Related papers: Syntactic Structure, Quantum Weights
One of the crucial generic techniques for quantum computation is amplitude encoding. Although several approaches have been proposed, each of them often requires exponential classical-computational cost or an oracle whose explicit…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to…
We give a syntactic characterization of abstract elementary classes (AECs) closed under intersections using a new logic with a quantifier for isomorphism types that we call structural logic: we prove that AECs with intersections correspond…
A gravitational scenario is proposed where the euclidean action is invariant under the isotropic and homogeneous version of the euclidean {\it U(1)} group of local transformations of the scale factor and scalar matter field, interpreting…
We introduce and investigate a weighted propositional configuration logic over commutative semirings. Our logic is intended to serve as a specification language for software architectures with quantitative features. We prove an efficient…
The Lorentzian metric structure used in any field theory allows one to implement the relativistic notion of causality and to define a notion of time dimension. This article investigates the possibility that at the microscopic level the…
Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is…
Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different…
The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that explains correctly the…
The minimum average number of bits need to describe a random variable is its entropy, assuming knowledge of the underlying statistics On the other hand, universal compression supposes that the distribution of the random variable, while…
Existential rules form an expressive Datalog-based language to specify ontological knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the…
A central method for analyzing the asymptotic complexity of a functional program is to extract and then solve a recurrence that expresses evaluation cost in terms of input size. The relevant notion of input size is often specific to a…
We consider the quantum mechanics of Einstein gravity linearised about flat spacetime. The two transverse-traceless components of the metric perturbation are the true physical degrees of freedom. They appear in the quantum theory as free…
A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…
Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified…
We develop a unified categorical theory of substructural abstract syntax with variable binding and single-variable (capture-avoiding) substitution. This is done for the gamut of context structural rules given by exchange (linear theory)…
We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental…
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at…