The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources (...) of classical logic. Among the contributions included in the volume, one chapter focuses on the “inferential preferential method”, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson’s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the role of logic in philosophy. (shrink)

Philosophers like G.H. von Wright and D. Makinson have pointed to serious challenges regarding the foundations of deontic logic. In this paper, I suggest that to deal successfully with these challenges a reconsideration of the research program of the discipline is useful. Some problems that have troubled this particular field of logical study for decades may disappear or appear more tractable if we view them from the perspective of a language game introduced by D. Lewis involving three characters: the Master, (...) the Slave and the Kibitzer. The adoption of this perspective opens a natural approach to a new layout of the domain of deontic studies. I propose dividing deontic logic into six sub-areas which are distinguished by their focus on the different idioms typical of the individual players, by conceiving the language game as either being static or as dynamic and by the aims of the logical inquiry. What kind of insights the proposed perspective provides is illustrated by an analysis of the so-called Ross paradox—a problem that has troubled deontic logic since its origins and, though it was many times pronounced solved, still keeps coming back ‘alive and kicking’. (shrink)

This article models legal interpretation through argumentation and provides a logical analysis of interpretive arguments, their conflicts, and the resulting indeterminacies. Interpretive arguments are modelled as defeasible inferences, which can be challenged and defeated by counterarguments and be reinstated through further arguments. It is shown what claims are possibly (defensibly) or necessarily (justifiably) supported by the arguments constructible from a given interpretive basis, i.e., a set of interpretive canons coupled with reasons for their application. It is finally established under what (...) conditions such arguments provide single outcomes or rather support alternative interpretive conclusions, thus leading to propositions of law whose truth‐value is undetermined. (shrink)

We shall introduce a set of fundamental legal concepts, providing a definition of each of them. This set will include, besides the usual deontic modalities (obligation, prohibition and permission), the following notions: obligative rights (rights related to other’s obligations), permissive rights, erga-omnes rights, normative conditionals, liability rights, different kinds of legal powers, potestative rights (rights to produce legal results), result-declarations (acts intended to produce legal determinations), and sources of the law.

This paper compares two ways of formalising defeasible deontic reasoning, both based on the view that the issues of conflicting obligations and moral dilemmas should be dealt with from the perspective of nonmonotonic reasoning. The first way is developing a special nonmonotonic logic for deontic statements. This method turns out to have some limitations, for which reason another approach is recommended, viz. combining an already existing nonmonotonic logic with a deontic logic. As an example of this method the language of (...) Reiter's default logic is extended to include modal expressions, after which the argumentation framework in default logic of [20, 22] is used to give a plausible logical analysis of moral dilemmas and prima facie obligations. (shrink)

In his last papers about deontic logic, von Wright sustained that there is no genuine logic of norms. We argue in this paper that this striking statement by the father of deontic logic should not be understood as a death sentence to the subject. Rather, it indicates a profound change in von Wright's understanding about the epistemic and ontological role of logic in the field of norms. Instead of a logical constructivism of deontic systems revealing a necessary structure of prescriptive (...) discourse, which marked his earlier efforts, he adopted the view that such systems should be seem as mere objects of comparison, i.e. as providing practical standards of rationality for normgiving activity. Within such view he proposed an interpretation of standard deontic logic in such a way to free deontic logicians from the philosophical difficulties related to the so-called Jørgensen's dilemma and deontic paradoxes. This effort, as we claim in the present paper, is an application of Wittgenstein's therapeutic method to dissolve philosophical difficulties caused by the use of logical tools to model relations between norms. (shrink)

The concept of legal power is important in the law since, with regard to actions having legal effect, the “exercise of legal power” delimits those actions for which manifestation of intention to achieve a legal effect is essential for the effect to ensue. The paper proposes a definition that captures this feature of legal power and marks it off from “direct effect,” as well as from permissibility and practical ability to achieve the legal effect. This analysis of power is limited (...) to the “immediate” legal power of a physical person characterized by the power-holder achieving a legal result by the power-holder's own behaviour. It is argued that in the literature on power the concept of legal power is frequently construed in such a way that it becomes either too broad or too narrow. (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 work adopts H. Kelsen’s concept of legal system, proposes a formal definition for such notion, and introduces an operational semantical framework for legal systems that are situated in agent societies. Agent societies are defined. Relevant formal properties of situated legal systems are discussed; the way they are exposed in the operational semantical framework is explained, and their truth formally proved. Also, for the sake of a better understanding of the legal-theoretic assumptions of the paper, recurring issues regarding Kelsen’s theory (...) of law are briefly reviewed. They are put in confrontation with the points of view of R. Dworkin, H. Hart, and J. Raz, and an attempt is made to clarify them from the perspective of the provided formalization. A brief case study in agent-based modeling and simulation of public policy processes is presented, as an illustration of the way of using situated legal systems, and the proposed operational semantical framework, in a practical application. (shrink)

Eugenio Bulygin mantiene la tesis según la cual la objetividad del derecho depende de la objetividad del conocimiento del derecho. Esta tesis depende de la distinción entre las normas y las proposiciones normativas. las proposiciones normativas son las que tienen que expresar ese conocimiento, en cuanto son aptas para ser verdaderas o falsas, a la inversa de las normas. Así, esa objetividad es una función de las condiciones de verdad de esas proposiciones. Como, además, según Bulygin, solo existen hechos en (...) la dimensión empírica, esas condiciones solo pueden referirse a esa clase de circunstancias. Sin embargo, se sostiene en este artículo, la distinción kelseniana entre sentidos subjetivos y objetivos y la idea correlativa de "validez normativa" plantean un problema a esa manera de entender las proposiciones normativas, a la hora de explicar la objetividad del derecho. Eugenio Bulygin supports the thesis according to which the objectivity of law depends on the objectivity of the knowledge of law. This thesis depends on the distinction between norms and normative propositions. Normative propositions are those that must express this knowledge, insofar as they are apt to be true or false, contrary to norms. Thus, this objectivity is a function of the truth conditions of these propositions. Also, as facts only exist in the empirical dimension according to Bulygin, these conditions can only refer to this class of circumstances. However, the Kelsenian distinction between subjective and objective senses and the idea of "normative validity", this article claims, poses a problem for this way of understanding normative propositions when it comes to explaining the objectivity of law. (shrink)

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)

Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results (...) and offers a list of unsolved problems that are in need of investigation. (shrink)

In the last papers published by Alchourrón, he attacked non-monotonic logics, which he considered philosophically unsound for the representation of defeasible reasoning. Instead of a non-monotonic consequence relation, he proposed a formal representation of defeasibility based on an AGM-like revision of implicit assumptions connected to the premises. Given that this is a procedure to generate non-monotonic logics, it is not clear, from a mathematical standpoint, why he was so suspicious of such logics. In the present paper we try to answer (...) this question based on Alchourrón' s convictions about epistemology, particularly the epistemology of law. We also propose another revision operator on theories called refinement, which provides a faithful representation of the sort of epistemic change considered by Alchourrón as intrinsic to defeasibility. En sus últimos escritos publicados, Alchourrón desarrolló un ataque contra las lógicas no-monotónicas, que consideraba filosóficamente inadecuadas a la representación del razonamiento derrotable. En vez de una relación de consecuencia no-monotónica, él propuso una representación formal de la derrotabilidad basada en un modelo de revisión de las asunciones implícitas ligadas a las premisas. Dado que éste es un procedimiento para generar lógicas no-monotónicas, no está claro -en el nivel matemático- por qué él era tan desconfiado de tales lógicas. En el presente texto intentamos contestar a esta pregunta basados en las convicciones de Alchourrón sobre epistemología, particularmente la epistemología jurídica. También proponemos otro operador de revisión aplicado a las teorías, llamado refinamiento, que proporciona una representación fiel de la especie de cambio epistémico considerado por Alchourrón como intrínseco a la derrotabilidad. (shrink)

El objeto principal de este trabajo consiste en discutir una propuesta de C. Alchourrón y A. Martino para hacer frente al problema de la fundamentación de la lógica deóntica, planteado por el dilema de Jørgensen. La propuesta criticada se basa en la idea de que no existe obstáculo alguno en compatibilizar la idea de que las normas carecen de valor de verdad con la idea de que poseen una lógica, una vez que se renuncia al "prejuicio filosófico" de que es (...) indispensable caracterizar semánticamente las relaciones y propiedades lógicas y se explica la lógica a partir de la noción abstracta de consecuencia, desligándola de las nociones de verdad y falsedad. Sostienen que el significado de los operadores deónticos, al igual que el de los términos lógicos en la deducción natural, puede quedar totalmente expresado una vez que se explicita su uso mediante reglas de introducción y eliminación. Para ilustrar su propuesta, pretenden ofrecer una fundamentación puramente sintáctica de la lógica deóntica standard. Mis críticas se centran en tres puntos: a) no utilizan auténticas reglas de introducción para los operadores deónticos; b) no derivan la lógica deóntica standard como pretenden haber hecho, y c) no se establecen criterios para relacionar las fórmulas del cálculo con el lenguaje normativo ordinario, con lo que no existen razones para considerar que se trata de una lógica deóntica. Defiendo la idea de que, a los fines de fundamentar semánticamente la lógica deóntica, sólo es necesario que existan interpretaciones admisibles que atribuyan valores de verdad a las normas, y que este requisito es cumplido por la semántica usual de la lógica deóntica standard, con lo que el dilema de Jørgensen resulta ser un seudoproblema. In this paper I discuss a proposal from C. Alchourrón and A. Martino with which they try to face the problem posed to the foundation of deontic logic by Jørgensen' s dilemma. Their proposal is based on the idea that there is no problem at all in compatibilizing the fact that norms lack truth values with their possession of a logic, once it is denied that it is absolutely necessary to offer a semantic characterization of logical properties and relations, and the abstract notion of consequence is taken as primitive. They claim that the meaning of deontic operators, like that of logical terms in natural deduction, is completely expressed through their use, which is explained by means of rules of introduction and elimination. As an illustration, they present a calculus with which they intend to offer a foundation for standard deontic logic. I make three objections: a) They don' t use real rules of introduction for deontic operators; b) They don' t have derived standard deontic logic as they claim; c) There are no criteria for relating the formulas with ordinary normative discourse; so there are no reasons for considering their calculus as a deontic logic. I claim that, in order to give a semantical foundation to deontic logic it is only necessary that there are admissible interpretations that assign truth values to norms, and that this requisite is satisfied by the usual semantic of standard deontic logic. I conclude that Jørgensen' s dilemma is a pseudoproblem. (shrink)

Carlos Eduardo Alchourrón y Eugenio Bulygin efectuaron contribuciones de fundamental importancia para el desarrollo de la teoría de los sistemas jurídicos. Sus ideas evidencian una evolución de la presentación de una visión estática a una visión dinámica de tales sistemas. El objetivo central del presente trabajo consiste en mostrar que existe, no obstante, una cierta tensión en las tesis sostenidas por los autores entre dos concepciones diferentes de los sistemas jurídicos: por una parte, aquella que trata de reconstruir el conjunto (...) de las normas que resultan relevantes para la solución de un caso; por la otra, aquella que trata de ofrecer una caracterización satisfactoria del derecho como institución. Las diferentes finalidades que cada una de esas reconstrucciones persiguen obligan a refinar algunas ideas vinculadas con la dinámica del derecho para evitar derivaciones incompatibles con las intuiciones jurídicas ordinarias. Carlos Eduardo Alchourrón and Eugenio Bulygin have made contributions of fundamental importance for the development of the theory of legal systems. Their ideas reflex an evolution from a static to a dynamic vision of such systems. The main purpose of the present paper is to show that, notwithstanding, there exists a certain tension in the thesis defended by Alchourrón and Bulygin between two different conceptions of a legal system. On the one hand, a conception related to the reconstruction of the set of relevant norms to solve a certain case; on the other, a conception related to a satisfactory characterization of law as an institution. The different concerns of each of those reconstructions force to refine certain ideas associated with the dynamics of law to avoid derivations which appear incompatible with ordinary legal intuitions. (shrink)

It is argued that the distinction between the normative and the descriptive interpretation of norm sentences can be regarded as a distinction between two kinds of utterances. A norm or a directive has as its content a normative proposition. A normative utterance of a normative proposition in appropriate circumstances makes the proposition true, and an assertive utterance has as its truth-maker the norm system to which it refers. This account of norms, norm-contents, and utterances of norm sentences solves Jørgensen's problem: (...) logical relations among norms can be defined in the usual way in terms of the truth-conditions of the normative propositions which form their content. There is no distinction between the logic of norms and the logic of normative propositions; in this respect the present account differs from Carlos Alchourrón and Eugenio Bulygin's account of the logic of normative propositions. Se argumenta que la distinción entre la interpretación normativa y la descriptiva de las oraciones normativas puede ser considerada como una distinción entre dos tipos de emisiones. Una norma o directiva tiene como su contenido una proposición normativa. Una emisión normativa de una proposición normativa en circunstancias apropiadas hace verdadera la proposición y es el sistema de normas al que se refiere una emisión asertiva el que la hace verdadera. Esta concepción de normas, contenidos de normas y emisiones de oraciones normativas resuelve el problema de Jörgensen: las relaciones lógicas entre normas pueden ser definidas de manera usual en términos de las condiciones de verdad de las proposiciones normativas que forman su contenido. No hay diferencia alguna entre la lógica de normas y la lógica de proposiciones normativas; en este aspecto la presente concepción difiere de la concepción de la lógica de proposiciones normativas de Carlos Alchourrón y Eugenio Bulygin. (shrink)

El profesor Juan Carlos Bayón ha sostenido que el positivismo incluyente resultaría inaceptable por apoyarse en la idea de una convención social de seguir criterios no convencionales: si hubiera acuerdo sobre el contenido de esos criterios, ellos resultarían convencionales, y sin acuerdo, no habría práctica social convergente y, por ende, no habría en realidad una regla convencional. Así, el positivismo incluyente quedaría enfrentado a un dilema: o bien resulta indistinguible del positivismo excluyente, o bien no es una postura convencionalista en (...) absoluto. Este trabajo evaluará la posibilidad de una salida al dilema. Para ello, se efectuará un análisis de las diversas versiones del positivismo incluyente y sus límites a la luz de la objeción planteada. También se intentará demostrar la viabilidad de un contraargumento centrado en los alcances de la tesis de la convencionalidad, que bloquearía la acusación de inconsistencia teórica esgrimida en su contra. Professor Juan Carlos Bayón has argued that Inclusive Legal Positivism should be rejected because its plausibility depends on the idea of a social convention to follow nonconventional criteria of validity. In his view, if there were agreement on the content of these criteria, it would be impossible to sustain its non-conventional character; and without agreement, there would not be a common social practice, and thus no social rule would exist. Therefore, Inclusive Positivism faces a dilemma: being indistinguishable from Exclusive Positivism or not being a genuine form of conventionalism at all. This article evaluates a possible way out of this dilemma. It explores the different versions of Inclusive Legal Positivism and its limits, and tries to build an opposing argument grounded on the scope of the conventionality thesis that would rescue Inclusive Legal Positivism from the accusation of theoretical inconsistency. (shrink)