Strong normalization results are obtained for a general language for collection types. An induced normal form for sets and bags is then used to show that the class of functions whose input has height (that is, the maximal depth of nestings of sets/bags/lists in the complex object) at most i and output has height at most o de nable in a nested relational query language without powerset operator ...

We present two results which shed some more light on the deep connection between ZFA and the standard ZF set theory: First of all we refine a result of Forti and Honsell (see [5]) in order to prove that the universe of ZFA can also be obtained (without appealing to choice) as the least fixed point of a continuous operator and not only as the greatest fixed point of the powerset operator. Next w...

Let CABA be the category of complete and atomic boolean algebras homomorphisms, let CSL meet-semilattices meet-homomorphisms. We show that forgetful functor from to has a left adjoint. This allows us describe an endofunctor H on such Alg(H) for is dually equivalent Coalg(P) coalgebras powerset P Set. As consequence, we derive Thomason duality Tarski duality, thus paralleling how J\'onsson-Tarsk...

Polarized unification grammar (PUG) is a linguistic formalism which uses polarities to better control the way grammar fragments interact. The grammar combination operation of PUG was conjectured to be associative. We show that PUG grammar combination is not associative, and even attaching polarities to objects does not make it order-independent. Moreover, we prove that no non-trivial polarity s...

My talk is divided into five parts. In the first part the relevance of the chiral fermion issue to fundamental particle physics and to numerical QCD will be explained. In the second part the basic ideas of the overlap construction will be reviewed. In the third part I shall focus on the algebraic (as opposed to kinematic) meaning of the overlap. In the fourth part I shall discuss in greater det...

This paper introduces a generalization of self-dual marked flattenings defined in the lattice of mappings. This definition provides a way to associate a self-dual operator to every mapping that decomposes an element into subelements (i.e. gives a cover). Contrary to classical flattenings whose definition relies on the complemented structure of the powerset lattices, our approach uses the pseudo...

Innnite behavior of nondeterministic nite state automata running over innnite trees or more generally over elements of an arbitrary algebraic structure is characterized by a calculus of xed point terms interpreted in powerset algebras. These terms involve the least and greatest xed point operators and disjunction as the only logical operation. A tight correspondence is established between a hie...