Related papers: A note on powers of Boolean spaces with internal s…
We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.
We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
There are many examples of dualities between topological spaces and algebras in the literature. Particularly, many of those examples come from the algebraic counterpart of a logical system, e.g, boolean and heyting algebras, MV-algebras,…
Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion…
Contextuality is a key signature of quantum non-classicality, which has been shown to play a central role in enabling quantum advantage for a wide range of information-processing and computational tasks. We study the logic of contextuality…
We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg's theorem. This theorem states that the lattice of all boolean algebras of regular languages…
We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on justification terms and equality predicate on terms. In…
We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant…
Necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Generalized conceptions of distances and dimensionality evaluation are…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of…
We study fragments of dependence logic defined either by restricting the number k of universal quantifiers or the width of dependence atoms in formulas. We find the sublogics of existential second-order logic corresponding to these…
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…
The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…
We define invariants of words in arbitrary groups, measuring how letters in a word are interleaving, perfectly detecting the dimension series of a group. These are the letter-braiding invariants. On free groups, braiding invariants coincide…
Quasi-Boolean algebras were introduced as the generalization of Boolean algebras in the setting of quantum computation logic. In this paper, we investigate the completeness and congruences of quasi-Boolean algebras. First, we discuss the…
It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…
Let $\mathrm{SO}^{\mathit{plog}}$ denote the restriction of second-order logic, where second-order quantification ranges over relations of size at most poly-logarithmic in the size of the structure. In this article we investigate the…
Semiring semantics of first-order logic generalises classical Boolean semantics by permitting truth values from a commutative semiring, which can model information such as costs or access restrictions. This raises the question to what…