Related papers: First-order separation over countable ordinals

We discuss the modifications of the Kripke trick simulating binary predicate letters of classical first-order formulas with monadic modal first-order formulas and the situations where the trick does not work. As a result, we obtain results…

Monadic decomposability is a notion of variable independence, which asks whether a given formula in a first-order theory is expressible as a Boolean combination of monadic predicates in the theory. Recently, Veanes et al. showed the…

Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…

We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.

Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which…

We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all…

We indicate a way of distinguishing between structures, for which, we call two structures distinguishable. Roughly, being distinguishable means that they differ in the number of realizations each gives for some formula. Being…

Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…

In a constructive setting, no concrete formulation of ordinal numbers can simultaneously have all the properties one might be interested in; for example, being able to calculate limits of sequences is constructively incompatible with…

Until recently, First-Order Temporal Logic (FOTL) has been little understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However,…

We study the problem of deciding satisfiability of first order logic queries over views, our aim being to delimit the boundary between the decidable and the undecidable fragments of this language. Views currently occupy a central place in…

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…

Let $\RR_S$ denote the expansion of the real ordered field by a family of real-valued functions $S$, where each function in $S$ is defined on a compact box and is a member of some quasianalytic class which is closed under the operations of…

Since the 1970s with the work of McNaughton, Papert and Sch\"utzenberger, a regular language is known to be definable in the first-order logic if and only if its syntactic monoid is aperiodic. This algebraic characterisation of a…

In this note, we present a characterization of sets definable in Skolem arithmetic, i.e., the first-order theory of natural numbers with multiplication. This characterization allows us to prove the decidability of the theory. The idea is…

We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…

We look at classes of languages associated to the fragment of first-order logic B{\Sigma}1 which disallows quantifier alternations. Each class is defined by choosing the set of predicates on positions that may be used. Two key such…

Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…

Using a recently introduced algebraic framework for the classification of fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the…

It is known due to the work of Van den Broeck et al [KR, 2014] that weighted first-order model counting (WFOMC) in the two-variable fragment of first-order logic can be solved in time polynomial in the number of domain elements. In this…