This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

A study in the logic of theory change, examining the properties of maxichoice contraction and revision operations.

This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of safe contraction of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its properties both in general and (...) under various natural constraints. (shrink)

Investigates the resolution of contradictions and ambiguous derogations in a code, by means of the imposition of partial orderings.

Investigates the resolution of contradictions and ambiguous derogations in a code, by means of the imposition of partial orderings. Although formulated as a study in the logic of norms, it provided the initial ideas for work on the logic of theory (or belief) change, developed by the authors in a series of papers by the authors and Peter Gardenfors beginning in 1985.

In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet contraction over that theory. The purpose (...) of the present paper is to study the relationship more finely, by seeking an explicit map between the component orderings involved in each of the two kinds of contraction. It is shown that at least in the finite case a suitable map exists, with the consequence that the relational, transitively relational, and antisymmetrically relational partial meet contraction functions form identifiable subclasses of the safe contraction functions, over any theory finite modulo logical equivalence. In the process of constructing the map, as the composition of four simple transformations, mediating notions of bottom and top contraction are introduced. The study of the infinite case remains open. (shrink)

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.

Between the two horns of Jørgensen's dilemma, the authors opt for that according to which logic deals not only with truth and falsity but also with those concepts not possessing this semantic reference. Notwithstanding the “descriptive” prejudice, deontic logic has gained validity among modal logics. The technical foundation proposed consists in an abstract characterization of logical consequence. By identifying in the abstract notion of consequence the primitive from which to begin, it is possible to define the connectives - even those (...) of obligation - by means of the rules of introduction or elimination in a context of derivation. (shrink)

The main purpose of this paper is to explore the role played by logic in the legal domain. In the traditional conception which underlies the movement of codification, judges are able to find in the legal system (the Master System) a unique answer for every legal problem. This entails its completeness, consistency and the possibility of deriving from it the contents of all judicial decisions. Although the ideal model of this conception is supported by important theoretical and political ideals, it (...) has significant shortcomings. The elements of normative systems (Master Systems) are “norms” and not mere “norm-formulations.” A “norm” is the meaning attributed to normative linguistic expressions. The set of all normative expressions, such as statutes, codes, etc. forms what is called the Master Book. One of the main problems for the ideal model is the identification of a normative system behind the Master Book. Interpretative arguments are the tools designed to solve these problems. Although the requirements of the model are not totally fulfilled in actual practice, it remains as an effective ideal rational goal behind legal activities linked to adjudication and most theoretical approaches to law. (shrink)

The main purpose of this paper is to explore the role played by logic in the legal domain. In the traditional conception which underlies the movement of codification, judges are able to find in the legal system (the Master System) a unique answer for every legal problem. This entails its completeness, consistency and the possibility of deriving from it the contents of all judicial decisions. Although the ideal model of this conception is supported by important theoretical and political ideals, it (...) has significant shortcomings. The elements of normative systems (Master Systems) are “norms” and not mere “norm‐formulations.” A “norm” is the meaning attributed to normative linguistic expressions. The set of all normative expressions, such as statutes, codes, etc. forms what is called the Master Book. One of the main problems for the ideal model is the identification of a normative system behind the Master Book. Interpretative arguments are the tools designed to solve these problems. Although the requirements of the model are not totally fulfilled in actual practice, it remains as an effective ideal rational goal behind legal activities linked to adjudication and most theoretical approaches to law. (shrink)

1. EI dilema de Jørgensen. 2. La salución propuesta. 3. Breve historia de un prejudicio filosófico. 4. Normas sin lógica. 4.1. Imperativos sin lógica. 4.2. Normas y proposicienesnormativas. 4.3. Proposiciones normativas y normas verdaderas. 4.4. Mundos posibles. 4.5. Validez e invalidez. 4.6. La racionalidad del legislador. 5. La noción abstracta, sintáctica y semántica de consecuencia. 5.1. La noción abstracta de consecuencia. 5.2. La noción sintáctica de consecuencia. 5.3. La noción semántica de consecuencia. 5.4. EI sentido dado por las reglas de (...) uso en un contexto. 5.5. Qué operadores para la lógica. 5.6. Solo en un contexto la parte cobra sentido. 6. La lógica deóntica. 7. De donde la solución del dilema interesa a toda la lógica. 8. Consecuendas para la informática. (shrink)

Standardly, the usual approach to rationality is based on the notion of ‘being a reason for’. Honouring the traditional distinction between practical and theoretical philosophy, reasons are classified as justificative and explicative. In both cases, a reason-statement has the form ‘’. For reasons of type , ‘A’ is a factual statement and ‘B’ is a statement which describes an action of the agent. The reason-statement has a prescriptive sense because ‘A is a reason for doing B’ means ‘A is a (...) reason an agent ought to do B’. So, it is advisable to schematize that kind of statements as ‘’, where ‘OB’ is a deontic statement prescribing the duty to do B. Reasons of type have a descriptive sense and do not require the above-mentioned constraint. But ‘being a reason for’ has different senses according to context, even when the distinction between justificative and explicative reasons is drawn. Accordingly, it is important to distinguish two basic types of reasons: sufficient and necessary, and two subordinate types of reasons: contributing and substitutive . A lot of attention has been paid, lately, to a sense of contributive reasons: prima facie reasons . The paper will deal with that kind of reasons. Its main thesis are: 1) prima facie reason-statements are defeasible conditionals ‘’ pointing out that A is a contributing condition of B, 2) a defeasible conditional has the properties of ‘’, where ‘ =>’ is a strict implication and ‘f’’ a revision-operator satisfying the conditions set up by the theory AGM on the rational change of theories. (shrink)