Related papers: First-Order Continuous Induction, and a Logical St…

Many theorems of mathematics have the form that for a certain problem, e.g. a differential equation or polynomial (in)equality, there exists a solution. The sequential version then states that for a sequence of problems, there is a sequence…

In this paper I introduce a new and intuitive first-order foundational theory (where the concept of set is not primitive) and use it to show that the power set of an infinite set does not exist. In particular, proofs of uncountability of a…

First-order logic (FOL) has proved to be a versatile and expressive tool as the basis of abstract modeling languages. Used to verify complex systems with unbounded domains, such as heap-manipulating programs and distributed protocols, FOL,…

We introduce INDUCTION, a benchmark for finite structure concept synthesis in first order logic. Given small finite relational worlds with extensionally labeled target predicates, models must output a single first order logical formula that…

In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…

We give a classification of non-orthogonality classes of trivial order 1 strongly minimal sets in differentially closed fields. A central idea is the introduction of $\tau$-forms, functions on the prolongation of a variety which are…

In this article we relate a family of methods for automated inductive theorem proving based on cycle detection in saturation-based provers to well-known theories of induction. To this end we introduce the notion of clause set cycles -- a…

Generalized Higman's Theorem is the direct counterpart of Higman's Theorem that asserts the closure of the class of \emph{better} quasi-orders, instead of the class of \emph{well} quasi-orders, under the construction $P\mapsto P^{<\omega}$…

Independence logic cannot be effectively axiomatized. However, first-order consequences of independence logic sentences can be axiomatized. In this article we give an explicit axiomatization and prove that it is complete in this sense. The…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

Well-known principles of induction include monotone induction and different sorts of non-monotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing…

We resolve the strong Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is a first-order sentence which characterizes this field within the class up to…

We investigate the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic theory of accelerated observers which has a model over every…

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 the problem of learning generalized first-order representations of concepts from a single example. To address this challenging problem, we augment an inductive logic programming learner with two novel algorithmic contributions.…

We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of several equivalent statements} borrowed from algebra, real analysis, general topology, and non-standard analysis. We also…

We deal with the monadic (second-order) theory of order. We prove all known results in a unified way, show a general way of reduction, prove more results and show the limitation on extending them. We prove (CH) that the monadic theory of…

We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…

The first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic…

Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…