Mental representation of logical connectives

Logical connectives, such as “AND”, “OR”, “IF . . . THEN”, and “IF AND ONLY IF” are ubiquitous in both language and cognition; however, reasoning with logical connectives is error-prone. We argue that some of these errors may stem from people's tendency to minimize the number of possibilities compatible with logical connectives and to construct a “minimalist” one-possibility representation. As a result, connectives denoting a single possibility (e.g., conjunctions) are likely to be represented correctly, whereas connectives denoting multiple possibilities (e.g., disjunctions or conditionals) are likely to be erroneously represented as conjunctions. These predictions were tested and confirmed in three experiments using different paradigms. In Experiment 1, participants were presented with a multiple-choice task and asked to select all and only those possibilities that would indicate that compound verbal propositions were true versus false. In Experiment 2, a somewhat similar task was used, except that participants were asked later to perform a cued recall of verbal propositions. Finally, Experiment 3 used an old/new recognition paradigm to examine participants' ability to accurately recognize different logical connectives. The results of the three experiments are discussed in relation to theories of representation of possibilities and theories of reasoning.     

Strict embedding of the elementary ontology into the monadic second-order calculus of predicates admitting the empty individual domain

There is given the proof of strict embedding of Leniewski's elementary ontology into monadic second-order calculus of predicates providing a formalization of the class of all formulas valid in all domains (including the empty one). The elementary ontology with the axiom S (S S) is strictly embeddable into monadic second-order calculus of predicates which provides a formalization of the classes of all formulas valid in all non-empty domains.     

Internal approach to external sets and universes

A problem which enthusiasts ofIST, Nelson's internal set theory, usually face is how to treat external sets in the internal universe which does not contain them directly. To solve this problem, we considerBST,bounded set theory, a modification ofIST which is, briefly, a theory for the family of thoseIST sets which are members of standard sets.We show thatBST is strong enough to incorporate external sets in the internal universe in a way sufficient to develop the most advanced applications of nonstandard methods. In particular, we define inBST an enlargement of theBST universe which satisfies the axioms ofHST, an external theory close to a theory introduced by Hrbaek. HST includes Replacement and Saturation for all formulas but contradicts the Power Set and Choice axioms (either of them is incompatible with Replacement plus Saturation), therefore to get an external universe which satisfies all ofZFC minus Regularity one has to pay by a restriction of Saturation. We prove thatHST admits a system of subuniverses which modelZFC (minus Regularity but with Power Set and Choice) and Saturation in a form restricted by a fixed but arbitrary standard cardinal.Thus the proposed system of set theoretic foundations for nonstandard mathematics, based on the simple and natural axioms of the internal theoryBST, provides the treatment of external sets sufficient to carry out elaborate external constructions.Partially supported by AMS grants in 1993 and 1994 and DFG grant in 1994.Presented byRobert Goldblatt     

Two types of ball-effector interaction and their relative contribution to soccer kicking

The study attempts a closer examination of the ball-foot interaction at the instant of soccer kicking using high speed videotaping. This allows a detailed biomechanical analysis of the collision. A central question is whether the ball-foot interaction can be modeled as an elastic impact, or as a mixture of ‘impact-like’ and ‘throwing-like’ patterns. The findings prove that the theory of conservation of momentum alone is not adequate for modeling kicking: additional momentum and mechanical energy is supplied to the system during the collision phase because of the muscle work. This is due to the relatively long duration of collision (about 16 ms) and the large ball-foot displacement (about 26.0 cm). More than 50% of the ball's speed and at least 30% of its kinetic energy is imparted to the ball without any contribution of the potential energy of the ball deformation.     

Sticking to common values: Neighbourhood social cohesion moderates the effect of value congruence on life satisfaction

This article aims to explicate the role of social cohesion in the relationship between adherence to common values and life satisfaction. Shared values are often assumed to be a constitutive element of social cohesion and are used in measurement of the concept. However, sociopsychological theory of values sees social cohesion rather as a moderator of the link between value congruence and life satisfaction, not as a constituent of value congruence. Based on a representative survey of the city of Bremen, Germany (N = 2605), we predict life satisfaction from person‐group value congruence and neighbourhood social cohesion. We find no relationship between value congruence and social cohesion, but a significant positive moderating effect of social cohesion on the relationship between value congruence and life satisfaction. The findings suggest that sticking to common values does not increase social cohesion, but that positive effects of value congruence are more pronounced in high‐cohesion neighbourhoods.     

When development and learning decrease memory. Evidence against category-based induction in children

Inductive inference is crucial for learning: If one learns that a cat has a particular biological property, one could expand this knowledge to other cats. We argue that young children perform induction on the basis of similarity of compared entities, whereas adults may induce on the basis of category information. If different processes underlie induction at different points in development, young children and adults would form different memory traces during induction, and would subsequently have different memory accuracy. Experiment 1 demonstrates that after performing an induction task, 5-year-olds exhibit more accurate memory than adults. Experiment 2 indicates that after 5-year-olds are trained to perform induction in an adultlike manner, their memory accuracy drops to the level of adults. These results, indicating that sometimes 5-year-olds exhibit better memory than adults, support the claim that, unlike adults, young children perform similarity-based rather than category-based induction.