Chisholm, Roderick M., Contrary-to-duty Imperatives and Deontic Logic. Analysis 24 (1963) 33-36  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Imperatives One of the most serious paradoxes in (standard) deontic logic involves the notion of contrary to duty imperatives. These have to do with the specification of norms in case some other norm(s) have already been violated. The best known example is the one given by Chisholm ([Chi63]) consider the following statements in natural language: i) iv) You ought to go to the party If you go to the party, you ought to tell you re coming If you don t go, you ought not to tell you re coming You don t go to the party. Intuitively, this set of statements is perfectly ....

R,M. Chisholm, Contrary-to-Duty Imperatives and Deontic Logic, Analysis 24, 1963, pp. 33-36.

....as the necessity of introducing hierarchies of sub sub ideal, sub sub sub ideal worlds and so forth. 6 Dealing with CTD Paradoxes Now, let us see how to deal in our system with some of the most infamous paradoxes of CTD reasoning. In particular, we want to give a formal account of Chisholm s [6] and Forrester s [7] paradoxes, Belzer s [4] Reykjavik scenario and Makinson s [12] Mobius strip example . Since these puzzles are well known in the deontic logic community we shall not recall any of their intuitive examples but we will confine our analysis to their logical representation in ....

R. M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33--36, 1963.

....Imperatives One of the most serious paradoxes in (standard) deontic logic involves the notion of contrary to duty imperatives. These have to do with the specification of norms in case some other norm(s) have already been violated. The best known example is the one given by Chisholm ([Chi63]) consider the following statements in natural language: i) ii) iii) You ought to go to the party If you go to the party, you ought to tell you re coming If you don t go, you ought not to tell you re coming 12 (iv) You don t go to the party. Intuitively, this set of statements is ....

R,M. Chisholm, Contrary-to-Duty Imperatives and Deontic Logic, Analysis 24, 1963, pp. 33-36. 19

....murder implies murder g k. Hansson [27] proposed a simple, but popular dyadic deontic logic which he called Dyadic Standard Deontic Logic 3 (DSDL3) DSDL3 was developed to formalize contrary to duty (CTD) reasoning as it occurs in Forrester s and Chisholm s notorious deontic paradoxes [15,25,52,53,71]. The obligation for given is true, which we write as (where Hansson writes ( j ) if the preferred worlds are worlds. For example, it can consistently represent Forrester s paradox by Smith should not murder Jones :k, but if he murders him, then he should do it gently k g ....

....not derive :a t from t, because once the obligation to go to the assistance has been violated you also do not have to tell them that you will come. In fact, we consistently may have that if your do not go, then you are forbidden to tell that you are coming, a:t, like in Chisholm s paradox [15]. Finally, the structural similarity between conditional obligation a f and the defeasible conditional a ) f is simply caused by the analogous semantic de nition, and does not hint at any deeper similarity. The relation between violability and defeasibility is a complex issue, which has ....

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R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33-36, 1963.

....of the form O t expressing that in all world courses that are possible from time t onwards and are as perfect as possible given that is the case in them is the case. Van Eck uses these modality ideas to solve contrary to duty paradoxes such as a certain version of the Chisholm paradox 1 [6, 19]. The notions of temporal necessity and obligation as considered by Van Eck are very different from our temporal and deontic operators. Van Eck s obligation may be viewed as a temporal variant of a (deontic) conditional, whereas our obligation operator has no such flavour. Some work that, in ....

Chisholm,R.M. Contrary-to-Duty imperatives and deontic logic. Analysis 24 (1963),33-36.

....where the deontic operators O (for Obligation) and P (for Permission) were introduced together with a small number of axioms stating their properties and interrelationships. It soon turned out, however, that von Wright s system entailed several nasty paradoxes, most notably the Chisholm paradox, [Chisholm63]. In attempts to avoid these paradoxes, several other deontic systems were developed during the following decades. In 1964, von Wright extended his original system to a system for dyadic logic [Wright64] where conditional obligations were introduced. In 1958, Anderson suggested in [Anderson58] a ....

R. M. Chisholm, "Contrary-to-duty Imperatives and Deontic Logic", Analysis, vol. 24, pp. 33-36, 1963.

....where the deontic operators O (for Obligation) and P (for Permission) were introduced together with a small number of axioms stating their properties and interrelationships. It soon turned out, however, that von Wright s system entailed several nasty paradoxes, most notably the Chisholm paradox, [Chisholm63]. In attempts to avoid these paradoxes, several other deontic systems were developed during the following decades. In 1964, von Wright extended his original system to a system for dyadic logic [Wright64] where conditional obligations were introduced. In 1958, Anderson suggested in [Anderson58] a ....

R. M. Chisholm, "Contrary-to-duty Imperatives and Deontic Logic", Analysis, vol. 24, pp. 33-36, 1963.

....where the obligation to keep promises is violated. Reasoning structures like ff 1 should be (done) but if :ff 1 is (done) then ff 2 should be (done) must be formalized without running into the notorious contrary to duty paradoxes of deontic logic like Chisholm s and 5 Forrester s paradoxes [Chi63, For84]. The conceptual issue of these paradoxes is how to proceed once a norm has been violated. Clearly this issue is of great practical relevance, because in most applications norms are violated frequently. Usually it is stipulated in the fine print of a contract what has to be done if a term in the ....

R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33--36, 1963.

....of the operators O (for Obligation) and P (for Permission) The usability of a deontic language does not, according to Hansson, entail the feasibility of employing a deontic logic. The reason for this, apparently, is that deontic logic is infamous for its paradoxes, most notably Chisholm s paradox [7]. There are two problems with Hansson s argument, as we see it. First, operating with a deontic language, only, i.e. a language for expressing the relationship between what obtains and what ought to obtain, does not necessarily make it clear what we mean by these terms. Having a deontic logic at ....

Roderick M. Chisholm. Contrary--to--duty imperatives and deontic logic. Analysis, 24:33-- 36, 1963.

....RL92, Smi94, Roy96] The problem, however, is that deontic logic is hampered by the so called deontic paradoxes. The contrary to duty paradoxes like the notorious Chisholm paradox are the classic benchmark problems of deontic logics, which have initiated developments of monadic deontic logics [Chi63, For84], dyadic deontic logics [Tom81] and temporal deontic logics [vE82] In this article we analyze certain aspects of the paradoxes in dyadic deontic logics, in which an obligation O## j ## is read as # should be the case if # is the case. An obligation O##j## is a contrary to duty obligation of the ....

....sets S = fO#:kj##;O#g k jk#g, S 0 = fO#aj##;O#tja#;O#:tj:a#g, and S 00 = fO#:a j##;O#a p j##;O#:p j a#g,where# stands for any tautology. S formalizes the Forrester paradox [For84] when k is read as killing someone and g k as killing someone gently, S 0 formalizes the Chisholm paradox [Chi63] when a is read as a certain man going to the assistance of his neighbors and t as the man telling his neighbors that he will come, and finally, S 00 formalizes the apples and pears example [TvdT96] when a is read as buying apples and p as buying pears. The last obligation of each premise ....

R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33--36, 1963.

....where the obligation to keep promises is violated. Reasoning structures like ff 1 should be (done) but if :ff 1 is (done) then ff 2 should be (done) must be formalized without running into the notorious contrary to duty paradoxes of deontic logic like Chisholm s and Forrester s paradoxes [9,13]. The conceptual issue of these paradoxes is how to proceed once a norm has been violated. Clearly this issue is of great practical relevance, because in most applications norms are violated frequently. Usually it is stipulated in the fine print of a contract what has to be done if a term in the ....

....most important deontic benchmark examples related to CP, DP and SP have been summarized in Table 1 below, in which stands for a contradiction like p :p. 2.1. Contrary to duty problem (CP) CP is the major problem of monadic deontic logic, as shown by the notorious Good Samaritan [2] Chisholm [9] and Forrester [13] paradoxes. The formalization of these paradoxes should be consistent. For example, the formalization of Forrester s paradox in monadic deontic logic is Smith should not kill Jones (O:k) if Smith kills Jones, then he should do it gently (k Og) and Smith kills Jones (k) ....

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R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33--36, 1963.

....is extended as follows. ffl if OE = ideal(ffjfi) then if pref(oe; fi) ff, then oe[OE] oe; otherwise, oe[OE] 1. ffl if OE = ideal (ffjfi) then if pref (oe; fi) ff, then oe[OE] oe; otherwise, oe[OE] 1. The following contrary to duty paradox called Chisholm s paradox (Chisholm, 1963) illustrates how the two operators oblige and ideal are combined, and a fortiori how the two inference patterns strengthening of the antecedent and weakening of the consequent are combined. The contraryto duty paradoxes are important benchmark problems of deontic logic. The examples also ....

Chisholm, R. (1963). Contrary-to-duty imperatives and deontic logic. Analysis, 24:33--36.

....conditional (a; x) if and only if b (a x) is classically inconsistent. Due to the consistency check, primary and secondary conditionals cannot be combined in a proof, nor can one be derived from the other. For example, consider a decision theoretic variant of the so called Chisholm paradox [1]. A robot may have the goal to get me some coffee ( c) to inform me that coffee will arrive if it gets me some coffee (c; i) and not to inform me that coffee will arrive if it does not get me coffee ( c; i) The secondary conditional ( c; i) refers to the no coffee context in which ....

....of reusable output can be combined with context sensitivity in a logic that is besides monotonic and compact also idempotent. This combination (without conflict tolerance) has been discussed during three decades of research in deontic logic, following the publication of Chisholm s paradox [1] and several other notorious deontic paradoxes, and more recently it has been discussed (together with conflict tolerance) in qualitative decision theory. Several approaches have been proposed, see e.g. 13] for a survey, but no consensus has been reached. The derivation of ( c; i) from ( c) and ....

R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33--36, 1963.

....prakken.tex Date: December 17, 1996 Time: 17:18 240 HENRY PRAKKEN AND MAREK SERGOT Another usage of the terms is that of Jones and P orn (1985) who also discuss CTD structures, but of a different form. We can illustrate it by reference to a timeless version of the Chisholm (1963) scenario, as in (Prakken and Sergot, 1994, 1996) Suppose that: there must be no dog around the house, and if there is no dog, there must be no warning sign, but if there is a dog, there must be a warning sign. Obviously, if there is a dog, the conditional obligation that there must be no sign ....

Chisholm, R. M. (1963). Contrary-to-duty imperatives and deontic logic. Analysis 24:33--36.

....be in force. Consequently, obligations are contextdependent. The so called violation context of an obligation distinguishes between ideal and varying sub ideal contexts to formalize contrary to duty (hereafter: CTD) reasoning as it occurs in Forrester s and Chisholm s notorious deontic paradoxes [9, 13, 23, 24, 36]. In these paradoxes obligations referring to the ideal context conflict with obligations referring to the sub ideal context. If the violation context is left implicit, then the paradoxes result in a counterintuitive inconsistency. This type of context should be distinguished from epistemic or ....

....consider this kind of semantic extensions. In contextual deontic logic we cannot represent the problematic conditions that occur later than the consequents, as the obligation in Chisholm s notorious paradox if the man goes to the assistance, then he should tell them before that he will come [9]. We thus solve the backwards version of the paradox by restricting the language, see [34] for a discussion. The following example adapted from Pearl [22] further illustrates the dynamic preference semantics. Example 3 (Switch [22] We will test the assertability of the following dialogue: ....

R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33-- 36, 1963.

.... the ideal state of the context of deliberation we have that Smith kills Jones gently (g) oblige :k; oblige(gjk) k fl oblige g T [oblige k] k k,g [k] k,g k k k, g [oblige (g k) k, g Figure 5: Forrester s paradox Our second example of contrary to duty paradoxes in dus is Chisholm s paradox (Chisholm, 1963). 14 Example 6 (Chisholm) Consider the sentences a certain man should go to the assistance of his neighbors (oblige a) if the man goes to their assistance, then he should tell them he will come (oblige(tja) if the man does not go to the assistance, then he should not tell them he will ....

Chisholm, R. (1963). Contrary-to-duty Imperatives and Deontic Logic. Analysis 24: 33--36.

....(done) For most ff and fi the first set can be transformed to the second one without changing the meaning of the sentences. It has been argued that temporal deontic logic therefore solves the paradox [vE82, LB83] However, this solution does not work for the original set given by Chisholm [Chi63] in which ff is read as a certain man goes to the assistance of his neighbors and fi as the man tells his neighbors that he will come. For example, 2. if a certain man goes to the assistance of his neighbors, then the man ought to tell his neighbors that he will come means something ....

....of Off 1 when fi logically implies ff 1 . The condition of an ATD obligation is satisfied only if the primary obligation is fulfilled. The Chisholm paradox can be represented in SDL by several different sets of SDL formulas, which are either inconsistent or logically dependent, see e.g. Chi63, Aqv67, Smi94] We first give an inconsistent representation. Example 1 (Chisholm paradox) Let T = fOa; O(a t) a O:t; ag, where a is read as a certain man goes to the assistance of his neighbors and t as he tells them that he will come. The second obligation is an ATD obligation and ....

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R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33-- 36, 1963.

.... the ideal state of the context of deliberation we have that Smith kills Jones gently (g) oblige :k; oblige(gjk) k fl ideal g T [oblige k] k k,g [k] k,g k k k, g [oblige (g k) k, g Figure 8: Forrester paradox Our second example of contrary to duty paradoxes in dus is the Chisholm paradox [Chi63]. Example 10 (Chisholm) Consider the sentences a certain man should go to the assistance of his neighbors (oblige a) if the man goes to their assistance, then he should tell them he will come (oblige(tja) if the man does not go to the assistance, then he should not tell them he will come ....

R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33--36, 1963.

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Chisholm, Roderick M., Contrary-to-duty Imperatives and Deontic Logic. Analysis 24 (1963) 33-36

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R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33-36, 1963.

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R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33-36, 1963.

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R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33--36, 1963.

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CHISHOLM R. M., "Contrary-To-Duty Imperatives and Deontic Logic", Analysis, vol. 24, 1963, p. 33--36.

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R,M. Chisholm, Contrary-to-Duty Imperatives and Deontic Logic, Analysis 24, 1963, pp. 33-36.

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#6# R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis,

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