Abstract It is proven that the homotopy time-slice axiom for many types of algebraic quantum field theories (AQFTs) taking values in chain complexes can be strictified. This includes cases Haag–Kastler-type AQFTs on a fixed globally hyperbolic Lorentzian manifold (with or without time-like boundary), locally covariant conformal two spacetime dimensions, one dimension, and relative Cauchy evolut...

  One of the most famous methods for recommendation is user-based Collaborative Filtering (CF). This system compares active user’s items rating with historical rating records of other users to find similar users and recommending items which seems interesting to these similar users and have not been rated by the active user. As a way of computing recommendations, the ultimate goal of the user-ba...

§9.1 The Axiom of Choice We come now to the most important part of set theory for other branches of mathematics. Although infinite set theory is technically the foundation for all mathematics, in practice it is perfectly valid for a mathematician to ignore it – with two exceptions. Of course most of the basic set constructions as outlined in chapter 2 (unions, intersections, cartesian products,...

This paper continues a line of work that studies individual preference upgrades in order to model situations akin to a process of public deliberation in collective decision making. It proposes a general upgrade policy, presenting its semantic definition and a corresponding modality for describing its effects as well as a complete axiom system.

we deal with a wide range of colors in our daily life. they are such ubiquitous phenomena that is hard and next to impossible to imagine even a single entity (be it an object, place, living creature, etc) devoid of them. they are like death and tax which nobody can dispense with. this omnipresence of colors around us has also made its way through abstract and less tangible entities via the inte...

We define a general family of hypersequent systems with well-behaved logical rules, of which the known hypersequent calculus for (propositional) Gödel logic, is a particular instance. We present a method to obtain (possibly, non-deterministic) many-valued semantics for every system of this family. The detailed semantic analysis provides simple characterizations of cut-admissibility and axiom-ex...

It is proved that the axiom of determinateness of Mycielski and Steinhaus for games in which players alternate in writing reals implies that co -» (co)" (i-e. for every partition of infinite sets of natural numbers into two classes there is an infinite set such that all its infinite subsets belong to the same class). For every infinite N C co, fi(A/) denotes the family of infinite subsets of N....

DL-Lite is a tractable fragment of Description Logics, which provides a powerful framework to compactly encode available knowledge with a low computational complexity of the reasoning process. Belief revision is an important problem that appears in many applications and especially in the semantic web area. This paper investigates the so-called “Removed Sets Revision” for revising DL-Lite knowle...

An argument often given for adopting the Axiom of Choice as an axiom is that it has a lot of obviously true consequences. This looks like a legitimate application of the practice of Inference to the Best Explanation. However, the standard examples of obvious-truths-following-from-AC all turn out, on closer inspection, to involve a fallacy of equivocation.

Properties like logical closure and consistency are important properties in any logical reasoning system. Caminada and Amgoud showed that not every logic-based argument system satisfies these relevant properties. But under conditions like closure under contraposition or transposition of the monotonic part of the underlying logic, ASPIC-like systems satisfy these properties. In contrast, the log...