Birkhoff-like sheaf representation for varieties of lattice expansions

Given a variety we study the existence of a class such that S1 every A can be represented as a global subdirect product with factors in and S2 every non-trivial A is globally indecomposable. We show that the following varieties (and its subvarieties) have a class satisfying properties S1 and S2: p-algebras, distributive double p-algebras of a finite range, semisimple varieties of lattice expansions such that the simple members form a universal class (bounded distributive lattices, De Morgan algebras, etc) and arithmetical varieties in which the finitely subdirectly irreducible algebras form a universal class (f-rings, vector groups, Wajsberg algebras, discriminator varieties, Heyting algebras, etc). As an application we obtain results analogous to that of Nachbin saying that if every chain of prime filters of a bounded distributive lattice has at most length 1, then the lattice is Boolean.We wish to thank Lic. Alfredo Guerin and Dr. Daniel Penazzi for helping us with linguistics aspects. We are indebted to the referee for several helpful suggestions. We also wish to thank Professor Mick Adams for providing us with several reprints and useful e-mail information on the subject.Suported by CONICOR and SECyT (UNC).     

Refuting the unfolding-argument on the irrelevance of causal structure to consciousness

The unfolding argument (UA) was advanced as a refutation of prominent theories, which posit that phenomenal experience is determined by patterns of neural activation in a recurrent (neural) network (RN) structure. The argument is based on the statement that any input–output function of an RN can be approximated by an “equivalent” feedforward-network (FFN). According to UA, if consciousness depends on causal structure, its presence is unfalsifiable (thus non-scientific), as an equivalent FFN structure is behaviorally indistinguishable with regards to any behavioral test. Here I refute UA by appealing to computational theory and cognitive-neuroscience. I argue that a robust functional equivalence between FFN and RN is not supported by the mathematical work on the Universal Approximator theorem, and is also unlikely to hold, as a conjecture, given data in cognitive neuroscience; I argue that an equivalence of RN and FFN can only apply to static functions between input/output layers and not to the temporal patterns or to the network’s reactions to structural perturbations. Finally, I review data indicating that consciousness has functional characteristics, such as a flexible control of behavior, and that cognitive/brain dynamics reveal interacting top-down and bottom-up processes, which are necessary for the mediation of such control processes.     

Admissibility of Cut in <Emphasis Type="Italic">LC</Emphasis> with Fixed Point Combinator

The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof. Presented by Robert Goldblatt     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

Fitts’ Theorem in Oculomotor Control: Dissociable Movement Times for Amplitude and Width Manipulations

The authors examined whether movement times (MT) for discrete saccades are constant given equivalent index of difficulty (ID) values (i.e., unitary nature of Fitts’ theorem). To that end, we contrasted ID/MT relations for saccades equated for ID but differing with respect to their target amplitudes and widths. Results showed that MT increased with increasing ID within amplitude and width conditions; however, the ID/MT slope was markedly steeper in the former condition. Thus, the amplitude condition imposed greater information processing demands than the width condition—a result indicating that the constituent elements of Fitts’ theorem are dissociable (i.e., nonunitary). Further, examination of saccade kinematics demonstrated that the optimal MT for a given target amplitude was largely independent of target width.     

The Undecidability of Grisin's Set Theory

We investigate a contractionless naive set theory, due to Grisin [11]. We prove that the theory is undecidable.     

Seek and ye shall find: test results are what you hypothesize they are

Expert clinicians were given batteries of psychodiagnostic test results (Rorschach, TAT, Draw-A-Person, Bender-Gestalt, Wechsler) to analyze. For half, a battery came along with a suggestion that the person suffers from Borderline Personality disorder, and for half, that battery was accompanied by a suggestion that he suffers from Paranoid Personality disorder. In Study 1, the suggestion was made indirectly, through a background story that preceded the test results. In Study 2, the suggestion was made directly, by the instructions given. The experts saw in the tests what they hypothesized to be there. In particular, the target diagnoses were rated higher when they were hypothesized than when they were not. Copyright © 1998 John Wiley & Sons, Ltd.     

迪昂问题及其解决

迪昂问题是当代科学哲学争论的主题之一。波普尔、拉卡托斯和库恩都曾经对此问题给予不同的对待或解决。本文对此背景给以扼要的介绍,然后着重介绍和评价一种新的解决方案——基于贝叶斯方法的解决。相比之下,后一方案较为令人满意。     

Early Examples of Resource-Consciousness

As with the development of several logical notions, it is shown that the concept of resource-consciousness, i. e. the concern over the number of times that a given sentence is used in the proof of another sentence, has its origin in the foundations of geometry, pre-dating its appearence in logical circles as BCK-logic or affine logic.     

意见收敛定理与休谟问题

意见收敛定理是主观主义概率论的一条重要定理,它表明随着证据的增加,验前概率的主观性将被验后概率的客观性所代替。意见收敛定理被看作主观概率的动态合理性原则,因而被用来解决休谟问题,即归纳合理性问题。然而,哈金有说服力地表明,意见收敛定理证明的是条件概率Pr（h／e）的收敛,而不是验后概率Pre（h）的收敛。主观主义概率论暗中接受的一个等式是：Pre（h）=Pr（h／e）,通常称之为“条件化规则”。这样,归纳法的合理性问题变成条件化规则的合理性问题。为此,本文提出一个新的合理性原则,即“最少初始概率原则”,将它同“局部合理性”观念结合起来便可为条件化规则的合理性加以辩护。