) ^ O¬E(y,A)' is contradictuous.

2

Herrestad & Krogh

The Right Direction

vice versa. Moreover, by calling the conjunction itself a type of right, we are led to think of 'x' or 'y' as either bearer or counterparty to a right-relation described by the whole conjunction. However, as noted by Makinson (1986:p 420) this does nothing to change the problematic representation of simple types of rights (which does make perfectly goods sense when taken alone). Furthermore, to think of the whole conjunction as itself a right-relation makes no sense. Assume that 'x' is the first party, then the party referred to in the other conjuncts may be anyone whatsoever, and this anyone may be entirely without relation to 'x'. For example two individuals 'x' and 'y' (living, maybe, at opposite parts of the globe) may both have the relative freedom of being permitted to eat or abstain from eating ice-cream. We may express their relative freedom as a conjunction of simple types of rights. But it is still not a right-relation between them as we are led to assume by Kanger's atomic types of right. Secondly, let us assume that 'x' has an obligation towards 'z' to see to it that 'A', and that 'y' has an obligation towards 'z' to see to it that 'A'. Here 'z' is the intuitive counterparty to each of the obligations, and the bearer of the right to 'A'. However, in Kanger's theory we would have to express this as: 'OE(x,A)^OE(y,A)'. Here, the bearer of the right is entirely missing. Moreover, the expression is equivalent to the expression of an Atomic right-relation of type (K3), and we are thus wrongly led to think of this as a right-relation between 'x' and 'y'. A final point is that the lack of direction in Kanger's right-relations make us at loss to decide as to whether it is a right of 'x' against 'y' or vice versa. 4.

R IGHTS WITHOUT A C OUNTERPARTY

As Claim(x,y,A) is explicated by Kanger as an obligation on the counterparty 'y', it is not possible to express claims without a counterparty in Kanger's theory. However, statements like.. (*) Children have a right to be nurtured

...seems rather frequent in legal parlance. If 'x' is a child, nothing follows from (*) about who has a duty to nurture 'x'. Without going into a discussion concerning the meaningfulness of making such statements, we want to maintain that they should be expressible in a formalisation of rights. 5.

I NDEXED S TANDARD D EONTIC L O G I C

Hansson (1970) suggested to develop a deontic logic indexed for bearer and counterparty. Makinson (1986) proposed that indexed deontic operators may solve the counterparty problem. We shall start by following this proposal. We construct a multilevel indexed deontic logic. It is our intention to show that obligations on different levels of generality and specificity may be employed in expressing 'rights'. We introduce an indexed obligation 'xOy', called 'directed obligation'. 'xOyA' is to be read 'x is obliged towards y to the effect that A'. 'x' is the bearer of the obligation and 'y' is the counterparty. 'A' is the object of the obligation. We say that the obligations has a direction from 'bearer' towards 'counterparty'. We axiomatise the logic as a two-indexed normal modal logic of type K: xOy.RN xOy.K def.xPy

if A then xOyA xOy(A->B) -> (xOyA -> xOyB) xPyA =def ¬xOy¬A

3

Herrestad & Krogh

The Right Direction

We further introduce an indexed obligation, 'xO', called 'obligation simpliciter'6. 'xOA' is to be read 'x is obliged to the effect that A'. 'x' is the bearer of the obligation. There is no counterparty. 'A' is the object of the obligation. We do not say that 'obligation simpliciter' has a direction. In a similar fashion, we introduce the indexed obligation 'Oy', called 'bearer free obligation'. 'Oy A' is to be read as 'there is an obligation towards y to the effect that A', or 'A is obligatory towards y'. 'A' is the object of the obligation. We do not say that 'bearer free obligations' has a direction. The logics of 'xO' and 'Oy' are axiomatised as one-indexed normal modal logics of type K: xO.RN xO.K def.xP

if A then xO A xO (A->B) -> (xO A -> xO B) xP A =def ¬xO¬A

Oy.RN Oy.K def.Py

if A then OyA Oy(A->B) -> (OyA -> OyB) PyA =def ¬Oy¬A

Then we introduce standard deontic logic (SDL). 'O A' is read (as usual) 'it is obligatory that A'. 'O' is called a 'general obligation'. As usual, SDL is axiomatised as a normal modal logic of type KD. O.RN O.K O.D def.P

if A then OA O(A->B) -> (OA -> OB) OA -> ¬O¬A PA =def ¬O¬A

We define four reduction axioms to connect the indexed logic and SDL: xOy>xO xOy>Oy xO>O Oy>O

xOyA -> xOA xOyA -> OyA xOA -> OA

OyA -> OA

We can now prove the following theorems: 1.

xOy>O

xOyA -> OA

2. 3. 4. 5. 6.

P>Py P>xP Py>xPy xP>xPy P>xPy

PA -> PyA PA -> xPA PyA -> xPyA xPA -> xPyA PA -> xPyA

6

From Hansson (1970)

4

Herrestad & Krogh

7. 8. 9.

xOy.D xO.D Oy.D

10. xOy.SC 11. xO.SC 12. Oy.SC

The Right Direction

xOyA -> xPyA xOA -> xPA

OyA -> PyA ¬ ¬ ¬

(xO yA ^ zO æ¬A) (xOA ^ zO¬A) (OyA ^ Oæ ¬A)

(1) is the inferred relation between directed obligations and general obligations. (This follows directly from xOy>xO and xO>O.) (2) through (6) gives the relation between indexed and unindexed permission (follows directly from the reduction axioms by taking contraposition, substituting '¬A' for 'A', and replacing 'P' for '¬O¬'). (7) through (9) are the indexed counterparts of the ubiquitous D-axiom, ensuring weak consistency among the obligations. (This follows from the reduction axioms, 'O.D', and the P-counterparts of the reduction axioms.) (10) through (12) are new versions of the D-axioms for indexed obligations, ensuring strong consistency among the obligations. There are two properties that are central in our representation of indexed deontic logic: (i) The strong consistency theorems (10-12), and (ii) that the following expressions are possible: 13. xOy.W 14. xO.W 15. Oy.W

xOyA ^ zPæ¬A xOA ^ zP¬A

O yA ^ Pæ¬A

We believe (i) to be questionable, and (ii) to be appropriate. The strong consistency theorems (10-12) ensure that if an obligation exist between two parties, no two parties (including the ones already mentioned) are allowed to hold an obligation to the effect of the opposite. This may indeed seem a bit naive and removed from reality. However, the logical properties of ISDL (Indexed Standard Deontic Logic) are such that we cannot have a reduction from indexed obligations to unindexed obligations – as well as the presense of 'O.D', and the definitions of indexed permission – without having this property. For this reason, we assume that we are operating within a system of norms that are internally consistent (conflict of norms, prima facie or defeasible obligations, etc., are not allowed), and leave this problem unsolved. (13) through (15) give us some added expressibility within our indexed deontic logic as compared to SDL, where their counterpart is the denial of the D-axiom. The intuitive reading of e.g. (13) is that 'x may be under an obligation towards y to the effect that A' and 'z may be permitted towards 'æ' to the effect that not A'. If we (just for the sake of the argument) consider the alternative to allowing the possibility of e.g. (13), we will find that this implies the following theorem... 16. xOy=O

xOyA -> zOæA

. ..which is quite unsatisfactory, as it would remove the distinction of indices of obligations.

5

Herrestad & Krogh

6.

The Right Direction

A MINIMAL A CCOUNT OF A GENCY

The final logical machinery we need before we start modelling Kanger's types of rights, is an account of agency. As usual, we define a minimal account of agency as the logic of an indexed action operator 'E(x,...)'. 'E(x,A)' is to be read as 'the agent x brings it about that A'. The logic of E is axiomatised as follows: Ex.RE. Ex.T.

7.

if A B then E(x,A) E(x,B) E(x,A) -> A

K ANGER 'S R IGHTS R EFORMULATED

Recall Kanger's reformulation of Hohfeld's types of right (called simple types of rights): (1) (2) (3) (4)

Claim (x,y,A) Liberty(x,y,A) Power (x,y,A) Immunity(x,y,A)

≡ ≡ ≡ ≡

OE(y,A) ¬OE(x,¬A) ¬O¬E(x,A) O¬E(y,¬A)

(5) (6) (7) (8)

Counter-Claim(x,y,A) Counter-Liberty(x,y,A) Counter-Power (x,y,A) Counter-Immunity(x,y,A)

≡ ≡ ≡ ≡

OE(y,¬A) ¬OE(x,A) ¬O¬E(x,¬A) O¬E(y,A)

In terms of the logical apparatus we have developed, we can express sentences of the form 'yOxE(y,A)', which can be read as follows: 'y is obliged towards x to the effect that y brings it about that A'. If we explicate the simple types of right in terms of directed obligations and permissions of an action to the effect that 'A' we get the following: (d1) (d2) (d3) (d4)

Claim (x,y,A) Liberty(x,y,A) Power (x,y,A) Immunity(x,y,A)

≡ ≡ ≡ ≡

yOx E(y,A) xPy ¬E(x,¬A) xPy E(x,A) yOx ¬E(y,¬A)

(d5) (d6) (d7) (d8)

Counter-Claim(x,y,A) Counter-Liberty(x,y,A) Counter-Power (x,y,A) Counter-Immunity(x,y,A)

≡ ≡ ≡ ≡

yOx E(y,¬A) xPy ¬E(x,A) xPy E(x,¬A) yOx ¬E(y,A)

As pointed out earlier, Kanger's explications are problematic because they do not explicitly mention both the bearer and the counterparty of the right: From a general obligation that 'y' should bring about 'A', we can infer that there exists a claim-right (1) for a bearer 'x' towards a counterparty, 'y', that 'y' should bring about 'A'. In our explication, this problem no longer arises because we cannot infer from an obligation simpliciter on 'y' to do 'A' (explicated as 'yOE(y,A)'), that there is a claim-right for an 'x' against 'y' that 'y' should do 'A' (explicated as 'yO x E(y,A)'). In other words, since the implication 'yO A -> yO x E(y,A)' does not hold, we do not have Kanger's problem. Furthermore, if we state that 'x' does not have a right of the simple type counter-immunity against 'y's walking in the garden of his neighbour 'z', the explication expresses that '¬yOx¬E(y,A)'. This is the equivalent of a statement to the effect that 'y' has a permission in relation to 'x' to walk in 'z's garden, which is compatible with 'y' having an obligation towards 'z' not to walk in z's garden. This, {yOz ¬E(y,A) ^ yPx E(y,A)}, is a variant of (13) , which is possible in our logic (hence this particular solution to the garden problem depends on the expressiveness of our system). The formulation in terms of rights, is that of the rather acceptable statement that 'y has a power in relation to x to walk in z's garden', and that, 'z has a counterimmunity against y that y not walks in z's garden' . If we attempt to rebuild Kanger's atomic types by means of directed simple types, we end up with Kanger's 26 atomic rights and an extra set of 8 which are due to the fact that the logic of our directed right (obligation) is more expressive than standard deontic logic. As an example of the fact that our positions correspond to Kanger's, consider the atomic position called K1:

6

Herrestad & Krogh

K1.

The Right Direction

Power(x,y,A), not immunity(x,y,A), counter-power(x,y,A), not counter-immunity(x,y,A)

In Kanger's system, this has the explication: K1E.

¬O¬E(x,A) ^ ¬(O¬E(y,¬A)) ^ ¬O¬E(x,¬A) ^ ¬(O¬E(y,A))

...which can be further simplified as: K1E'.

PE(x,A) ^ PE(y,¬A) ^ PE(x,¬A) ^ PE(y,A)

In our system, K1 is explicated as: K1E.d.

xPy E(x,A) ^ xPy E(x,¬A) ^ yPx E(y,¬A) ^ yPx E(y,A)

In the same manner, it can be shown that all of Kanger's original 26 atomic rights have their 'directional' counterparts in our explication. A translation from 26 of our atomic rights to Kanger's atomic rights can easily be formulated7. Appendix 1 lists up the directed atomic rights corresponding to Kanger's 26. The main problems with atomic O-rights as referred earlier in the paper, no longer exists; we can no longer infer a rights-relation between two hitherto unrelated parties. From the obligations simpliciter, 'xO ¬E(x,A)', and 'yO E(y,A)', we cannot infer that there exists a rights -relation (Kanger's atomic right no.7) of 'Claim(x,y,A) and ¬ Power(x,y,A)'. This is due to the fact that we cannot infer 'xOy ¬E(x,A)' from 'xO ¬E(x,A)'. However, we still have Kanger's problems for P-rights. Since we in our indexed deontic logics have the theorem 'xP A -> xPy A', it is also possible to go from hitherto unrelated instances of one-party permissions to instances of two-party permissions. I.e. from... 22.

xP E(x,A) ^ xP E(x,¬A)

...and... 23.

Py E(y,A) ^ Py E(y,¬A)

...we can infer... 24.

xPy E(x,¬A) ^ xPy E(x,A) ^ yPx E(y,¬A) ^ yPx E(y,A)

(24) is the indexed explication of Kanger's atomic right no. 1. We will call this the P-right problem. Still another point which deserves attention is the extra atomic rights we have due to the increased expressibility of directed obligations as compared to general obligations. An example of such a right is... 25.

xOy E(x,A) ^ yPx E(x,¬A) ^ yPx E(x,A)

The logical reason for all eight of these 'new' rights is simply that the expression 'xOy A ^ yPx ¬A' is a possibility in our system. This again stems from the requirement that we do not want it to be possible to infer that an obligation between two parties is an obligation between two other parties. In real life we often come across situations where two parties may be under an obligation to the effect of something, and that two other parties is not under an obligation to see to it that the same thing is the case. (25) does not seem to signal trouble in the sense that it is counterintuitive. Neither does the other seven extra positions (all eight are listed in appendix 2). 7

Syntactically this can be done by dropping the inidices on permissions and obligations.

7

Herrestad & Krogh

The Right Direction

Turning to 'rights without a counterparty', we shall explicate the simple types of right in terms of non-directed O-rights and P-rights, making only the bearer explicit in the explication. A statement of type 'OxE(y,A)' simply reads 'there is a (bearerfree) obligation towards x that y brings about A', or alternatively 'that y bring about A is obliged towards x'. Here the strict relation between the obligation and the action is broken; 'y' is not a bearer of the obligation, only the effector of the action of bringing about 'A'. We may explicate non-directed simple types of rights as: (n1) (n2) (n3) (n4)

Claim (x,A) Liberty(x,A) Power (x,A) Immunity(x,A)

≡ ≡ ≡ ≡

Ox E(y,A) xP ¬E(x,¬A) xP E(x,A) Ox ¬E(y,¬A)

(n5) (n6) (n7) (n8)

Counter-Claim(x,A) Counter-Liberty(x,A) Counter-Power (x,A) Counter-Immunity(x,A)

≡ ≡ ≡ ≡

Ox E(y,¬A) xP ¬E(x,A) xP E(x,¬A) Ox ¬E(y,A)

We may express the right 'Children have a right to be nurtured' as Claim(x,A) where 'A' express 'that x is nurtured', and the explication 'Ox E(y,A)' intuitively says that 'it is a (bearerfree) obligation towards x that y brings about that x is nurtured'. This seems to be able to convey a general right, which is not an obligation for anybody in particular, that a child, 'x', has the right to be nurtured by 'y'. We may, of course drop the action-description if we consider this problematic, and rephrase the right as 'OxA'. Then we cannot infer anything to the effect of whom is the bearer of these obligation, which is what we expect. To sum up. We have tried to solve the counterparty problem by explicating directional rights in terms of directional obligations. Even though we were able to express counterparty-free obligations, and model the garden-walking problem, it seems like we have only been able to solve half of Stig Kanger's problems with atomic rights (referring to the P-right problem above). However, it may be argued that we have solved the most serious part, since infering rights of obligations appear more dangerous than infering rights of permission. We thus have a solution to the problems presented initially which is not too bad, but which is suffering from some slightly contra-intuitive properties (e.g. the strong consistency notion described in (17), above). However, in the present setting, the solution of the garden-walking problem, the eight extra atomic rights, and the P-rights transferability (from general to specific) is entangled in the same requirements (basically the strong consistency requirement, the reduction axioms, and the requirement that '¬(xOy A -> zOy A)'). This makes one wonder whether there might be some other formalisation where these matters are not so entangled. 8.

E XPLICATING THE N OTION OF B EARER AND C OUNTERPARTY – LINDAHL 'S APPROACH

With our indexed logics we have only made expressible that there is a relation from 'bearer' to 'counterparty'. We have not attempted to explicate these notions in themselves. Makinson (1986:p.423) suggests the following informal account: "...x bears an obligation towards y that F under the system N of norms iff in the case that F is not true then y has a power under the code N to initiate legal action against x for non-fulfilment of F (or in the case of a moral rather than a legal code, iff in such case y is 'entitled to complain' of x for non-fulfilment of F)." In other words, the meaning of being a counterparty is to be one who is being wronged in the case of non-fulfilment of an obligation to which he is the counterparty, and to be one who has a limited legal power (or moral entitlement); I.e. the legal power to initiate legal action (or moral entitlement to complain) when he is being wronged. Lindahl (1991) apparently tries to kill two birds in one throw by making a notion of 'wronging' the core of his explication of right. First, his predicate constant W(y,x), reading 'y is wronged by x' has the technical purpose of making explicit the relation of bearer and counterparty in

8

Herrestad & Krogh

The Right Direction

Lindahl's concept of right. Second, he uses W(y,x) in making an Andersonian type reduction of rights to mean that the bearer is being wronged in case of non-fulfilment. This is close to the first step of our restatement of Makinson's explication of what it means to be a counterparty to an obligation. Hence Lindahl appears to have achieved both an expression of the directionality of rights and an explication of what it means to be a bearer having a right. We believe there are strong reasons for factoring out the problem of expressing the directionality of rights from the problem of explicating the meaning of the notions of a 'bearer' and a 'counterparty'. First, the latter task is difficult, as noted by Makinson, and to express that a bearer is someone being wronged in case of non-fulfilment is only one element in such an explication. Following Makinson, one would also want to include the notion of legal power8 in such an explication. Furthermore, a relation between wrongings and legal power (which excludes other legal powers than the power to initiate legal action when a wronging has taken place) seems crucial. This explication require a suitable explication of the notion of legal power, something Lindahl (1977) argues is lacking, but which is subject to ongoing research9. Second, Lindahl's explication is problematic in that it only expresses that the counterparty of the right has wronged the bearer in the case he does not see to it that F – not that the counterparty has an obligation to see to it that F. Taken that 'wronging' is a normative notion, we find it intuitively unclear that the counterparty may be wronging the bearer in the absence of (the un-fulfilment of) an obligation on the first party. Wrongings appears to come as a result of a breach of obligation, rather than having an independent meaning. Furthermore, it makes sense to say that a right for 'x' entails an obligation for 'y', and then nothing more. Saying that someone has been wronged seems to call for some further account of what is meant by being wronged. The notion of 'wronged' is so to speak entrenched in the difficult issues concerning what may be inferred from a breach of obligations, while simply stating that something is an obligation is not. In summary, Lindahl attempts both to solve Kanger's counterparty problem and to make a new explication of rights. We find his explication unconvincing in that it is only telling a half told story concerning violation of norms. It may rather be seen as an explication of 'having a right' than of 'right'. Rather than attempting to tell the full story, we have had the limited ambition of solving the problems concerning the relation between bearer and counterparty. Factoring out this problem for systematic treatment, we may then encounter the problems of telling the story without having to make the story bear on a need to solve the problems with this relation. 9.

C ONCLUDING R EMARKS

We have described two problems in Kanger's theory of rights, related to counterparties: i) Who the counterparty is, and ii) How to express rights without a counterparty. We have put forwards a candidate solutions by means of introducing obligations with direction. We have reexplicated Kanger's simple and atomic rights by means of this approach, and commented on its strength and weakness. In addition we have showed that rights without counterparties are expressible in a sensible way. A previous attempt by Lars Lindahl at solving the counterparty problem has been discussed and contrasted with respect to some properties of our approach.

8 Or, as above, moral entitelment in the case of a moral right or obligation. 9 E.g. A. Jones & M. Sergot's account of power from ICAIL '93.

9

Herrestad & Krogh

The Right Direction

What are the properties in our approach that caused us most problems10, and what properties enabled us to express what we wanted? We may answer this double question be means of two points: i) Relational operators ii) 'PA -> xPyA' In our analysis of the counterparty-problem we found that the one major issue that were missing was more structure to the relation between bearer and counterparty. The introduction of indexation as a means of enforcing such relational structure is building on proposals of Hansson, Makinson, and Lindahl. We did indeed find that this enforcement of structure, or making explicit the lack of structure (e.g. in bearer-free obligations), enabled us to handle several examples that were problematic for Kanger's theory. We found that even if we could handle a fair amount of the problematic issues involved in Kanger's atomic rights, we still had one problem: Because of the theorem 'PA -> xPyA', we could infer permittive rights between any parties in the presense of a general permission. We must admit that although this problem is not as serious as the one we solved (infering obligatory rights between any parties in the presense of a general obligation), we would quite like to get rid of it, preferably without losing the connection to SDL, or the reduction schemes from specific to less specific obligations. One (amongst other) formal requirement for a better formalisation would thus be that that it should allow inference neither from general to specific permissions, nor from general to specific obligations. Throughout the paper we have built on the assumption that relations between parties in a theory of rights should be expressed through relations in the obligation. Apart from this possibility already having been 'aired' in earlier publications, the intuitions behind it seems to rest on the close connection between obligations and rights (i.e. 'a right for x towards y is an obligation for y towards x'). An alternative, and in our view just as justifiable, analysis, focuses on the observation that rights are based on actions having effects on the parties. The actions are now seen as the glue that relates the parties involved and a state of affairs. Thus in this analysis, action operators of two indices relates states of affairs to an effector and a counterparty. Obligations may now simply be seen as unindexed modal qualifications on such directed actions. This may seem closer to Kanger's original conception, as he embedded the (weakly expressed) direction of his rights in the one-indexed action operators. What would such a formula look like? We suggest 'O xEy A' which would read 'it is obligatory that x does A to y', and which might be useful as an explication of 'Claim(y,x,A)'. Assuming only the possibility of a reduction from directed to non-directed action (e.g. infer 'xE A' from 'xEy A', and not vice versa), we would be able to solve both the counterparty problem (e.g. no inference from 'O x E A' to 'Ox E y A', and hence to 'Claim(y,x,A)'), and our problem of inferring a permissive right between two parties from a general permission (e.g. no inference from 'P xE A' to 'PxEy A'). Furthermore, if Lindahl's conception of 'right' as embedding the notion of wrong is correct, useful conceptions of 'wrongdoings' easily lends themselves: That 'x does wrong to y' could for instance be explicated as 'O xEy A ^ ¬A'. However, these are but some very rough scetches made upon a large canvas. There are quite a number of questions that have to be answerred, some which may be nontrivial. But if our hunch is correct, this direction might just be right enough to shed a little more light on what we mean by saying that someone has a certain right. Oslo, 1993

1 0 In relation to directed obligations being interpreted as 'rights' (i.e. we will not consider the strong

consistency requirements).

10

Herrestad & Krogh

The Right Direction

A CKNOWLEDGEMENTS

We would like to thank Prof. Andrew Jones and Prof. Carlos Alchourrón for many helpful comments when discussing this paper with us.

REFERENCES

Hanson, Bengt (1970), Deontic Logic and Different Levels of Generality, Theoria, vol. 36, pp. 241 - 248. Hohfeld, Wesley Newcomb (1913) (1966), Fundamental Legal Conceptions - As Applied in Judicial Reasoning, Yale University Press, New Haven USA. Jones, Andrew J.I. & Sergot, Marek (1992), “Formal Specification of Security Requirements using the Theory of Normative Positions”, Proceedings of the European Symposium on Research in Computer Security - ESCORICS-92, Toulouse, November 1992. Kanger, Stig & Kanger, Helle (1966), "Rights and Parliamentarism", Theoria, vol. 32, pp. 85115. Kanger, Stig (1957) (1971), "New Foundation for Ethical Theory", in Hilpinen, Risto (ed.), Deontic Logic: Introductory and Systematic Readings, D. Reidel Publishing Company, Dordrecht Holland. Kanger, Stig (1972), “Law and Logic”, in Theoria, Vol. 38, pp. 105-132. Lindahl, Lars (1977), Position and Change - A Study in Law and Logic, D. Reidel Publishing Company, Dordrecht Holland. Lindahl, Lars (1991), "Stig Kanger's Theory of Rights", 9th Int. Congress of Logic, Methodology and Philosophy of Science, Uppsala Sweden. Makinson, David (1986), "On the Formal Representation of Right Relations", Journal of Philosophical Logic, Vol 15, s. 403-442.

11

Herrestad & Krogh

A PPENDIX 1

The Right Direction

K ANGER -E QUIVALENT A TOMIC P OSITIONS WITH I N D E X E D O BLIGATIONS

Note that 'O¬E(x,A) ^ O¬E(x,¬A)' is rewritten as 'O Passivex A'. Nº1 Nº2 Nº3 Nº4 Nº5 Nº6 Nº7 Nº8 Nº9 Nº10 Nº11 Nº12 Nº13 Nº14 Nº15 Nº16 Nº17 Nº18 Nº19 Nº20 Nº21 Nº22 Nº23 Nº24 Nº25 Nº26

xOy E(x,A) ^ yOx ¬E(y,¬A) ^ yPx E(y,A) ^ yPx ¬E(y,A) xOy E(x,A) ^ yOx E(y,A) xOy E(x,A) ^ yOx Passivey A xOy E(x,¬A) ^ yPx E(y,¬A) ^ yOx ¬E(y,A) ^ yPx ¬E(y,¬A) xOy E(x,¬A) ^ yOx E(y,¬A) xOy E(x,¬A) ^ yOx Passivey A xOy Passivex A ^ yPx E(y,¬A) ^ yPx E(y,A) xOy Passivex A ^ yPx E(y,¬A) ^ yOx ¬E(y,A) ^ yPx ¬E(y,¬A) xOy Passivex A ^ yOx E(y,¬A) xOy Passivex A ^ yOx ¬E(y,¬A) ^ yPx E(y,A) ^ yPx ¬E(y,A) xOy Passivex A ^ yOx E(y,A) xOy Passivex A ^ yOx Passivey A xPy ¬E(x,A) ^ xOy ¬E(x,¬A) ^ xPy E(x,A) ^ yPx E(y,¬A) ^ yPx E(y,A) xPy ¬E(x,A) ^ xOy ¬E(x,¬A) ^ xPy E(x,A) ^ yPx E(y,¬A) ^ yOx ¬E(y,A) ^ yPx ¬E(y,¬A) xPy ¬E(x,A) ^ xOy ¬E(x,¬A) ^ xPy E(x,A) ^ yOx ¬E(y,¬A) ^ yPx E(y,A) ^ yPx ¬E(y,A) xPy ¬E(x,A) ^ xOy ¬E(x,¬A) ^ xPy E(x,A) ^ yOx ¬E(y,¬A) ^ yOx E(y,A) xPy ¬E(x,A) ^ xOy ¬E(x,¬A) ^ xPy E(x,A) ^ yOx Passivey A xPy ¬E(x,¬A) ^ xPy E(x,¬A) ^ xOy ¬E(x,A) ^ yPx E(y,¬A) ^ yPx E(y,A) xPy ¬E(x,¬A) ^ xPy E(x,¬A) ^ xOy ¬E(x,A) ^ yPx E(y,¬A) ^ yOx ¬E(y,A) ^ yPx ¬E(y,¬A) xPy ¬E(x,¬A) ^ xPy E(x,¬A) ^ xOy ¬E(x,A) ^ yOx E(y,¬A) xPy ¬E(x,¬A) ^ xPy E(x,¬A) ^ xOy ¬E(x,A) ^ yOx ¬E(y,¬A) ^ yPx E(y,A) ^ yPx ¬E(y,A) xPy ¬E(x,¬A) ^ xPy E(x,¬A) ^ xOy ¬E(x,A) ^ yOx Passivey A xPy E(x,¬A) ^ xPy E(x,A) ^ yPx E(y,¬A) ^ yPx E(y,A) xPy E(x,¬A) ^ xPy E(x,A) ^ yPx E(y,¬A) ^ yOx ¬E(y,A) ^ yPx ¬E(y,¬A) xPy E(x,¬A) ^ xPy E(x,A) ^ yOx ¬E(y,¬A) ^ yPx E(y,A) ^ yPx ¬E(y,A) xPy E(x,¬A) ^ xPy E(x,A) ^ yOx Passivey A

A PPENDIX 2 Nº1 Nº2 Nº3 Nº4 Nº5 Nº6 Nº7 Nº8

E XTRA A TOMIC P OSITIONS WITH I NDEXED O BLIGATIONS

xOy E(x,A) ^ yPx E(y,¬A) ^ yPx E(y,A) xOy E(x,A) ^ yPx E(y,¬A) ^ yOx ¬E(y,A) ^ yPx ¬E(y,¬A) xOy E(x,¬A) ^ yPx E(y,¬A) ^ yPx E(y,A) xOy E(x,¬A) ^ yOx ¬E(y,¬A) ^ yPx E(y,A) xPy ¬E(x,A) ^ xOy ¬E(x,¬A) ^ xPy E(x,A) ^ yOx E(y,¬A) xPy ¬E(x,¬A) ^ xPy E(x,¬A) ^ xOy ¬E(x,A) ^ yOx E(y,A) xPy E(x,¬A) ^ xPy E(x,A) ^ yOx E(y,¬A) xPy E(x,¬A) ^ xPy E(x,A) ^ yOx E(y,A)

12