In this note we remark on the problem of equality of objects in categories formalized in Martin-Löf’s constructive type theory. A standard notion of category in this system is E-category, where no such equality is specified. The main observation here is that there is no general extension of E-categories to categories with equality on objects, unless the principle Uniqueness of Identity Proofs (...

The fluted fragment is a of first-order logic (without equality) in which, roughly speaking, the order quantification variables coincides with which those appear as arguments predicates. It known that this has finite model property. We consider extensions various numbers transitive relations, well equality predicate. In presence one relation (together equality), property lost; nevertheless, we ...

Links between heterogeneous data sets may be found by using a generalisation of keys in databases, called linkkeys, which apply across data sets. This paper considers the question of characterising such keys in terms of formal concept analysis. This question is natural because the space of candidate keys is an ordered structure obtained by reduction of the space of keys and that of data set par...

In this paper, a displacement-constrained volume-minimizing topology optimization model is present for two-dimensional continuum problems. The new model is a generalization of the displacement-constrained volume-minimizing model developed by Yi and Sui [1] in which the displacement is constrained in the loading point. In the original model the displacement constraint was formulated as an equali...

We study subtyping of recursive types in the presence of associative and commutative products—that is, subtyping modulo a restricted form of type isomorphisms. We show that this relation, which we claim is useful in practice, is a composition of the usual subtyping relation with the recently proposed notion of equality up to associativity and commutativity of products, and we propose an efficie...

In this paper we present an analysis of assembly code for safetycritical embedded environments. Since local and global variables are the core concepts affecting the control flow of such programs, we first concentrate on classifying memory accesses as candidates for local or global variables. This is achieved by an interprocedural analysis of affine equality relations. We present how to refine t...

In a typing system, there are two approaches that may be taken to the notion of equality. One can use some external relation of convertibility defined on the terms of the grammar, such as β-convertibility or βη-convertibility; or one can introduce a judgement form for equality into the rules of the typing system itself. For quite some time, it has been an open problem whether the two systems pr...

In systems driven away from equilibrium, the velocity correlation function and the linear-response function to a small perturbation force do not satisfy the fluctuation-response relation (FRR) due to the lack of detailed balance in contrast to equilibrium systems. In this Letter, an equality between an extent of the FRR violation and the rate of energy dissipation is proved for Langevin systems...

The paper considers an early approach toward a (fuzzy) set theory with a graded membership predicate and a graded equality relation which had been developed by the German mathematician D. Klaua in 1965. In the context of the mathematical fuzzy logic MTL of left-continuous t-norms we discuss some properties of these graded relations. We compare the simultaneous recursive definitions of these rel...