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Today, claims for social justice seem to divide into two types: claims for the redistribution of resources and claims for the recognition of cultural difference. Increasingly, these two kind of claims are polarized against one another. As a result, we are asked to choose between class politics and identity politics, social democracy and multiculturalism, redistribution and recognition. These, h...

Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences as the strong sub-additivity of von Neumann entropy, the Golden-Thompson trace inequality and the monotonicity of the Holevo quantitity. The relation to quantum Markov states is briefly ind...

The paper presents a generalization of the main theorem of fuzzy concept lattices. The theorem is investigated from the point of view of fuzzy logic. There are various fuzzy order types which differ by incorporated relation of antisymmetry. This paper focuses on fuzzy order which uses fuzzy antisymmetry defined by means of multiplication operation and fuzzy equality.

We prove an extensionality theorem for the “type-in-type” dependent type theory with Σ-types. We suggest that in type theory the notion of extensional equality be identified with the logical equivalence relation defined by induction on type structure. 1998 ACM Subject Classification F.4.1 Mathematical Logic

Linear constraints occur naturally in many reasoning problems and the information that they represent is often uncertain. There is a difficulty in applying AI uncertainty formalisms to this situation, as their representation of the underlying logic, either as a mutually exclusive and exhaustive set of possibilities, or with a propositional or a predicate logic, is inappropriate (or at least unh...

Wolfson for their helpful comments and suggestions. This paper represents the views of the authors and does not necessarily reflect the opinions of Statistics Canada.