Related papers: First-Order Continuous Induction, and a Logical St…
We introduce a new logic, called \emph{cluster first-order logic}, a restricted fragment of first-order logic specifically designed to study order invariance. An order-invariant formula is one on a vocabulary that contains an order;…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
We show that many principles of first-order arithmetic, previously only known to lie strictly between $\Sigma_1$-induction and $\Sigma_2$-induction, are equivalent to the well-foundedness of $\omega^\omega$. Among these principles are the…
The one-variable fragment of a first-order logic may be viewed as an "S5-like" modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have…
Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms…
A geometric first-order axiomatization of differentially closed fields of characteristic zero with several commuting derivations, in the spirit of Pierce-Pillay, is formulated in terms of a relative notion of prolongation for Kolchin-closed…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
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…
First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…
We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is…
Given a first-order theory $T$ formulated in the usual language of first-order arithmetic, we say that $T$ is of *restricted complexity* if there is some natural number $n$ and some set $\mathcal A$ of $\Sigma_n$-sentences such that $T$ can…
Many of the theorems of real analysis, against the background of the ordered field axioms, are equivalent to Dedekind completeness, and hence can serve as completeness axioms for the reals. In the course of demonstrating this, the article…
Dependence logic, introduced in [8], cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized, and this is what we shall do in this paper. We give an explicit axiomatization and prove the…
We investigate the properties of Inclusion Logic, that is, First Order Logic with Team Semantics extended with inclusion dependencies. We prove that Inclusion Logic is equivalent to Greatest Fixed Point Logic, and we prove that all…
By a well-known result of Shepherdson, models of the theory IOpen (a first order arithmetic containing the scheme of induction for all quantifier free formulas) are exactly all the discretely ordered semirings that are integer parts of…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
Let $G$ be a finite group. Then there exists a first-order statement $S(G)$ in the language of rings without parameters and depending only on $G$ such that, for any field $K$, we have that $K\models S(G)$ if and only if $K$ has a Galois…
A first-order theory $T$ is a model-complete core theory if every first-order formula is equivalent modulo $T$ to an existential positive formula; the core companion of a theory $T$ is a model-complete core theory $S$ such that every model…
First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…