We investigate the complexity of several decision, enumeration and counting problems in axiom pinpointing in Description Logics. We prove hardness results that already hold for the propositional Horn fragment. We show that for this fragment, unless p = np, all minimal subsets of a given TBox that have a given consequence, i.e. MinAs, cannot be enumerated in a specified lexicographic order with ...

We study properties of closure operators of singular cofinality, and introduce several ZFC sufficient and equivalent conditions for the existence of antichain sequences in posets of singular cofinality. We also notice that the Proper Forcing Axiom implies the Milner-Sauer conjecture.

For axiom A diffeomorphisms and equilibrium state, we prove a Large deviation result for the sequence of successive return times into a fixed open set, under some assumption on the boundary. Our result relies on and extends the work by Chazottes and Leplaideur who where considering cylinder sets of a Markov partition.

In this note we interpret Voevodsky’s Univalence Axiom in the language of (abstract) model categories. We then show that any posetal locally Cartesian closed model category Qt in which the mapping Hom(w)(Z × B,C) : Qt −→ Sets is functorial in Z and represented in Qt satisfies our homotopy version of the Univalence Axiom, albeit in a rather trivial way. This work was motivated by a question repo...

The paper investigates navigability with imperfect information. It shows that the properties of navigability with perfect recall are exactly those captured by Armstrong’s axioms from database theory. If the assumption of perfect recall is omitted, then Armstrong’s transitivity axiom is not valid, but it can be replaced by a weaker principle. The main technical results are soundness and complete...

A choice correspondence is weak justified if a non-chosen alternative is dominated by any other obtainable alternative, and for each discarded alternative there is some chosen alternative which dominates it. This definition allows us to build a connection between the behavioral property expressed by the weak axiom of revealed non-inferiority and a weak form of maximality. It is weaker than the ...

We show that the product of infranilmanifolds with certain aspherical closed manifolds do not support Anosov diffeomorphisms. As a special case, we obtain that products of a nilmanifold and negatively curved manifolds of dimension at least 3 do not support Anosov diffeomorphisms. Mathematics Subject Classification. Primary 37D20; Secondary 55R10, 57R19, 37C25.

This paper uses an atomistic ontology of universals, individuals, and facts to provide a semantics for ramified type theory. It is shown that with some natural constraints on the sort of universals and facts admitted into a model, the axiom of reducibility is made valid.

In this paper, we study trees of uncountable regular heights containing ascending paths of small width. This combinatorial property of trees generalizes the concept of a cofinal branch and it causes trees to be non-special not only in V, but also in every cofinality-preserving outer model of V. Moreover, under certain cardinal arithmetic assumptions, the non-existence of such paths through a tr...

We study the projective posets and their properties as forcing notions. We also define Martin’s axiom restricted to projective sets, MA(proj), and show that this axiom is weaker than full Martin’s axiom by proving the consistency of ZFC + XH + MA(proj) with “there exists a Suslin tree”, “there exists a non-strong gap”, “there exists an entangled set of reals” and “there exists K < 2No such that...