Related papers: Characterizing Strongly First Order Dependencies: …
We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
Large Language Models (LLMs) have demonstrated outstanding performance in mathematical reasoning capabilities. However, we argue that current large-scale reasoning models primarily rely on scaling up training datasets with diverse…
We study extensions of expressive decidable fragments of first-order logic with circumscription, in particular the two-variable fragment FO$^2$, its extension C$^2$ with counting quantifiers, and the guarded fragment GF. We prove that if…
This paper proposes decoupling the dependency tree from word order, such that surface ordering is not determined by traversing the dependency tree. We develop the notion of a \emph{word order domain structure}, which is linked but…
We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem…
The Tarskian classical relevant logic TR arises from Tarski's work on the foundations of the calculus of relations and on first-order logic restricted to finitely many variables, presented by Tarski and Givant their book, A Formalization of…
We develop team semantics for Linear Temporal Logic (LTL) to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties. Conceptually, we consider an asynchronous and a…
Current language models have demonstrated their capability to develop basic reasoning, but struggle in more complicated reasoning tasks that require a combination of atomic skills, such as math word problem requiring skills like arithmetic…
Large complexity classes, like the exponential time hierarchy, received little attention in terms of finding complete problems. In this work a generalization of propositional logic is investigated which fills this gap with the introduction…
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
Weighted First Order Model Counting (WFOMC) is fundamental to probabilistic inference in statistical relational learning models. As WFOMC is known to be intractable in general ($\#$P-complete), logical fragments that admit polynomial time…
Courcelle's celebrated theorem states that all MSO-expressible properties can be decided in linear time on graphs of bounded treewidth. Unfortunately, the hidden constant implied by this theorem is a tower of exponentials whose height…
A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that…
Definite descriptions are phrases of the form 'the $x$ such that $\varphi$', used to refer to single entities in a context. They are often more meaningful to users than individual names alone, in particular when modelling or querying data…
The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…
This paper proposes an extension to classical regular expressions by the addition of two operators allowing the inclusion of boolean formulae from the zeroth order logic. These expressions are called constrained expressions. The associated…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
We investigate the relationship between axiomatic set theory and the first-order theory of homeomorphism groups of manifolds in the language of group theory, concentrating on first-order rigidity and type versus conjugacy. We prove that…
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…
We remark that forcing on fiber bundles of structures of first order languages is not a compatible semantics with the pullback (of fiber bundles) and we describe a semantics which behaves well with respect to it. This new semantics uses…