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Several philosophers have proposed an "algebraic" view of universals according to which there are operations from universals to universals. It is not obvious, nevertheless, how those operations should be interpreted, and what impact they have for the conditions of identity of universals. There are two main interpretations of the algebra of universals. On one hand, it has been interpreted as ways to "construct" complex universals. On the other hand, it has been interpreted as "morphisms" or "mappings", but not as something that "builds" complex universals from others more basic. In this paper, the comparative advantages of both conceptions are assessed and reasons are offered to prefer the second conception. [ABSTRACT FROM AUTHOR]

In this paper, we show general properties of total rings of fractions and of Hermite rings. We study the relationships between those rings and the finite dimensional K--algebras. A finite dimensional K--algebras is a commutative algebra with unit such that this is finite dimensional as vector space over a field K. We proof that the finite dimensional K--algebras are total rings of fractions and also Hermite rings. In addition, we show that direct product of fields is another example of total ring of fractions and Hermite ring. [ABSTRACT FROM AUTHOR]

In this paper we propose a tableaux method for the intermediate syllogistic of Peterson and Thompson by using the algebra of Sommers and Englebretsen. The result is an analytic tableaux method capable of modeling inference in basic, relational, and intermediate syllogistic. [ABSTRACT FROM AUTHOR]

This paper presents an image synthesis algorithm for rendering views of a real scene taken with a virtual camera which is located between two real cameras. Specifically, this paper presents how, under certain conditions, a pair of views is enough to obtain a full set of possible views by following the line that joins their optical centers (baseline) without reconstructing explicit 3D models. Test results show the viability of the proposed algorithm for simple scenes (an object with a simple geometry, which is opaque, and does not present any occlusions). [ABSTRACT FROM AUTHOR]

The goals of this paper fall into two closely related areas. First, we develop a formal framework for deterministic unital quantities in which measurement unitization is understood to be a built-in feature of quantities rather than a mere annotation of their numerical values with convenient units. We introduce this idea within the setting of certain ordered semigroups of physical-geometric states of classical physical systems. States are assumed to serve as truth makers of metrological statements about quantity values. A unital quantity is presented as an isomorphism from the target system's ordered semigroup of states to that of positive reals. This framework allows us to include various derived and variable quantities, encountered in engineering and the natural sciences. For illustration and ease of presentation, we use the classical notions of length, time, electric current and mean velocity as primordial examples. The most important application of the resulting unital quantity calculus is in dimensional analysis. Second, in evaluating measurement uncertainty due to the analog-to-digital conversion of the measured quantity's value into its measuring instrument's pointer quantity value, we employ an ordered semigroup framework of pointer states. Pointer states encode the measuring instrument's indiscernibility relation, manifested by not being able to distinguish the measured system's topologically proximal states. Once again, we focus mainly on the measurement of length and electric current quantities as our motivating examples. Our approach to quantities and their measurement is strictly state-based and algebraic in flavor, rather than that of a representationalist-style structure-preserving numerical assignment. [ABSTRACT FROM AUTHOR]

This paper presents the partial results of a research on the professional knowledge of mathematics olympiad evaluators teachers put into action when analyzing errors relating to algebra. By means of two tests on errors interpretation and by using analysis inspired by the grounded theory, we obtained dimensions for the characterization of knowledge in understanding about errors. In the results section, we describe a teacher's knowledge related to practice and knowledge about students' learning. [ABSTRACT FROM AUTHOR]