Two approaches to the formalisation of defeasible deontic reasoning

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.An earlier version of this article was written while the author was working at the Department of Computing, Imperial College London, supported by ESRC/MRC/SERC Joint Council Initiative Project G9212036. Work on the present version was supported by a research fellowship of the Royal Netherlands Academy of Arts and Sciences, and by Esprit WG 8319 Modelage. I thank one of the referees for his interesting comments. Also, many thanks are due to Marek Sergot for valuable discussions on the topic of this paper.     

Moral dilemmas,disjunctive obligations,and Kant's principle that ‘ought’ implies ‘can’

In moral dilemmas, where circumstances prevent two or more equally justified prima facie ethical requirements from being fulfilled, it is often maintained that, since the agent cannot do both, conjoint obligation is overridden by Kant's principle that ought implies can, but that the agent nevertheless has a disjunctive obligation to perform one of the otherwise obligatory actions or the other. Against this commonly received view, it is demonstrated that although Kant's ought-can principle may avoid logical inconsistency, the principle is incompatible with disjunctive obligation in standard deontic logic, and that it entails paradoxically that none of the conflicting dilemma actions will in fact occur. The principle appears to provide the only plausible safeguard against deontic antinomy, but cannot be admitted because of its collision with considered moral judgments.     

Deontic database constraints,violation and recovery

The paper discusses the potential value of a deontic approach to database specification. More specifically, some different types of integrity constraints are considered and a distinction is drawn between necessary (hard) and deontic (soft) constraints.Databases are compared with other normative systems. A deontic logic for database specification is proposed and the problems of how to react to, and of how to correct, or repair, a situation which arises through norm violation are discussed in the context of this logic. The limitations of the proposed logic and possible modifications and extensions of it are analysed.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

The Definition of Moral Dilemmas: A Logical Problem

This paper concerns one of the undecided disputes of modern moral philosophy: the possibility of moral dilemmas. Whereas proponents of the possibility of moral dilemmas often appeal to moral experience, many opponents refer to ethical theory and deontic logic. My aim in this paper is to clarify some of the tension between moral experience and ethical theory with respect to moral dilemmas. In Part One I try to show that a number of logical arguments against the possibility of moral dilemmas, though apparently very different, turn out to be basically the same, as they are all based on the following concept of ought: if A ought to be done, doing B is impermissible and doing A itself is permissible. In Part Two I present an overview of several definitions of moral dilemmas that have been given by proponents of moral dilemmas: definitions that define moral dilemmas in terms of oughts and definitions that define them in terms of reasons. I conclude that, while reason is to weak, ought is too strong a concept to define moral dilemmas with. In this way, the arguments from Part One create a logical problem for proponents of the possibility of moral dilemmas to define moral dilemmas.     

Why we need a relevant theory of conditionals

This paper presents ConR (Conditional R), a logic of conditionals based on Anderson and Belnap's system R. A Routley-Meyer-style semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, A Relevant Theory of Conditionals (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis' theory of causation, Lewis' dyadic deontic logic, and Chellas' dyadic deontic logic.I am of course deeply indebted to André Fuhrmann, who co-wrote the paper on which the present effort is based. Perhaps I should also thank the Social Sciences and Humanities Research Council of Canada because the original research for this project was funded by them in the form of a post-doctoral fellowship.     

From negation to “notion”: Cognitive processes and argumentative strategies

Summary This article deals with the role of negation as a language and cognitive operation. Such a topic is treated here within the framework of the argumentative strategies which consist in making certain cognitive landmarks of the discourse flip over with the intent of imposing the necessity to choose between two types of notions, aiming at the transformation of this choice into an implication. The reference here to the Aristotelian logic of Prior Analytics appears to be more efficient than any other contemporary logic and the author intends to give account of the role of negation as contrary coming into play on an operational and cognitive basis in all the argumentative strategies which oscillate reciprocally from universal to particular.     

On the non-availability of Dawson-modeling into certain relevance alethic modal logics

This paper shows that the Dawson technique of modelling deontic logics into alethic modal logics to gain insight into deontic formulas is not available for modelling a normal (in the spirit of Anderson) relevance deontic modal logic into either of the normal relevance alethic modal logics R _S4or R _M. The technique is to construct an extension of the well known entailment matrix set M ₀and show that the model of the deontic formula P (A v B). PA v PB is excluded.     

Modal Logics of Succession for 2-Dimensional Integral Spacetime

We consider the problem of axiomatizing various natural successor logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages, and prove completeness theorems. We also establish that the irreflexive successor logic in the standard modal language (i.e. the language containing and ) is not finitely axiomatizable.     

Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours

In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough.     

Predicate Logics on Display

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem's modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap's display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules.     

The "Natural" and the "Formal"

The paper presents an argument against a metaphysical conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: the realm of the natural, constituted by the things of our empirical world, and the realm of the formal, constituted by the structures that we use as prisms to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic.     

Is “some-other-time” sometimes better than “sometime” for proving partial correctness of programs?

The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal logic increases the program verifying power of Bur. The change can be described either technically as replacing the reflexive version of S5 with an irreflexive version, or intuitively as using the modality some-other-time instead of sometime. Some insights into the nature of computational induction and its variants are also obtained.This project was supported by the Hungarian National Foundation for Scientific Research, Grant No. 1810.     

State-spaces and meaning relations among predicates

It has often been suggested that the meaning of terms is theory dependent. Bas van Fraassen has proposed a particular way of inferring which sentences are true in virtue of meaning, given a theory in so-called state-space format. I examine his claims by means of simple examples.     

Reasoning and logic

Gilbert Harman, in Logic and Reasoning (Synthese 60 (1984), 107–127) describes an unsuccessful attempt ... to develop a theory which would give logic a special role in reasoning. Here reasoning is psychological, a procedure for revising one's beliefs. In the present paper, I construe reasoning sociologically, as a process of linguistic interaction; and show how both reasoning in the psychologistic sense and logic are related to that process.     

Variations in use of the term “or”

Two studies showed that adults' responses to questions involving the term or varied markedly depending upon the type of question presented. When presented with various objects (A's and B's) and asked to circle all things which are A or B subjects tended to circle A's as well as B's, whereas when asked to circle all the A's or B's subjects showed a relatively stronger tendency to circle one or the other. Moreover the nature of the sets of objects (As and Bs) influenced behavior as well. There was also evidence that the effects due to question wording or set type transferred.     

On Extensions of Intermediate Logics by Strong Negation

In this paper we will study the properties of the least extension n() of a given intermediate logic by a strong negation. It is shown that the mapping from to n() is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n (). This summarizes results that can be found already in [13,14] and [4]. Furthermore, we determine the structure of the lattice of extensions of n(LC).     

The concept of a proposition in classical and quantum physics

A proposition is associated in classical mechanics with a subset of phase space, in quantum logic with a projection in Hilbert space, and in both cases with a 2-valued observable or test. A theoretical statement typically assigns a probability to such a pure test. However, since a pure test is an idealization not realizable experimentally, it is necessary — to give such a statement a practical meaning — to describe how it can be approximated by feasible tests. This gives rise to a search for a formal representation of feasible tests, which leads via mixed tests (weighted means of pure tests) to vague tests (convex sets of mixed tests). A model is described in which the latter form a continuous lattice; the pure and mixed tests are the maximal elements and the feasible tests form a basis. Each type of test has its own logic; this is illustrated by the passage from mixed tests to pure tests, which corresponds to the transition from L to classical logic.This work was supported by a grant from the National Research Council of Canada.     

On seeing oneself as “left out”: The chronically complaining patient in psychotherapy

A clinical observation regarding patients who complain about feeling left out and/or second best provides the framework for this paper. What is expressed is a form of separation anxiety coupled with a loser self-concept. It is suggested that these patients represent a milder form of the moral masochism. Early theoretical formulations include Freud and his emphasis on the superego and Reich's emphasis on the masochist's fear of being left alone. Kramer's little man phenomenon is an example of a more current theoretical formulation which takes account of the complexities of the ego, and composite self and identity in the clinical phenomena observed. A case of a latency-aged child is provided.