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We trace self-reference phenomena to the possibility of namingfunctions by names that belong to the domain over which thefunctions are defined. A naming system is a structure of theform (D, type( ),{ }), where D is a non-empty set; for everya D, which is a name of a k-ary function, {a}: Dk D is thefunction named by a, and type(a) is the type of a, which tellsus if a is a name and, if it is, the arity of the named function.Under quite general conditions we get a fixed point theorem,whose special cases include the fixed point theorem underlyingGödel's proof, Kleene's recursion theorem and many othertheorems of this nature, including the solution to simultaneousfixed point equations. Partial functions are accommodated byincluding "undefined" values; we investigate different systemsarising out of different ways of dealing with them. Many-sortednaming systems are suggested as a natural approach to generalcomputatability with many data types over arbitrary structures.The first part of the paper is a historical reconstruction ofthe way Gödel probably derived his proof from Cantor'sdiagonalization, through the semantic version of Richard. Theincompleteness proofincluding the fixed point constructionresultfrom a natural line of thought, thereby dispelling the appearanceof a "magic trick". The analysis goes on to show how Kleene'srecursion theorem is obtained along the same lines. 相似文献
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Lori R. Van Wallendael 《决策行为杂志》1995,8(4):245-264
Past research suggests that people may make use of diagnosticity information when explicit data regarding P(D | H) and P(D | ? H) are given to them. However, people fall victim to pseudodiagnosticity biases and ignore P(D | ? H) when such data must be actively sought. This series of four experiments utilized judgment problems in which subjects have knowledge of P(D | ? H) but must recognize the relevance of that knowledge for the judgment at hand. It was hypothesized that subjects who genuinely understood the role of P(D | ? H) in hypothesis testing would respond to this manipulation of implicit diagnosticity by exhibiting greater confidence and lesser information buying when given evidence of relatively high diagnosticity. In the first three studies, subjects attempted to judge the guilt or innocence of suspects in several fictional crimes. In the fourth experiment, subjects attempted to judge the club membership status of students at their own university. Greater amounts of information were bought when the only available information was of low diagnosticity. Subjects also expressed greater confidence in judgments made using highly diagnostic information. However, within the legal scenario, sensitivity to diagnosticity was dependent upon the implication of the cues received. Results are discussed with respect to Bayesian probability, expected value theory, and a confidence criterion model of information purchasing. 相似文献
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Thomas Forster 《Studia Logica》2008,90(2):249-256
Sharvy’s puzzle concerns a situation in which common knowledge of two parties is obtained by repeated observation each of the other, no fixed point being reached in finite time. Can a fixed point be reached? 相似文献
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Boudewijn de Bruin 《Synthese》2008,163(1):79-97
Using epistemic logic, we provide a non-probabilistic way to formalise payoff uncertainty, that is, statements such as ‘player
i has approximate knowledge about the utility functions of player j.’ We show that on the basis of this formalisation common knowledge of payoff uncertainty and rationality (in the sense of
excluding weakly dominated strategies, due to Dekel and Fudenberg (1990)) characterises a new solution concept we have called
‘mixed iterated strict weak dominance.’ 相似文献
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This paper addresses a problem for theories of epistemic democracy. In a decision on a complex issue which can be decomposed
into several parts, a collective can use different voting procedures: Either its members vote on each sub-question and the
answers that gain majority support are used as premises for the conclusion on the main issue (premise based-procedure, pbp), or the vote is conducted on the main issue itself (conclusion-based procedure, cbp). The two procedures can lead to different results. We investigate which of these procedures is better as a truth-tracker,
assuming that there exists a true answer to be reached. On the basis of the Condorcet jury theorem, we show that the pbp is universally superior if the objective is to reach truth for the right reasons. If one instead is after truth for whatever
reasons, right or wrong, there will be cases in which the cbp is more reliable, even though, for the most part, the pbp still is to be preferred. 相似文献
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Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss
the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and
establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain
interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.
Dedicated to the memory of Willem Johannes Blok 相似文献
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We show that the loosely guarded and packed fragments of first-order logic have the finite model property. We use a construction of Herwig and Hrushovski. We point out some consequences in temporal predicate logic and algebraic logic. 相似文献
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