Related papers: Definiteness properties of first-order schemes

We propose to consider non confluence with respect to implicit complexity. We come back to some well known classes of first-order functional program, for which we have a characterization of their intentional properties, namely the class of…

We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of several existing categorical structures for differentiation,…

We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…

This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…

The formalization of First Passage schemes is revisited and the emerging of a conceptual contradiction is underlined. We then show why, despite such a contradiction, the numerical results are not explicitly affected. Through a different…

Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…

Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…

For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…

We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number…

We consider several formalizations in the language of second-order arithmetic of "The formula $\phi$ is a theorem of $\omega$-logic", including some which have been studied in the literature and a new variant defined via a least fixed…

A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…

In this paper, the (infinite) direct product of fields is investigated. In particular, the finiteness of a given set is characterized in terms of some ring-theoretic observations. Next, a certain localization (whose multiplicative set…

Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…

Informally speaking, the categoricity of an axiom system means that its non-logical symbols have only one possible interpretation that renders the axioms true. Although non-categoricity has become ubiquitous in the second half of the 20th…

The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…

Program semantics can often be expressed as a (many-sorted) first-order theory S, and program properties as sentences $\varphi$ which are intended to hold in the canonical model of such a theory, which is often incomputable. Recently, we…

We introduce some notions of invariant elementary definability which extend the notions of first-order order-invariant definability, and, more generally, definability invariant with respect to arbitrary numerical relations. In particular,…

Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…

We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…

First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…