On deontic logic

Some requirements concerning deontic logic are formulated and discussed. Stress is laid on the need to distinguish between theories and deductive systems. It is argued that deontic theories need not be closed under the rule of detachment. Two deontic calculi, called DSC₁, DSC², are presented and talked over.This paper was delivered before the Conference on Practical and Philosophical Motivations of Non-Classical Logics, Toru, August 16, 1979.     

A deontic logic of action

The formal language studied in this paper contains two categories of expressions, terms and formulas. Terms express events, formulas propositions. There are infinitely many atomic terms and complex terms are made up by Boolean operations. Where and are terms the atomic formulas have the form = ( is the same as ), Forb ( is forbidden) and Perm ( is permitted). The formulae are truth functional combinations of these. An algebraic and a model theoretic account of validity are given and an axiomatic system is provided for which they are characteristic.The closure principle, that what is not forbidden is permitted is shown to hold at the level of outcomes but not at the level of events. In the two final sections some other operators are considered and a semantics in terms of action games.     

Conditional permission in deontic logic

Conclusion In the face of the considerations set forth above, I submit that Anderson's proposed definition (D) does not represent an acceptable construction of the concept of conditional permission. This, in turn, suggests that conditional permission must be viewed as a viable deontic relationship in its own right, and is not definable in terms of unconditional deontic concepts. It appears, then, that a reduction of conditional to unconditional deontic logic is not warranted.     

Moral relativism and deontic logic

If a native of India asserts “Killing cattle is wrong” and a Nebraskan asserts “Killing cattle is not wrong”, and both judgments agree with their respective moralities and both moralities are internally consistent, then the moral relativist says both judgments are fully correct. At this point relativism bifurcates. One branch which we call content relativism denies that the two people are contradicting each other. The idea is that the content of a moral judgment is a function of the overall moral point of view from which it proceeds. The second branch which we call truth value relativism affirms that the two judgments are contradictory. Truth value relativism appears to be logically incoherent. How can contradictory judgments be fully correct? For though there will be a sense of correctness in which each judgment is correct — namely by that of being correct relative to the morality relative to which each was expressed — if contradictory, the judgments cannot both be true, and thus cannot both be correct in this most basic sense of correctness. We defend truth value relativism against this sort of charge of logical incoherence by showing it can be accommodated by the existing semantical metatheories of deontic logic. Having done this we go on to argue that truth value relativism is the best version of relativism.     

A logic for deontic dilemmas

The possibility of deontic dilemmas poses a significant problem for deontic logic. Here I review some proposals to resolve this problem, and then offer a new account. This is a simple modification of standard deontic logic that enables the system to accommodate deontic dilemmas without inconsistency and without deontic explosion, while at the same time accounting for the range of genuinely valid inferences.     

A reasoning method for a paraconsistent logic

A proof method for automation of reasoning in a paraconsistent logic, the calculus C1* of da Costa, is presented. The method is analytical, using a specially designed tableau system. Actually two tableau systems were created. A first one, with a small number of rules in order to be mathematically convenient, is used to prove the soundness and the completeness of the method. The other one, which is equivalent to the former, is a system of derived rules designed to enhance computational efficiency. A prototype based on this second system was effectively implemented.     

Individualistic formal approach to deontic logic

Some people approve of certain general rules of behavior, or some concrete cases. The others disapprove of or are indifferent to them. In this paper I suggest an axiom system which formalizes the use of these utterances. It may be considered as a special (individualistic) approach to deontic logic.     

A utilitarian semantics for deontic logic

I am idebted to members of the Wellington Logic Seminar for useful discussions of work of which this essay forms part, in particular to M. J. Cresswell for comments in the earlier stages of the investigation and to R. I. Goldblatt who suggested the definition ofB _infD ^supu and made numerous other suggestions.     

Blueprint for a dynamic deontic logic

Extending the idiom of dynamic logic we outline a deontic logic in which deontic operators operate on terms rather than on formulæ. In a second step we distinguish between what we call real and deontic actions.     

Detachment and defeasibility in deontic logic

The purpose of the paper is to present a logical framework that allow to formalize a kind of prima facie duties, defeasible conditional duties, indefeasible conditional duties and actual (indefeasible) duties, as well as to show their logical interconnections.