Related papers: Nominal Topology for Data Languages
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to 'recover' the properties of classical…
We systematically study some basic properties of the theory of pre-topological spaces, such as, pre-base, subspace, axioms of separation, connectedness, etc. Pre-topology is also known as knowledge space in the theory of knowledge…
Word embeddings represent language vocabularies as clouds of $d$-dimensional points. We investigate how information is conveyed by the general shape of these clouds, instead of representing the semantic meaning of each token. Specifically,…
Starting from Boolean algebras of languages closed under quotients and using duality theoretic insights, we derive the notion of Boolean spaces with internal monoids as recognisers for arbitrary formal languages of finite words over finite…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
We define topological orthoalgebras (TOAs) and study their properties. While every topological orthomodular lattice is a TOA, the lattice of projections of a Hilbert space is an example of a lattice-ordered TOA that is not a toplogical…
Eilenberg's variety theorem marked a milestone in the algebraic theory of regular languages by establishing a formal correspondence between properties of regular languages and properties of finite monoids recognizing them. Motivated by…
We consider two-variable first-order logic FO2 over infinite words. Restricting the number of nested negations defines an infinite hierarchy; its levels are often called the half-levels of the FO2 quantifier alternation hierarchy. For every…
Nominal automata models serve as a formalism for data languages, and in fact often relate closely to classical register models. The paradigm of name allocation in nominal automata helps alleviate the pervasive computational hardness of…
This paper is devoted to the problems of ontology-based mathematical knowledge management and representation. The main attention is paid to the development of a formal model for the representation of mathematical statements in the Open…
We give a domain-theoretic semantics to a statistical programming language, using the plain old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably, our monad of minimal valuations is commutative, which…
We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to…
For every fixed class of regular languages, there is a natural hierarchy of increasingly more general problems: Firstly, the membership problem asks whether a given language belongs to the fixed class of languages. Secondly, the separation…
Given a regular language L, we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary semigroups generated by the pseudovariety R of all finite…
We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Reversible weighted automata are introduced and considered in a specific setting where the weights are taken from a nontrivial locally finite commutative ring such as a finite field. It is shown that the supports of series realised by such…
We present several naturally occurring classes of spectral spaces using commutative algebra on pointed monoids. For this purpose, our main tools are finite type closure operations and continuous valuations on monoids which we introduce in…