Several axioms concerning probabilistic beliefs are examined here, and the relations between them are established, using belief spaces that generalize Harsanyi type spaces. Two axioms concerning highorder probabilistic beliefs are investigated in particular. The first is the triviality axiom, which says that one is certain (that is, has a belief of degree one) of one’s own beliefs. The second i...

Automatic knowledge base enrichment methods rely critically on candidate axiom scoring. The most popular scoring heuristics proposed in the literature are based on statistical inference. We argue that such a probability-based framework is not always completely satisfactory and propose a novel, alternative scoring heuristics expressed in terms of possibility theory, whereby a candidate axiom rec...

We study the spectrum of forcing notions between the iterations of σ-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of α-proper forcings for indecomposable countable ordinals α as well as the Axiom A forcings. We focus on the bounded forcing axioms for the hierarchy of αproper forcings. Following ideas of Shelah we separate them for distinct countable indec...

We recast Selinger’s CPM-construction of completely positive maps [11] as an axiomatization of maximally mixed states. This axiomatization also guarantees categories of completely positive maps to satisfy the preparation-state agreement axiom of [3], and admits a physical interpretation in terms of purification of mixed states and CPMs. Internal traces, which are crucial in quantum information ...

In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $C(X)$,  the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter ...

Themain aim of this paper is to provide a construction of the Banaschewski compactification of a zero-dimensional Hausdorff topological space as a structure space of a ring of ordered field-valued continuous functions on the space, and thereby exhibit the independence of the construction from any completeness axiom for an ordered field. In the process of describing this construction we have gen...

By a space, we always mean topological space. Throughout the paper, we mostly use the standard topological notions as in [1] or [3] with the exception that all spaces are assumed without any separation axioms. Especially, compactness is understood without the Hausdorff separation axiom. Some definitions (with broad references and explanations) of less standard notions (related especially to non...

This theorem is stronger than a result which Iohvidov [3] derived from the fundamental theorem of [6]. Iohvidov's theorem is so related to Pontrjagin's fundamental theorem that either one can be obtained from the other by a transform analogous to the Cayley transform (see [4]). Pontrjagin's proof of his theorem uses delicate and rather complicated arguments. Kreïn's proof of the theorem stated ...

Cantor proved in 1874 [Cantor G (1874) J Reine Angew Math 77:258-262] that the continuum is uncountable, and Hilbert's first problem asks whether it is the smallest uncountable cardinal. A program arose to study cardinal invariants of the continuum, which measure the size of the continuum in various ways. By Gödel [Gödel K (1939) Proc Natl Acad Sci USA 25(4):220-224] and Cohen [Cohen P (1963) P...