Husserl’s philosophy of mathematics: its origin and relevance

This paper offers an exposition of Husserl's mature philosophy of mathematics, expounded for the first time in Logische Untersuchungen and maintained without any essential change throughout the rest of his life. It is shown that Husserl's views on mathematics were strongly influenced by Riemann, and had clear affinities with the much later Bourbaki school.

Proof-Theoretic Modal PA-Completeness I: A System-Sequent Metric

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we calculate a canonical characteristic fomula H of S (char(S)) so that _G H (S) and _GL-LIN H, and the complexity of H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of H with H = char(S) and ( H) = d(S, G).     

A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.     

Applying a Theory of Change Approach to Interagency Planning in Child Mental Health

This paper describes the use of a theory of change approach to community-based cross-agency service planning for children with serious emotional disturbance and their families. Public agency planners in Contra Costa County, California used the theory of change approach to organize service planning for a population of youth who had been arrested and involved with juvenile probation. The theory of change process described in this paper links community outcomes with planned activities with the assumptions or principles that underlie the community planning efforts. When complete, a theory of change logic model can serve as a guide for implementation, ensuring that community plans for service delivery remain true to their intent. The theory of change development process includes twelve stages and is based on a step-by-step approach. Theory of change logic models establish a context for articulating a community's shared beliefs and prompt local stakeholders to establish logical connections between the population to be served, expected results, and strategies intended to achieve those results.     

Substructural Logics in Natural Deduction

Extensions of Natural Deduction to Substructural Logics of IntuitionisticLogic are shown: Fragments of Intuitionistic Linear, Relevantand BCK Logic. Rules for implication, conjunction, disjunctionand falsum are defined, where conjunction and disjunction respectcontexts of assumptions. So, conjunction and disjunction areadditive in the terminology of linear logic. Explicit contractionand weakening rules are given. It is shown that conversionsand permutations can be adapted to all these rules, and thatweak normalisation and subformula property holds. The resultsgeneralise to quantification.     

Modification of impulse generation during piqué turns with increased rotational demands

During initiation of a piqué turn, a dancer generates impulse to achieve the desired lateral translation and whole-body rotation. The goal of this study was to determine how individuals regulate impulse generation when initiating piqué turns with increased rotational demands. Skilled dancers (n = 10) performed single (∼360°) and double (∼720°) piqué turns from a stationary position. Linear and angular impulse generated by the push and turn legs were quantified using ground reaction forces and compared across turn conditions as a group and within a dancer using probability-based statistical methods. The results indicate that as the rotation demands of the piqué turn increased, the net angular impulse generated increased whereas net lateral impulse decreased. Early during turn initiation, the free moment contributed to angular impulse generation. Later during turn initiation, horizontal reaction forces were controlled to generate angular impulse. As rotational demands increased, the moment applied increased primarily from redirection of the horizontal reaction force (RFh) at the push leg and a combination of RFh magnitude and moment arm increases at the turn leg. RFh at each leg were coordinated to limit unwanted net linear impulse. Knowledge of observed subject-specific mechanisms is important to inform the design of turning performance training tools.     

Relational semantics for full linear logic

Relational semantics, given by Kripke frames, play an essential role in the study of modal and intuitionistic logic. In [4] it is shown that the theory of relational semantics is also available in the more general setting of substructural logic, at least in an algebraic guise. Building on these ideas, in [5] a type of frames is described which generalise Kripke frames and provide semantics for substructural logics in a purely relational form.In this paper we study full linear logic from an algebraic point of view. The main additional hurdle is the exponential. We analyse this operation algebraically and use canonical extensions to obtain relational semantics. Thus, we extend the work in [4], [5] and use their approach to obtain relational semantics for full linear logic. Hereby we illustrate the strength of using canonical extension to retrieve relational semantics: it allows a modular and uniform treatment of additional operations and axioms.Traditionally, so-called phase semantics are used as models for (provability in) linear logic [8]. These have the drawback that, contrary to our approach, they do not allow a modular treatment of additional axioms. However, the two approaches are related, as we will explain.     

Highly reflective reasoners show no signs of belief inhibition

The processes underlying individual differences in reasoning performance are not entirely understood. What do people who do well on reasoning tasks where beliefs and logic conflict do differently from other people? Because abundant evidence shows that even poorer reasoners detect these conflicts, it has been suggested that individual differences in reasoning performance arise from inhibition failures later in the reasoning process. The present paper argues that a minority of highly skilled reasoners may deviate from this general reasoning process from an early stage. Two studies investigated signs of belief inhibition using a lexical access paradigm (Study 1) and a negative priming paradigm (Study 2). Study 1 showed that while other people exhibited signs of belief inhibition following a belief–logic conflict, people with the highest disposition for cognitive reflection did not. In Study 2, this finding was replicated and similar results were also obtained when comparing groups with higher and lower general cognitive ability. Two possible explanations are discussed.