We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conflicts, and (ii) map each premise set to a sufficiently rich consequence set. In order to meet (i), we define the logic LNP, a conflict- and gap-tolerant logic of norm-propositions capable of formalizing both normative conflicts and normative gaps within the object language. Next, we strengthen LNP within the adaptive logic framework for non-monotonic reasoning in order to meet (...) (ii). This results in the adaptive logics LNPr and LNPm, which interpret a given set of premises in such a way that normative conflicts and normative gaps are avoided ‘whenever possible’. LNPr and LNPm are equipped with a preferential semantics and a dynamic proof theory. (shrink)

We present the inconsistency-adaptive deontic logic DP r , a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as O A ∧ O ∼A, O A ∧ P ∼A or even O A ∧ ∼O A. On the other hand, DP r still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DP r interprets a given premise set ‘as normally (...) as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DP r , others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DP r. (shrink)

Deontic logic as a way of formally reasoning about norms, an important area in AI and law, has traditionally concerned itself about formalising provisions of general statutes. Despite the long history of deontic logic, given the wide scope of the logic, it is difficult, if not impossible, to formalise all these notions in a single formalism, and there are still ongoing debates on appropriate semantics for deontic modalities in different contexts. In this paper, we restrict our attention to contracts between (...) interactive parties, which are both general enough to be an interesting object of study but specific enough so as to narrow down the debates regarding the meaning of modalities, and present a formalism for reasoning about them. (shrink)

This article examines the anxiety expressed by von Wright over the status of the deontic permission, P, as an independent normative category, given the interdefinability between P and O at the foundation of deontic logic. Two concerns are noted: the reducibility of P to O, and the inadequacy of P to convey a full permission in a social setting. Drawing on resources from the Hohfeldian analytical framework, the relational and aggregate features of permission are explored, and an aggregate conception of (...) permission, P, is recognized. With the assistance of insights from Demey and Smessaert on duals, Hansson on formalization, and Soames on interdefinability, it is concluded that the interdefinability thesis can be defended without threatening the independent status of P. Additional grounds for reaching this conclusion are provided from a detailed analysis of the relationship between P and P. Some implications of the more expansive notion of permission, P, are considered with regard to the resources of deontic logic and their application. (shrink)

The program put forward in von Wright's last works defines deontic logic as ``a study of conditions which must be satisfied in rational norm-giving activity'' and thus introduces the perspective of logical pragmatics. In this paper a formal explication for von Wright's program is proposed within the framework of set-theoretic approach and extended to a two-sets model which allows for the separate treatment of obligation-norms and permission norms. The three translation functions connecting the language of deontic logic with the language (...) of the extended set-theoretical approach are introduced, and used in proving the correspondence between the deontic theorems, on one side, and the perfection properties of the norm-set and the ``counter-set'', on the other side. In this way the possibility of reinterpretation of standard deontic logic as the theory of perfection properties that ought to be achieved in norm-giving activity has been formally proved. The extended set-theoretic approach is applied to the problem of rationality of principles of completion of normative systems. The paper concludes with a plaidoyer for logical pragmatics turn envisaged in the late phase of Von Wright's work in deontic logic. (shrink)

This paper provides an analysis of contrary-to-duty reasoning from the proof-theoretical perspective of category theory. While Chisholm’s paradox hints at the need of dyadic deontic logic by showing that monadic deontic logics are not able to adequately model conditional obligations and contrary-to-duties, other arguments can be objected to dyadic approaches in favor of non-monotonic foundations. We show that all these objections can be answered at one fell swoop by modeling conditional obligations within a deductive system defined as an instance of (...) a symmetric monoidal closed category. Using category theory as a foundational framework for logic, we show that it is possible to model conditional normative reasoning and conflicting obligations within a monadic approach without adding further operators or considering deontic conditionals as primitive. (shrink)

Moral obligation and permissibility are usually thought to be interdefinable. Following the pattern of the duality definitions of necessity and possibility, we have that something’s being permissible could be defined as its not being obligatory to not do it. And that something’s being obligatory could be defined as its not being permissible to not do it. In this paper, I argue that neither direction of this alleged interdefinability works. Roughly, the problem is that a claim that some act is obligatory (...) or permissible entails that there is a moral law, whereas a negative claim that some act is not obligatory or not permissible does not. Nevertheless, one direction of the interdefinability can potentially be salvaged. I argue that, if we do not require the conceptual possibility of moral dilemmas, then there is a way to plausibly define obligation in terms of permissibility. I conclude that permissibility is the only feasible deontic primitive. (shrink)

This paper concerns a thorny problem posed by conditional requirements: we expect some modal conditionals of the form ‘if p, then it must be that p’ to be false, yet they all come out true given two basic assumptions needed to account for ordinary conditional requirement like ‘If the light turns red, then cars must stop’. The first assumption is a semantic expectation linking conditional requirements with absolute ones, the second is the possible-worlds-based definition of modal sentences. Keeping the former (...) means giving up the latter, a result with profound implications for Kratzer’s formal semantics, modifications thereof, as well as deontic logics. (shrink)

Two parallelism hypotheses have been adopted and the third one on their relationship has been put forward. The illocutionary logic hypothesis states that the logic of linguistic commitments runs parallel to the logic of intentionality. The normative pragmatics hypothesis states that the logic of utterances runs parallel to the logic of linguistic commitments. According to the third stance or the logic projection hypothesis, the logic of utterances is the origin of all other logics used in describing psychological and social realities. (...) Consequently, the imperative logic or logic of utterances constitutes an independent but not self-sufficient research topic. The logic of utterances manifests itself in its meaning effects such as deontic and bouletic ones. It can be studied only in relation to deontic logics of the hearer’s obligation and the speaker’s linguistic commitments and in relation to logics of intentionality of the speaker’s expression and the hearer’s impression. Therefore, research in logic of imperative and other utterances must include investigation of relations between logics. (shrink)

Deontic logic is standardly conceived as the logic of true statements about the existence of obligations and permissions. In his last writings on the subject, G. H. von Wright criticized this view of deontic logic, stressing the rationality of norm imposition as the proper foundation of deontic logic. The present paper is an attempt to advance such an account of deontic logic using the formal apparatus of update semantics and dynamic logic. That is, we first define norm systems and a (...) semantics of norm performatives as transformations of the norm system. Then a static modal logic for norm propositions is defined on that basis. In the course of this exposition we stress the performative nature of (i) free choice permission, (ii) the sealing legal principle and (iii) the social nature of permission. That is, (i) granting a disjunctive permission means granting permission for both disjuncts; (ii) non-prohibition does not entail permission, but the authority can declare that whatever he does not forbid is thereby permitted; and (iii) granting permission to one person means that all others are committed to not prevent the invocation of that permission. (shrink)

In this paper, the set-theoretic approach in the logical theory of normative systems is extended using Broome’s definition of the normative code function. The syntax and semantics for first order metanormative language is defined, and metanormative language is applied in the formalization of the basic principles in Broome’s approach and in the construction of a logical typology of normative systems. Special attention is given to the types of normative systems which are not definable in terms of the properties of singular (...) sets of requirements (e.g. the realization equivalence of codes, the social compatibility of codes, and the compatibility of codes issued by different normative sources). Examples are given of the application of the typology in the interpretation of philosophical texts. Von Wright’s hypothesis on the connection of logical properties of normative systems, conceived set-theoretically, with standard deontic logic is proved by introducing the translation function between the metanormative language and the restricted language of standard deontic logic. The translation reveals that von Wright’s hypothesis must be appended. The problems of narrow and wide scope readings of the deontic conditionals and of the meaning of iterated deontic operators are addressed using the distinction between relative and absolute normative codes. The theorem on the existence of a realization equivalent absolute code for any relative code is proved. (shrink)

The programmatic statement put forward in von Wright's last works on deontic logic introduces the perspective of logical pragmatics, which has been formally explicated here and extended so to include the role of norm-recipient as well as the role of norm-giver. Using the translation function from the language of deontic logic to the language of set-theoretical approach, the connection has been established between the deontic postulates, on one side, and the perfection properties of the norm-set and the counter-set, on the (...) other side. In the study of conditions of rational norm-related activities it has been shown that diverse dynamic second-order norms related to the concept of the consistency norm-system hold: -- the norm-giver ought to restore ``classical'' consistency by revising an inconsistent system, -- the norm-recipient ought to preserve an inconsistent system by revision of its logic so that inconsistency does not imply destruction of the system. Dialetheic deontic logic of Priest is a suitable logic for the purpose since it preserves other perfection properties of the system. (shrink)