One of the main applications of the logic of theory change is to the epistemic analysis of conditionals via the so-called Ramsey test. In the first part of the present note this test is studied in the limiting case where the theory being revised is inconsistent, and it is shown that this case manifests an intrinsic incompatibility between the Ramsey test and the AGM postulate of success. The paper then analyses the use of the postulate of success, and a weakening (...) of it, generating axioms of conditional logic via the test, and it is shown that for certain purposes both success and weak success are quite superfluous. This suggests the proposal of abandoning both success and weak success entirely, thus permitting retention of the postulate of preservation discarded by Gärdenfors. (shrink)
We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey-Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).'Expectation' is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form (...) of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. (shrink)
How to accept a conditional? F. P. Ramsey proposed the following test in (Ramsey 1990).(RT) If A, then B must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B.
The paper studies first order extensions of classical systems of modal logic (see (Chellas, 1980, part III)). We focus on the role of the Barcan formulas. It is shown that these formulas correspond to fundamental properties of neighborhood frames. The results have interesting applications in epistemic logic. In particular we suggest that the proposed models can be used in order to study monadic operators of probability (Kyburg, 1990) and likelihood (Halpern-Rabin, 1987).
The article focuses on representing different forms of non-adjunctive inference as sub-Kripkean systems of classical modal logic, where the inference from □A and □B to □A ∧ B fails. In particular we prove a completeness result showing that the modal system that Schotch and Jennings derive from a form of non-adjunctive inference in (Schotch and Jennings, 1980) is a classical system strictly stronger than EMN and weaker than K (following the notation for classical modalities presented in Chellas, 1980). The unified (...) semantical characterization in terms of neighborhoods permits comparisons between different forms of non-adjunctive inference. For example, we show that the non-adjunctive logic proposed in (Schotch and Jennings, 1980) is not adequate in general for representing the logic of high probability operators. An alternative interpretation of the forcing relation of Schotch and Jennings is derived from the proposed unified semantics and utilized in order to propose a more fine-grained measure of epistemic coherence than the one presented in (Schotch and Jennings, 1980). Finally we propose a syntactic translation of the purely implicative part of Jaśkowski's system D₂ into a classical system preserving all the theorems (and non-theorems) explicilty mentioned in (Jaśkowski, 1969). The translation method can be used in order to develop epistemic semantics for a larger class of non-adjunctive (discursive) logics than the ones historically investigated by Jaśkowski. (shrink)
An important trend in contemporary epistemology centers on elaborating an old idea of pragmatist pedigree: theory selection (and in general the process of changing view and fixing beliefs) presupposes epistemic values. This article focuses on analyzing the case where epistemic values are indeterminate or when the sources of valuation are multiple (epistemic values like coherence and simplicity need not order options in compatible ways). According to the theory that thus arises epistemic alternatives need not be fully ordered by an underlying (...) notion of information-value and therefore the usual economic techniques of optimization cannot be applied in order to compute optimal contractions. But in cases of this sort it is still rational to maximize, i.e. to deem an option as choosable when it is not known to be worse that any other. We present here basic results about a notion of liberal contraction based on maximizing quasi-orderings. This requires the previous solution of some open problems in the theory of rational choice functions, namely a full characterization of choice functions rationalizable in terms of maximization of quasi-transitive relations. We conclude by discussing the problem of what is the adequate feasible set for calculating maximizing solutions for contraction problems and by considering the epistemological roots of some counterexamples against the most fundamental axioms on choice functions (like α). While the first part of the paper shows how economic insights can be used to improve our understanding of the principles of belief formation and change, this final section reverses this strategy by showing the utility of epistemological insights and techniques for providing invariance conditions capable of regulating the applicability of the pure principles of choice. (shrink)
S. Jakowski introduced the discussive prepositional calculus D 2as a basis for a logic which could be used as underlying logic of inconsistent but nontrivial theories (see, for example, N. C. A. da Costa and L. Dubikajtis, On Jakowski's discussive logic, in Non-Classical Logic, Model Theory and Computability, A. I. Arruda, N. C. A da Costa and R. Chuaqui edts., North-Holland, Amsterdam, 1977, 37–56). D 2has afterwards been extended to a first-order predicate calculus and to a higher-order logic (cf. the (...) quoted paper). In this paper we present a natural version of D 2, in the sense of Jakowski and Gentzen; as a consequence, we suggest a new formulation of the discussive predicate calculus (with equality). A semantics for the new calculus is also presented. (shrink)
Je me propose une évaluation du travail effectué par Jeanne Hersch sur les droits de l�homme. A-t-elle tenté de «fonder» les droits, c�est-a-dire, de développer des argumentations contraignantes qui en établissent la validité ? Elle dérive les droits d�une conception normative de la nature humaine, s�appuyant sur la volonté, qui doit être libre, plutôt que sur la raison. Ses «fondements» ne sont pas des argumentations, mais des présupposés anthropologiques. Elle tente d�expliquer les échecs des droits de l�homme par une analyse (...) de leur tendance naturelle à se multiplier, se différencier, s�opposer l�un à l�autre. (shrink)
Electron diffraction has been used to study the structure of the ? phase precipitated in large-grained TaC specimens prepared by solid-state diffusion. The observed patterns confirm the main features of the structure as recently determined by x-ray diffraction techniques; hhcc (D5 3d) Sn4P3 type structure, space group R3m (D5 3d). In addition, for at least some of the crystals, extra lines of diffuse spots seem to furnish evidence of a carbon atom ordering inside the close-packed planes. This order corresponds to (...) the composition Ta3C2. (shrink)
En este artículo me ocupo de la cuestión de cómo en las teorías de proceso dual se puede dar cuenta del autoengaño y su conexión con la racionalidad. Presento las versiones intencionalista y no intencionalista del autoengaño y muestro cómo el debate entre ellas puede dirimirse de manera más completa y satisfactoria en el marco de una teoría dual. En éste suelen aceptarse dos sistemas de razonamiento, uno heurístico (S1) y otro analítico (S2), que compiten por el control de nuestras (...) inferencias y acciones, pero a veces interactúan y colaboran entre sí. Se defiende que si predomina la respuesta de S1, se puede ver el patrón del autoengaño como una forma de razonamiento heurístico y no únicamente como un vínculo causal. Se sugiere que las evaluaciones en cuanto a la racionalidad del proceso del autoengaño, dependerá del modo en que intervenga en el patrón de razonamiento y del sistema desde el cual se lleve a cabo. In this paper I discuss the phenomenon of self-deception and its connection with the notion of rationality linked to the dual process theories. I present the intentionalist and nonintentionalist accounts of self-deception and aim to show how the debate between them can be resolved in a more comprehensive and satisfactory manner, if it is placed in the frame of the dual process theories. The dual model usually accepts two kinds of reasoning processes, heuristic and analytic, referred to two different systems, S1 and S2. These processes compete for control of our inferences and actions, but sometimes they interact and collaborate. It is suggested that in a dual model, the evaluations in terms of the rationality of the process will depend on the way in which self-deception participates in the reasoning process and on the system from which the evaluation takes place. (shrink)
In view of the presertt state of development of non cktssicallogic, especially of paraconsistent logic, a new stand regardmg the relatzons between logtc and ontology is deferded In a parody of a dicturn of Quine, my stand may be summarized as follows To be is to be the value of a vanable a specific language with a given underlymg logic Yet my stand differs from Qutne's, because, among other reasons, I accept some first order heterodox logIcs as genutne alternatwes to (...) ciassical logic I aiso discuss some questions of non classical logic to substantzate my argument, and suggest that rny position complements and extends some uleas advanced by L Apostei. (shrink)
One of the main applications of the logic of theory change is to the epistemic analysis of conditionals via the so-called Ramsey test. In the first part of the present note this test is studied in the “limiting case” where the theory being revised is inconsistent, and it is shown that this case manifests an intrinsic incompatibility between the Ramsey test and the AGM postulate of “success”. The paper then analyses the use of the postulate of success, and a weakening (...) of it, generating axioms of conditional logic via the test, and it is shown that for certain purposes both success and weak success are quite superfluous. This suggests the proposal of abandoning both success and weak success entirely, thus permitting retention of the postulate of “preservation” discarded by Gärdenfors. (shrink)
Daniel Ellsberg presented in Ellsberg (The Quarterly Journal of Economics 75:643–669, 1961) various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage (1972). Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky (1995) an explanation of Ellsberg’s two-color problem (...) in terms of a psychological effect: ambiguity aversion . The ‘comparative ignorance’ hypothesis articulates how this effect works and explains why it is important to an understanding of the typical pattern of responses associated with Ellsberg’s two-color problem. In the first part of this article we challenge Fox and Tversky’s explanation. We present first an experiment that extends Ellsberg’s two-color problem where certain predictions of the comparative ignorance hypothesis are not confirmed. In addition the hypothesis seems unable to explain how the subjects resolve trade-offs between security and expected pay-off when vagueness is present. Ellsberg offered an explanation of the typical behavior elicited by his examples in terms of these trade-offs and in section three we offer a model of Ellsberg’s trade-offs. The model takes seriously the role of imprecise probabilities in explaining Ellsberg’s phenomenon. The so-called three-color problem was also considered in Fox and Tversky (1995). We argue that Fox and Tversky’s analysis of this case breaks a symmetry with their analysis of the two-color problem. We propose a unified treatment of both problems and we present a experiment that confirms our hypothesis. (shrink)
This article elaborates on foundational issues in the social sciences and their impact on the contemporary theory of belief revision. Recent work in the foundations of economics has focused on the role external social norms play in choice. Amartya Sen has argued in [Sen93] that the traditional rationalizability approach used in the theory of rational choice has serious problems accommodating the role of social norms. Sen’s more recent work [Sen96, Sen97] proposes how one might represent social norms in the theory (...) of choice, and in a very recent article [BS07] Walter Bossert and Kotaro Suzumura develop Sen’s proposal, offering an extension of the classical theory of choice that is capable of dealing with social norms. The first part of this article offers an alternative functional characterization of the extended notion of rationality employed by Bossert and Suzumura in [BS07]. This characterization, unlike the one offered in [BS07], represents a norm-sensitive notion of rationality in terms of a pure functional constraint unmediated by a notion of revealed preference (something that is crucial for the application developed in the second part of this article). This functional characterization is formulated for general domains (as is Bossert and Suzumura’s characterization) and is therefore empirically more applicable than usual characterizations of rationality. Interestingly, the functional constraint we propose is a variant of a condition first entertained in [AGM85] by Carlos Alchourr´on, Peter Gärdenfors and David Makinson in the area of belief change. (shrink)
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