We study a relationship between the Int construction of Joyal et al. and a weakening of biproducts called semibiproducts. We then provide an application of geometry of interaction interpretation for the multiplicative additive linear logic (MALL for short) of Girard. We consider not biproducts but semibiproducts because in general the Int construction does not preserve biproducts. We show that ...

Definition 1. The category Mot∼ is the Karoubian envelope (or idempotent completion) of the quotient of Mot ∼ by the ideal consisting of morphisms factoring through an object of the form M ⊗L, where L is the Lefschetz motive. This is a tensor additive category. If M ∈ Mot ∼ , we denote by M̄ its image in Mot∼. Lemma 1 ([6, Lemmas 5.3 and 5.4]). Let X, Y be two smooth projective irreducible k-var...

ANCHOR is an integrated memory-based scaling model that accounts for a wide range of phenomena in category rating and absolute identification. The model uses anchors stored in memory that serve as prototypes for each response category. The stimuli are represented by magnitudes. Two alternative formulations of the magnitude variability are considered: additive noise, which leads to logarithmic s...

An experiment was conducted to test the effectiveness of brief instruction in information structuring (i.e., representing and integrating information) for improving the coherence of probability judgments and binary choices among intelligence analysts. Forty-three analysts were presented with comparable sets of Bayesian judgment problems before and immediately after instruction. After instructio...

Tropical friezes are the tropical analogues of Coxeter-Conway frieze patterns. In this note, we study them using triangulated categories. A tropical frieze on a 2-Calabi-Yau triangulated category C is a function satisfying a certain addition formula. We show that when C is the cluster category of a Dynkin quiver, the tropical friezes on C are in bijection with the n-tuples in Z, any tropical fr...

The present study investigates some novel categorical properties of soft sets. By combining categorical theory with soft set theory, a categorical framework of soft set theory is established. It is proved that the category SFun of soft sets and soft functions has equalizers, finite products, pullbacks, and exponential properties. It is worth mentioning that we find that SFun is both a topologic...

A game semantics of the (−−∗,→)-fragment of the logic of bunched implications, BI, is presented. To date, categorical models of BI have been restricted to two kinds: functor category models; and the category Cat itself. The game model is not of this kind. Rather, it is based on Hyland-Ong-Nickau-style games and embodies a careful analysis of the notions of resource sharing and separation inhere...

ANCHOR is an integrated memory-based scaling model that accounts for a wide range of phenomena in category rating and absolute identification. The model uses anchors stored in memory that serve as prototypes for each response category. The stimuli are represented by magnitudes. Two alternative formulations of the magnitude variability are considered: additive noise, which leads to logarithmic s...

This paper presents a batch classifier that splits dataset into tree branches depending on the category type. It has been improved from earlier version and fixed mistake in paper. Two important changes have made. The first is to represent each with separate classifier. Each then classifies its own subset of data rows, using input values create centroid also itself. If contains more than one how...