Geometric analogue of holographic reduced representation

Holographic reduced representations (HRRs) are distributed representations of cognitive structures based on superpositions of convolution-bound n-tuples. Restricting HRRs to n-tuples consisting of ±1, one reinterprets the variable binding as a representation of the additive group of binary n-tuples with addition modulo 2. Since convolutions are not defined for vectors, the HRRs cannot be directly associated with geometric structures. Geometric analogues of HRRs are obtained if one considers a projective representation of the same group in the space of blades (geometric products of basis vectors) associated with an arbitrary n-dimensional Euclidean (or pseudo-Euclidean) space. Switching to matrix representations of Clifford algebras, one can always turn a geometric analogue of an HRR into a form of matrix distributed representation. In typical applications the resulting matrices are sparse, so that the matrix representation is less efficient than the representation directly employing the rules of geometric algebra. A yet more efficient procedure is based on ‘projected products’, a hierarchy of geometrically meaningful n-tuple multiplication rules obtained by combining geometric products with projections on relevant multivector subspaces. In terms of dimensionality the geometric analogues of HRRs are in between holographic and tensor-product representations.     

Synonymy in sentential languages: a pragmatic view

In this note two notions of meaning are considered and accordingly two versions of synonymy are defined, weaker and stronger ones. A new semantic device is introduced: a matrix is said to be pragmatic iff its algebra is in fact an algebra of meanings in the stronger sense. The new semantics is proved to be universal enough (Theorem 1), and it turns out to be in some sense a generalization of Wójcicki's referential semantics (Theorem 3).     

The existence of matrices strongly adequate for E,R and their fragments

A logic is a pair (P,Q) where P is a set of formulas of a fixed propositional language and Q is a set of rules. A formula is deducible from X in the logic (P, Q) if it is deducible from XP via Q. A matrix is strongly adequate to (P, Q) if for any , X, is deducible from X iff for every valuation in , is designated whenever all the formulas in X are. It is proved in the present paper that if Q = {modus ponens, adjunction } and P {E, R, E ⁺, R ⁺, E ^I, R ^I } then there exists a matrix strongly adequate to (P, Q).     

Temporal stability of the Czech translation of the Satisfaction with Life Scale: test-retest data over one week

The present study supplemented the limited 1999 psychometric data by Lewis, et al. on the Czech translation of the Satisfaction With Life Scale by examining the temporal stability of the measure over a 1-wk. period for 64 Czech undergraduate university students. Analysis indicated stability across the two administrations was very high (r=.90), and there was no significant change between Time 1 (M=23.7, SD=5.1) and Time 2 (M=24.1, SD=5.5). Short-term test-retest reliability of this Czech translation is supported.     

Undefinability of propositional quantifiers in the modal system S4

We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation fromS4² (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and □.     

Formal systems for modal operators on locales

In the paper [8], the first author developped a topos- theoretic approach to reference and modality. (See also [5]). This approach leads naturally to modal operators on locales (or spaces without points). The aim of this paper is to develop the theory of such modal operators in the context of the theory of locales, to axiomatize the propositional modal logics arising in this context and to study completeness and decidability of the resulting systems.     

Self-Assessed Risk of HIV and Other STIs Among Young Adults in Norway and Croatia

The purpose of the present study is to explore how sexually active young Norwegian and Croatian adults assess the risk of being infected with HIV and other STIs. Study results are based on a 2009–2010 large-scale national probability survey of young adults aged 18–24 in Croatia (n = 1,005) and Norway (n = 871). A majority of sexually active young adults in Croatia and Norway assessed the risk of becoming infected with HIV or other STIs as low or negligible. Among non-condom users, 85–98% determined they had low or no risk of getting infected with HIV. The corresponding figures for STIs were 77–79%. In both countries a higher HIV risk self-assessment was observed among those who had had same-sex sexual experience, those who reported a higher number of sex partners during the past year, and those who were single. When investigating the patterns of HIV/STI risk assessment, gender and country-related differences appeared. Condom use associated with higher risk assessment was significant only among Croatian men. The strong perception of condom use as being a male responsibility in Croatia may be the reason for a higher risk assessment for unwanted pregnancy and HIV/STIs when protection fails. The risk assessment for HIV/STIs was not associated with partner turnover in Croatian men. New campaigns need to develop gender-sensitive messages, particularly targeting men who believe that a great number of sexual partners is a sign of manliness and women who shy away from their responsibility to use protection.