Theories of Types and Names with Positive Stratified Comprehension

We introduce a certain extension of -calculus, and show that it has the Church-Rosser property. The associated open-term extensional combinatory algebra is used as a basis to construct models for theories of Explict Mathematics (formulated in the language of "types and names") with positive stratified comprehension. In such models, types are interpreted as collections of solutions (of terms) w.r. to a set of numerals. Exploiting extensionality, we prove some consistency results for special ontological axioms which are refutable under elementary comprehension.     

Paradoxes in Double Extension Set Theories

Three systems of double extension set theory have been proposed by Andrzej Kisielewicz in two papers. In this paper, it is shown that the two stronger systems are inconsistent, and that the third, weakest system does not admit extensionality for general sets or the use of general sets as parameters in its comprehension scheme. The parameter-free version of the comprehension principle of double extension set theory is also shown to be inconsistent with extensionality. The definitions of the systems and a self-contained exposition of their properties is given, sufficient to develop the inconsistency proofs.     

On the Strength of the Local Attachment Preference

This paper investigates the strength of the local attachment preference in syntactic ambiguity resolution, based on a study of a novel ambiguity for which the predictions of local attachment contrast with the predictions of a wide range of other ambiguity resolution principles. In sentences of the form Because Rose praised the recipe I made ... we show that the ambiguous clause I made is preferentially attached as a relative clause under some circumstances, as predicted by local attachment, and preferentially attached as a matrix clause under other circumstances. The implications for accounts of locality in parsing are discussed.     

Isomorphism and Equational Equivalence of Continuous λ-Models

We will present several results on two types of continuous models of -calculus, namely graph models and extensional models. By introducing a variant of Engeler's model construction, we are able to generalize the results of [7] and to give invariants that determine a large family of graph models up to applicative isomorphism. This covers all graph models considered in the litterature so far. We indicate briefly how these invariants may be modified in order to determine extensional models as well.Furthermore, we use our construction to exhibit graph models that are not equationally equivalent. We indicate once again how the construction passes on to extensional models.     

State-of-affairs Semantics for Positive Free Logic

In the following the details of a state-of-affairs semantics for positive free logic are worked out, based on the models of common inner domain–outer domain semantics. Lambert's PFL system is proven to be weakly adequate (i.e., sound and complete) with respect to that semantics by demonstrating that the concept of logical truth definable therein coincides with that one of common truth-value semantics for PFL. Furthermore, this state-of-affairs semantics resists the challenges stemming from the slingshot argument since logically equivalent statements do not always have the same extension according to it. Finally, it is argued that in such a semantics all statements of a certain language for PFL are state-of-affairs-related extensional as well as salva extensione extensional, even though their salva veritate extensionality fails.     

Subvocalization in auditory-verbal imagery: just a form of motor imagery?

Previous studies have provided evidence for subvocal rehearsal (inner voice) and phonological storage (inner ear) in auditory-verbal imagery. The question remains to be answered whether the inner voice mainly involves higher-order language systems, or primarily relies on motor systems associated with articulatory-kinesthetic processing. On the basis of models of auditory imagery and working memory, we predicted that, if auditory-verbal imagery is a form of motor imagery, performance on a novel auditory-verbal imagery task would be affected by concurrent articulatory suppression as well as by concurrent finger tapping. In contrast, we predicted that performance on a visuospatial control task would be significantly affected by concurrent tapping only. The auditory imagery task consisted of indicating, for bisyllabic words, the syllable that carried the stress. A significant interaction was observed between task (verbal vs. visual) and type of interference (articulatory suppression vs. tapping). Tapping affected reaction times on the visual task significantly more than articulatory suppression. However, both interference conditions affected the verbal task to an equal extent. The present findings confirm the role of subvocalization in auditory-verbal imagery and provide evidence for a strong involvement of articulatory-kinesthetic motor processing.     

A State-of-Affairs-Semantic Solution to the Problem of Extensionality in Free Logic

Journal of Philosophical Logic - If one takes seriously the idea that a scientific language must be extensional, and accepts Quine’s notion of truth-value-related extensionality, and also...     

Recycling prosodic boundaries

The present study investigates the role of prosodic structure in selecting a syntactic analysis at different stages of parsing in silent reading of Japanese relative clauses. Experiments 1 and 2 (sentence-completion questionnaires) revealed an effect of the length of the sentence-initial constituent on the resolution of a clause boundary ambiguity in Japanese. Experiment 3 (fragment-reading) showed that this length manipulation is also reflected in prosodic phrasing in speech. Its influence on ambiguity resolution is attributed to recycling of prosodic boundaries established during the first-pass parse. This explanation is based on the implicit prosody proposals of Bader (1998) and Fodor (1998). Experiment 4 (self-paced reading) demonstrated the immediacy of the influence on ambiguity resolution on-line. Experiment 5 (self-paced reading) found support for the additional prediction that when no boundary is available to be recycled, processing the relative clause construction is more difficult.     

Monotone Majorizable Functionals

Several properties of monotone functionals (MF) and monotone majorizable functionals (MMF) used in the earlier work by the author and van de Pol are proved. It turns out that the terms of the simply typed lambda-calculus define MF, but adding primitive recursion, and even monotonic primitive recursion changes the situation: already Z.Z(1 — sg) is not MMF. It is proved that extensionality is not Dialectica-realizable by MMF, and a simple example of a MF which is not hereditarily majorizable is given.     

A note on the system of propositional calculus with primitive rule of extensionality

Summary The present paper deals with a systemS of propositional calculus, conjunction, equivalence and falsum being its primitive terms. The only primitive rule inS is the rule of extensionality defined by the scheme:      

The Implicit Assumptions of Dividing a Cake: Political or Comprehensive?

Rawls's recent modification of his theory of justice claims that political liberalism is free-standing and falls under the category of the political. It works entirely within that domain and does not rely on anything outside it In this article I pursue the metatheoretical goal of obtaining insight into the anthropological assumptions that have remained so far unacknowledged by Rawls and critics alike. My argument is that political liberalism has a dependence on comprehensive liberalism and its conception of a self-serving subjectivity that is far more binding as well as undesirable than it has been so far acknowledged. I proceed with a heuristic approach that introduces us to the possibility that political liberalism presupposes tacitly the Occidental metanarrative of reason harnessing rampant self-interest and subordinating it to a higher-order interest. As the presuppositions of political liberalism emerge, I draw from the debate between Rawls and Habermas in order to illustrate my argument for the existence of a dependence on these presuppositions. I outline some implications of the anthropological basis of political liberalism and conclude by exemplifying them with reference to Rawls's comments on the division of a cake.     

Groups to Resolve Conflicts Between Groups: Diplomacy with a Therapeutic Dimension

The group self, an individual's self-perception as a member of a group, is distinguished from the group's self, a personification of the group as a person with a self. The perceived group's self of an opposing other group is often a repository for attributes group members are not ready to recognize in their own group's self. Theoretically, the need for an adversarial other to hold one's own group's unwanted attributes—and thus to complete one's own group's self—contributes, however unconsciously, to the apparent intractability of intergroup disputes. In dealing with these issues, I compare intergroup conflict resolution (ICR) groups with therapy groups, on the one hand, and advocacy groups on the other. All of this sets the stage for a presentation of two ICR projects and their analysis in group-developmental terms.     

Correlates of sociometric status in school children in Buenos Aires

Teacher ratings on Spanish translations of the Comprehensive Behavior Rating Scale for Children and peer nominations were obtained for 110 school children (42 boys and 68 girls) in grades 2– 5 at a public elementary school in Buenos Aires. Nominations of likes best were negatively correlated with language processing deficits, attention problems, and sluggish tempo as rated by both teachers and peers, and positively correlated with teacher ratings of social competence, for both boys and girls. The reverse pattern was found for nominations of likes least. Children were assigned to sociometric status groups of popular (n=27), rejected (n=28), neglected (n=7) controversial (n=11), and average (n=37) based on number of LL and LB nominations. Rejected and popular children could be differentiated by teacher and peer ratings of linguistic information processing deficits, inattention, and sluggish tempo. Behavioral characteristics of motor hyperactivity, impulsivity, and aggression were significantly associated with being male but did not differ by sociometric status group.The assistance of Claudia Colon, Educational District of Buenos Aires, and Viviana Smith, Department of the Interior, Argentina, in the translation of measures is gratefully acknowledged. Particular thanks are also extended to the teachers and personnel of Escuela Normal 9 — Domingo F. Sarmiento.     

Proto-Semantics for Positive Free Logic

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of non-existing objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth non unlike the notion of truth at world found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization).     

On Extensions of Intermediate Logics by Strong Negation

In this paper we will study the properties of the least extension n() of a given intermediate logic by a strong negation. It is shown that the mapping from to n() is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n (). This summarizes results that can be found already in [13,14] and [4]. Furthermore, we determine the structure of the lattice of extensions of n(LC).     

On constructive functions ranging over propositions

It is shown that there is no constructive extensional truth-value mapping from the speciesP of all propositions into known constructive structures P.I thank W. Friedrich for discussion and a referee for remarks on this paper.     

Two-group classification in latent trait theory: Scores with monotone likelihood ratio

This paper deals with two-group classification when a unidimensional latent trait,, is appropriate for explaining the data,X. It is shown that ifX has monotone likelihood ratio then optimal allocation rules can be based on its magnitude when allocation must be made to one of two groups related to. These groups may relate to probabilistically via a non-decreasing functionp(), or may be defined by all subjects above or below a selected value on.In the case where the data arise from dichotomous items, then only the assumption that the items have nondecreasing item characteristic functions is enough to ensure that the unweighted sum of responses (the number-right score or raw score) possesses this fundamental monotone likelihood ratio property.     

Combined Individual/Marital Therapy: A Conflict Resolution Framework and Ethical Considerations

This paper illustrates how couple and individual treatment formats can be intertwined. A conflict resolution theoretical framework structures treatment around three goals: (1) relieving symptoms (anger, depression, and marital distress), (2) facilitating resolution of the couple's conflicts, and (3) building communication and conflict resolution skills. The literature review focuses on why combining individual and couple therapy is often important for married clients. Two Bicycles, an illustrative case incorporating both conjoint and individual interventions, is presented and analyzed with regard to when each format seems beneficial. Ethical and practical issues raised by dual format treatment include potential harm, informed consent, dual roles, confidentiality, and time and financial costs.