We logically model uncertainty by expanding language without changing logical reasoning rules. We expand the language of set theory by adding new predicate symbols, uncertain membe...
: Many of the Internet's problems are related to names. There are many empirical ideas of the further development of naming on the Internet. However, there are no theoretical ...
Sets play a key role in foundations of mathematics. Why? To what extent is it an accident of history? Imagine that you have a chance to talk to mathematicians from a far-away plane...
Abstract. We have designed a programming logic based on an integration of functional programming languages with classical set theory. The logic merges a classical view of equality ...
Abstract. Set theory is the common language of mathematics. Therefore, set theory plays an important r^ole in many important applications of automated deduction. In this paper, we ...
This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. O...
We consider the problem of providing formal support for working tract syntax involving variable binders. Gabbay and Pitts have shown in their work on Fraenkel-Mostowski (FM) set th...
Set theories are traditionally based on first-order logic. We show that in a constructive setting, basing a set theory on a dependent logic yields many benefits. To this end, we...
Abstract. Both fuzzy set theory and rough set theory play an important role in data-driven, systems modelling and analysis. They have been successfully applied to building various ...