Related papers: Going higher in the First-order Quantifier Alterna…

We prove that there are single Henkin quantifiers such that first order logic augmented by one of these quantifiers is undecidable in the empty vocabulary. Examples of such quantifiers are given.

We have reviewed some results on quantized shuffling, and in particular, the grading and structure of this algebra. In parallel, we have summarized certain details about classical shuffle algebras, including Lyndon words (primes) and the…

In this article we provide effective characterisations of regular languages of infinite trees that belong to the low levels of the Wadge hierarchy. More precisely we prove decidability for each of the finite levels of the hierarchy; for the…

In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…

It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of…

The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…

We study the expressive power of fragments of inclusion and independence logic defined by restricting the number k of universal quantifiers in formulas. Assuming the so-called strict semantics for these logics, we relate these fragments of…

Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary…

We show that the existence of a first-order formula separating two monadic second order formulas over countable ordinal words is decidable. This extends the work of Henckell and Almeida on finite words, and of Place and Zeitoun on…

We introduce Bifurcation Logic, BL, which combines a basic classical modality with separating conjunction * together with its naturally associated multiplicative implication, that is defined using the modal ordering. Specifically, a formula…

We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an $\exists^*\forall^*$ quantifier prefix (over variables, functions…

In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all…

We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…

In recent years, G\"odel's ontological proof and variations of it were formalized and analyzed with automated tools in various ways. We supplement these analyses with a modeling in an automated environment based on first-order logic…

The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been…

We prove level-by-level upper and lower bounds on the strength of determinacy for finite differences of sets in the hyperarithmetical hierarchy in terms of subsystems of finite-and transfinite-order arithmetic, extending the…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

Classically, in saturation-based proof systems, unification has been considered atomic. However, it is also possible to move unification to the calculus level, turning the steps of the unification algorithm into inferences. For calculi that…

We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…

Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…