Related papers: A Completeness Theorem for "Total Boolean Function…
This paper introduces a novel quantum algorithm that is able to classify a hierarchy of classes of imbalanced Boolean functions. The fundamental characteristic of imbalanced Boolean functions is that the proportion of elements in their…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds of applicative system. Each faithful cartesian club…
We give a semantics for the lambda-calculus based on a topological duality theorem in nominal sets. A novel interpretation of lambda is given in terms of adjoints, and lambda-terms are interpreted absolutely as sets (no valuation is…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random…
Textual Concept Bottleneck Models (TCBMs) are interpretable-by-design models for text classification that predict a set of salient concepts before making the final prediction. This paper proposes Complete Textual Concept Bottleneck Model…
The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: we prove that the notion of overlap morphism corresponds…
We give a new proof of a classical theorem on approximation of continuous functions on totally real sets
We characterise Tychonoff spaces X so that C(X) is universally {\sigma}-complete and universally complete, respectively.
In this note, we investigate the algebraic and topological representation theory of cylindric ortholattices and cylindric Boolean algebras. The first contribution demonstrates that cylindric ortholattices are closed under canonical…
The classical lemma of Borel reads: any power series with real coefficients is the Taylor series of a smooth function. Algebraically this means the surjectivity of the completion map at a point, $C^\infty(\Bbb{R}^n) \twoheadrightarrow…
Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability…
The aim of this paper is twofold. Firstly, we give easy-to-handle criteria to determine whether a given family of subsets of a vector space is a neighbourhood basis of the origin for a complete vector topology. Then, we apply these criteria…
We introduce full diffeomorphism-invariant Colombeau algebras with added $\varepsilone$-dependence in the basic space. This unites the full and special settings of the theory into one single framework. Using locality conditions we find the…
Boolos's proof of incompleteness is extended straightforwardly to yield simple ``diagonalization-free'' proofs of some classical limitative theorems of logic.
A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…
Classical (or Boolean) type theory is the type theory that allows the type inference $\sigma \to \bot) \to \bot => \sigma$ (the type counterpart of double-negation elimination), where $\sigma$ is any type and $\bot$ is absurdity type. This…
This paper introduces a model theory for resolution on Higher Order Hereditarily Harrop formulae (HOHH), the logic underlying the Lambda-Prolog programming language, and proves soundness and completeness of resolution. The semantics and the…
We give a new completion for the quasi-uniform spaces. We call the whole procedure {\it $\tau$-completion} and the new space {\it $\tau$-complement of the given}. The basic result is that every $T_{_0}$ quasi-uniform space has a…