Related papers: Incomplete Descriptions and Qualified Definiteness

Let A be a finite or countable alphabet and let $\theta$ be a literal (anti-)automorphism onto A * (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…

Let $G$ be a finite abelian group and $s$ be a positive integer. A subset $A$ of $G$ is called a {\em perfect $s$-basis of $G$} if each element of $G$ can be written uniquely as the sum of at most $s$ (not-necessarily-distinct) elements of…

This paper presents a version of simple type theory called ${\cal Q}^{\rm uqe}_{0}$ that is based on ${\cal Q}_0$, the elegant formulation of Church's type theory created and extensively studied by Peter B. Andrews. ${\cal Q}^{\rm uqe}_{0}$…

A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…

This paper presents an advance in the direction of working with probabilities in a paracomplete setting using Logics of Formal Undeterminedness (LFUs). The undeterminedness is interpreted here as missing evidence. A theorem of total…

We introduce a new real valued invariant for finitely presented groups called residual deficiency. Its main property is the following. Let G be a finitely presented group. If the residual deficiency of G is greater than one, then G has a…

By a proper cover of a finite group G we mean an extension of a nontrivial finite group by G. Our purpose is to show that a proper cover of a finite simple group L of Lie type always contains an element whose order differs from the element…

In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion…

We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an…

In this paper we consider a general way of constructing profinite struc- tures based on a given framework - a countable family of objects and a countable family of recognisers (e.g. formulas). The main theorem states: A subset of a family…

Four constructions result from a desire to create enhancements to Cantor's infinite real set cardinality. Each continues to keep Cantor's cardinality formulation in place while providing new comparisons of arbitrary infinite sets. To…

In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…

Nearly a decade ago, the science community was introduced to the $h$-index, a proposed statistical measure of the collective impact of the publications of any individual researcher. It is of course undeniable that any method of reducing a…

Two types of approximation to the paradoxical Russell Set are presented, one approximating it from below, one from above. It is shown that any lower approximation gives rise to a better approximation containing it, and that any upper…

We focus on explaining image classifiers, taking the work of Mothilal et al. [2021] (MMTS) as our point of departure. We observe that, although MMTS claim to be using the definition of explanation proposed by Halpern [2016], they do not…

In this paper, we provide a new characterization of uniformly recurrent words with finite defect based on a relation between the palindromic and factor complexity. Furthermore, we introduce a class of morphisms P_ret closed under…

Labeled examples (i.e., positive and negative examples) are an attractive medium for communicating complex concepts. They are useful for deriving concept expressions (such as in concept learning, interactive concept specification, and…

The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…

The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…

Sentences containing definite descriptions, expressions of the form `The $F$', can be formalised using a binary quantifier $\iota$ that forms a formula out of two predicates, where $\iota x[F, G]$ is read as `The $F$ is $G$'. This is an…