Axiomatization of a Branching Time Logic with Indistinguishability Relations

Trees with indistinguishability relations provide a semantics for a temporal language “composed by” the Peircean tense operators and the Ockhamist modal operator. In this paper, a finite axiomatization with a non standard rule for this language interpreted over bundled trees with indistinguishability relations is given. This axiomatization is proved to be sound and strongly complete.     

Non-Commutative Topology and Quantales

The relationship between q-spaces (c.f. [9]) and quantum spaces (c.f. [5]) is studied, proving that both models coincide in the case of Spec A, the spectrum of a non-commutative C*-algebra A. It is shown that a sober T ₁ quantum space is a classical topological space. This difficulty is circumvented through a new definition of point in a quantale. With this new definition, it is proved that Lid A has enough points. A notion of orthogonality in quantum spaces is introduced, which permits us to express the usual topological properties of separation. The notion of stalks of sheaves over quantales is introduced, and some results in categorial model theory are obtained.     

A Grim Semantics For Logics of Belief

Patrick Grim has presented arguments supporting the intuition that any notion of a totality of truths is incoherent. We suggest a natural semantics for various logics of belief which reflect Grim’s intuition. The semantics is a topological semantics, and we suggest that the condition can be interpreted to reflect Grim’s intuition. Beyond this, we present a natural canonical topological model for K4 and KD4.     

Moment/History Duality in Prior’s Logics of Branching-Time

The basic notions in Prior’s Ockhamist and Peircean logics of branching-time are the notion of moment and that of history (or course of events). In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical (and ontological) dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of a non-Archimedean topology on the set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories.     

Towards a Semantics Based on the Notion of Justification

Suppose we want to take seriously the neoverificationist idea that an intuitionistic theory of meaning can be generalized in such a way as to be applicable not only to mathematical but also to empirical sentences. The paper explores some consequences of this attitude and takes some steps towards the realization of this program. The general idea is to develop a meaning theory, and consequently a formal semantics, based on the idea that knowing the meaning of a sentence is tantamount to having a criterion for establishing what is a justification for it. Section 1 motivates a requirement of epistemic transparency imposed onto justifications conceived as mental states. In Section 2, the formal notion of justification for an atomic formula is defined, in terms of the notion of cognitive state. In Section 3, the definition is extended to logically complex formulas. In Section 4, the notion of truth-ground is introduced and is used to give a definition of logical validity.     

Lattice-based similarity measures between ordered trees

A clustering algorithm has recently been developed by Reitman and Rueter to express both the structure of chunking in multi-trial free recall and the order of chunk production. The resulting ordered trees differ from ordinary rooted trees in that the elements of a chunk, at any level, may be restricted to a specific ordering. In order to make comparisons of long-term memory structures between subjects, a measure of the similarity between trees is needed. Previously developed similarity measures are shown to be inadequate for ordered trees. Lattice theory is used to generate new similarity measures suited to these richer structures. First, ordered trees are shown to form a nonmodular, graded lattice. Then, moves through this lattice are defined and used to produce several distance measures. These new measures are compared both to each other, and to existing measures, by examining the properties of each measure, and through application to hypothetical trees. The lattice-based measures prove to be theoretically superior, but lack computational ease. The general problem of describing paths in a nonmodular lattice is discussed.     

Hyperstructures, Topology and Datasets

In the natural sciences higher order structures often occur. There seems to be a need for good methods of describing what we mean by higher order structures in various contexts. This is what hyperstructures are intended to do. We motivate and introduce this new concept. Next we illustrate how it can be applied in various types of genomic analysis—particular the correlations between single nucleotide polymorphisms and diseases. The suggested structure is quite general and may be applied to a variety of situations. Finally we discuss how data sets (f. ex. genomic) may lead to topological spaces, giving new invariants and lead to the prediction of hyperstructures.     

"CONTENT VALIDITY" IN MODERATION

"Content validity" has been widely but unwisely hailed as a solution to many problems in employee selection. The enthusiasm and its scope must be tempered. The arguments of this paper begin with the recognition that sampling from content domains cannot logically be substituted for criterion-related validity. Moreover, it must be recognized that the psychometric notion of validity ordinarily refers to scores, not to the stimulus content of a test. It is therefore suggested that evaluations of scores be based on the principle of construct validation; that is, that possible sources of contamination be considered as alternative hypotheses about what is measured by a content sample as it is scored.     

Beyond Pleasure: Exploring the Eudaimonic Entertainment Experience

We examine the notion of eudaimonic entertainment during exposure to a sad but meaningful movie, using a new measure consisting of 5 dimensions derived from research on positive psychology. We, thereby, transfer the conception of eudaimonic well‐being to the conception of entertainment. Results of a confirmatory factor analysis show that the 5 dimensions can be further condensed into 2 second‐order factors. We applied these new measures in a study in which the ending of a movie was manipulated (sad vs. happy). The results provide both discriminant and convergent validity and show that hedonic entertainment measures were affected by the manipulation, but that eudaimonic entertainment measures were unaffected. A second study provided further evidence for the validity of the construct.     

Passive and Active Compensability Multicriteria ANnalysis (PACMAN)

Determining intercriteria relations is an important issue in MCDA. In order to handle this problem, this paper presents a new approach to the concept of compensation in multicriteria analysis, named PACMAN (Passive and Active Compensability Multicriteria ANalysis). The notion of compensability introduced here is decision maker oriented, relying only on information provided by him. In PACMAN compensability is analysed by taking into consideration two criteria at a time and distinguishing the compensating criterion from the compensated one. Separating active and passive effects of compensation allows one to point out a possible asymmetry of the notion of compensability. A valued binary relation of compensated preference is introduced. Compensated preference can be used for a modelization of the preference structure. © 1998 John Wiley & Sons, Ltd.     

Statistical approaches to language acquisition and the self-organizing consciousness: a reversal of perspective

Recent years have seen the upsurge of a new approach to language that moves away from the rule-based conventional framework. In this approach, mostly supported by the success of connectionist models, children learn language by exploiting the distributional properties of the input. It is argued in this paper that, in the same way as conforming to rules does not imply the existence of mental rules, conforming to statistical regularities does not imply that statistical computations are performed mentally. Sensitivity to statistical regularities can alternatively be conceived of as a by-product of the recurrent interplay between the properties of the current conscious content and the properties of the linguistic and extralinguistic environment. The validity of including the content of conscious experiences in an otherwise standard dynamical approach rooted in the notion of self-organization is discussed.     

Hyperalgebraic primitive elements for relational algebraic and topological algebraic models

Using nonstandard methods, we generalize the notion of an algebraic primitive element to that of an hyperalgebraic primitive element, and show that under mild restrictions, such elements can be found infinitesimally close to any given element of a topological field.Presented by Robert Goldblatt     

Structural Indeterminacy

The threat of ontological deflationism (the view that disagreement about what there is can be non-substantive) is averted by appealing to realism about fundamental structure—or so tells us Ted Sider. In this paper, the notion of structural indeterminacy is introduced as a particular case of metaphysical indeterminacy; then it is argued that structural indeterminacy is not only compatible with a metaphysics of fundamental structure, but it can even safeguard it from a crucial objection; finally, it is shown that, if there are instances of structural indeterminacy, a hitherto unacknowledged variety of ontological deflationism will arise. Unless structure is shown to be determinate, ontological deflationism remains a live option. Furthermore, I will consider whether structural indeterminacy could be challenged by adopting a naturalistic epistemology of structure; the question is answered in the negative on the basis of a formal result concerning theory choice. Finally, I submit a new way of articulating the epistemology of structure, which hinges on the very possibility of structural indeterminacy.     

Seeking one’s heading through eye movements

A study of eye movements during simulated travel toward a grove of four stationary trees revealed that observers looked most at pairs of trees that converged or decelerated apart. Such pairs specify that one’s direction of travel, calledheading, is to the outside of the near member of the pair. Observers looked at these trees more than those that accelerated apart; such pairs do not offer trustworthy heading information. Observers also looked at gaps between trees less often when they converged or diverged apart, and heading can never be between such pairs. Heading responses were in accord with eye movements. In general, if observers responded accurately, they had looked at trees that converged or decelerated apart; if they were inaccurate, they had not. Results support the notion that observers seek out their heading through eye movements, saccading to and fixating on the most informative locations in the field of view.     

拓扑几何在知觉组织与空间概念形成中的运用

陈霖的拓扑知觉理论运用几何性质解释知觉组织,并强调拓扑性质的优先性——拓扑知觉是其他几何知觉的基础,拓扑知觉先于其他几何知觉发生。皮亚杰的拓扑首位理论认为儿童的空间概念发展顺序为先发展拓扑几何概念,之后再发展射影与欧式几何概念。两大理论都运用拓扑性质来解释心理现象,其研究对象、研究方法存在很大不同,但它们在理论结构上具有高度一致性,对几何学在心理学上的运用有非常重要的启示意义。     

Validity and Necessity

In this paper I argue against the commonly received view that Kripke’s formal Possible World Semantics (PWS) reflects the adoption of a metaphysical interpretation of the modal operators. I consider in detail Kripke’s three main innovations vis-à-vis Carnap’s PWS: a new view of the worlds, variable domains of quantification, and the adoption of a notion of universal validity. I argue that all these changes are driven by the natural technical development of the model theory and its related notion of validity: they are dictated by merely formal considerations, not interpretive concerns. I conclude that Kripke’s model theoretic semantics does not induce a metaphysical reading of necessity, and is formally adequate independently of the specific interpretation of the modal operators.     

Supervaluationism and Logical Consequence: A Third Way

It is often assumed that the supervaluationist theory of vagueness is committed to a global notion of logical consequence, in contrast with the local notion characteristic of modal logics. There are, at least, two problems related to the global notion of consequence. First, it brings some counterexamples to classically valid patterns of inference. Second, it is subject to an objection related to higher-order vagueness. This paper explores a third notion of logical consequence, and discusses its adequacy for the supervaluationist theory. The paper proceeds in two steps. In the first step, the paper provides a deductive notion of consequence for global validity using the tableaux method. In the second step, the paper provides a notion of logical consequence which is an alternative to global validity, and discusses i) whether it is acceptable to the supervaluationist and ii) whether it plays a better role in a theory of vagueness in the face of the problems related to the global notion.     

Against structured referring expressions

Following Neale, I call the notion that there can be no such thing as a structured referring expression ‘structure skepticism’. The specific aim of this paper is to defuse some putative counterexamples to structure skepticism. The general aim is to bolster the case in favor of the thesis that lack of structure—in a sense to be made precise—is essential to reference.