In recent years, much work has been dedicated by logicians, computer scientists and economists to understanding awareness, as its importance for human behaviour becomes evident. Although several logics of awareness have been proposed, little attention has been explicitly dedicated to change in awareness. However, one of the most crucial aspects of awareness is the changes it undergoes, which have countless important consequences for knowledge and action. The aim of this paper is to propose a formal model of awareness change, and (...) to derive from it logics of awareness change. In the first part of the paper, the model of epistemic states of bounded agents proposed in Hill (Stud Log 89(1):81–109, 2008a ) is extended with operations modelling awareness change. In the second part of the paper, it is shown how this model naturally extends the “standard” logic of awareness to yield a logic of awareness change. (shrink)

The Intergovernmental Panel on Climate Change has developed a novel framework for assessing and communicating uncertainty in the findings published in their periodic assessment reports. But how should these uncertainty assessments inform decisions? We take a formal decision-making perspective to investigate how scientific input formulated in the IPCC’s novel framework might inform decisions in a principled way through a normative decision model.

Contemporary decision theory places crucial emphasis on a family of mathematical results called representation theorems, which relate criteria for evaluating the available options to axioms pertaining to the decision-maker’s preferences. Various claims have been made concerning the reasons for the importance of these results. The goal of this article is to assess their semantic role: representation theorems are purported to provide definitions of the decision-theoretic concepts involved in the evaluation criteria. In particular, this claim shall be examined from the perspective (...) of philosophical theories of the meaning of theoretical terms. (shrink)

Reports of the Intergovernmental Panel on Climate Change (IPCC) employ an evolving framework of calibrated language for assessing and communicating degrees of certainty in findings. A persistent challenge for this framework has been ambiguity in the relationship between multiple degree-of-certainty metrics. We aim to clarify the relationship between the likelihood and confidence metrics used in the Fifth Assessment Report (2013), with benefits for mathematical consistency among multiple findings and for usability in downstream modeling and decision analysis. We discuss how our (...) proposal meshes with current and proposed practice in IPCC uncertainty assessment. (shrink)

Abstract:The standard, Bayesian account of rational belief and decision is often argued to be unable to cope properly with severe uncertainty, of the sort ubiquitous in some areas of policy making. This paper tackles the question of what should replace it as a guide for rational decision making. It defends a recent proposal, which reserves a role for the decision maker’s confidence in beliefs. Beyond being able to cope with severe uncertainty, the account has strong normative credentials on the main (...) fronts typically evoked as relevant for rational belief and decision. It fares particularly well, we argue, in comparison to other prominent non-Bayesian models in the literature. (shrink)

It is well-known that classical models of belief are not realistic representations of human doxastic capacity; equally, models of actions involving beliefs, such as decisions based on beliefs, or changes of beliefs, suffer from a similar inaccuracies. In this paper, a general framework is presented which permits a more realistic modelling both of instantaneous states of belief, and of the operations involving them. This framework is motivated by some of the inadequacies of existing models, which it overcomes, whilst retaining technical (...) rigour in so far as it relies on known, natural logical and mathematical notions. The companion paper (Towards a “sophisticated” model of belief dynamics. Part II) contains an application of this framework to the particular case of belief revision. (shrink)

This article is concerned with the representation of preferences which do not satisfy the ordinary axioms for state-independent utilities. After suggesting reasons for not being satisfied with solutions involving state-dependent utilities, an alternative representation shall be proposed involving state-independent utilities and a situation-dependent factor. The latter captures the interdependencies between states and consequences. Two sets of axioms are proposed, each permitting the derivation of subjective probabilities, state-independent utilities, and a situation-dependent factor, and each operating in a different framework. The first (...) framework involves the concept of a decision situation—consisting of a set of states, a set of consequences and a preference relation on acts; the probabilities, utilities and situation-dependent factor are elicited by referring to other, appropriate decision situations. The second framework, which is technically related, operates in a fixed decision situation; particular “subsituations” are employed in the derivation of the representation. Possible interpretations of the situation-dependent factor and the notion of situation are discussed. (shrink)

In the companion paper (Towards a “sophisticated” model of belief dynamics. Part I), a general framework for realistic modelling of instantaneous states of belief and of the operations involving them was presented and motivated. In this paper, the framework is applied to the case of belief revision. A model of belief revision shall be obtained which, firstly, recovers the Gärdenfors postulates in a well-specified, natural yet simple class of particular circumstances; secondly, can accommodate iterated revisions, recovering several proposed revision operators (...) for iterated revision as special cases; and finally, offers an analysis of Rott’s recent counterexample to several Gärdenfors postulates [32], elucidating in what sense it fails to be one of the special cases to which these postulates apply. (shrink)

In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.

In ‘A Defence of the Ramsey Test’, Richard Bradley makes a case for not concluding from the famous impossibility results regarding the Ramsey Test — the thesis that a rational agent believes a conditional if he would believe the consequent upon learning the antecedent — that the thesis is false. He lays the blame instead on one of the other premisses in these results, namely the Preservation condition. In this paper, we explore how this condition can be weakened by strengthening (...) the notion of consistency which appears in it. After considering the effects of such weakenings for Bradley's argument, we propose a refinement of the Preservation condition which does not fall prey to Bradley's argument nor to Gärdenfors's impossibility theorem. We briefly compare it to Bradley's suggested restriction of Preservation. (shrink)

The goal of this article is to take a step toward the resolution of the problem of finding an analytic sequent calculus for the logic of proofs. For this, we focus on the system Ilp, the intuitionistic version of the logic of proofs. First we present the sequent calculus Gilp that is sound and complete with respect to the system Ilp; we prove that Gilp is cut-free and contraction-free, but it still does not enjoy the subformula property. Then, we enrich (...) the language of the logic of proofs and we formulate in this language a second Gentzen calculus Gilp∗. We show that Gilp∗ is a conservative extension of Gilp, and that Gilp∗ satisfies the subformula property. (shrink)

There has been a recent surge of interest among economists in developing models of doxastic states that can account for some aspects of human cognitive limitations that are ignored by standard formal models, such as awareness. Epistemologists purport to have a principled reason for ignoring the question of awareness: under the equilibrium conception of doxastic states they favour, a doxastic state comprises the doxastic commitments an agent would recognise were he fully aware, so the question of awareness plays no role. (...) The objective of this paper is to scrutinize this argument. A thesis underlying the argument, which we call the independence of doxastic commitments with respect to awareness, is identified, and examples are given where it appears to be violated. By considering these examples, one can get an idea of the price of accepting this thesis. On the one hand, one can escape the conclusion that the thesis is violated, but only at the expense of another principle espoused by all major formal models of belief, which we call constant doxastic rest; and abandoning this principle necessitates extensive revision of current models of belief. On the other hand, there are epistemologically valid reasons for thinking that the thesis fails to hold in the examples, which have to be rebutted if the thesis, and the equilibrium justification for ignoring the issue of awareness, are to be retained. (shrink)

RÉSUMÉ : Depuis l’ouvrage classique de Goodman, on sait que toute théorie de l’induction doit comporter une composante non formelle. Or, la liberté théorique offerte par le recours à un tel élément implique des responsabilités. Cet article propose comme desideratum d’une théorie de l’induction qu’elle rende compte de la dynamique de sa composante non formelle. Ce desideratum, qui est nouveau, n’est pas satisfait par les principales théories existantes de l’induction. L’identification de l’importance de la dynamique a pourtant l’avantage de suggérer (...) une voie vers une théorie plus acceptable et plus compléte de l’induction. ABSTRACT: Since Goodman’s classic monograph, it has been known that any reasonable theory of induction must involve non formal elements. However, the right to make theoretical use of such an element comes with responsibilities. This article argues for an apparently new desideratum for a theory of induction: namely, that it accounts for the dynamics of the non formal element used. None of the main existing theories of induction satisfies this desideratum. The recognition of the importance of dynamics does however have the advantage of suggesting where to look for a more acceptable and complete theory of induction. (shrink)

Growing concern about a shrinking cultural consensus on values, coupled with religious pluralisation and the realisation that schooling is not, and cannot be, value-neutral,have led to proposals to teach ethics in schools, interpreted as a contribution of the discipline of philosophy to the common curriculum. To the extent that this approach is seen to hinge on the alleged autonomy of ethics, it has the potential to indoctrinate the contestable view that rationality is the prime motivator of moral commitment. A case (...) is made for regarding philosophical ethics and religious studies not as alternative avenues to values education but each as a core curriculum priority, different but complementary to the other in its content. (shrink)

In this paper we present a finitary sequent calculus for the S5 multi-modal system with common knowledge. The sequent calculus is based on indexed hypersequents which are standard hypersequents refined with indices that serve to show the multi-agent feature of the system S5. The calculus has a non-analytic right introduction rule. We prove that the calculus is contraction- and weakening-free, that (almost all) its logical rules are invertible, and finally that it enjoys a syntactic cut-elimination procedure. Moreover, the use of (...) the non-analytic rule can be restricted so that the calculus can be considered as suitable for proof search. (shrink)