Related papers: Algebraic classifications for fragments of first-o…

We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…

One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a…

Modal logics are widely used in computer science. The complexity of their satisfiability problems has been an active field of research since the 1970s. We prove that even very "simple" modal logics can be undecidable: We show that there is…

The objectives of this research work which is intimately related to pattern discovery and management are threefold: (i) handle the problem of pattern manipulation by defining operations on patterns, (ii) study the problem of enriching and…

We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…

Given a fine abelian group grading on a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero, with universal grading group $G$, it is shown that the induced grading by the free group $G/\tor(G)$ is…

We classify, up to equivalence, all finite-dimensional simple graded division algebras over the field of real numbers. The grading group is any finite abelian group.

We consider the four fragments FO2, the intersection of Sigma2 and FO2, the intersection of Pi2 and FO2, and Delta2 of first-order logic FO[<] over finite and infinite words. For all four fragments, we give characterizations in terms of…

The general aim of this article is to study the negation fragment of classical logic within the framework of contemporary (Abstract) Algebraic Logic. More precisely, we shall find the three classes of algebras that are canonically…

This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…

In spite of the amazing results obtained by deep learning in many applications, a real intelligent behavior of an agent acting in a complex environment is likely to require some kind of higher-level symbolic inference. Therefore, there is a…

We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier…

We introduce a quantum analogue of classical first-order logic (FO) and develop a theory of quantum first-order logic as a basis of the productive discussions on the power of logical expressiveness toward quantum computing. The purpose of…

We study property testing of properties that are definable in first-order logic (FO) in the bounded-degree graph and relational structure models. We show that any FO property that is defined by a formula with quantifier prefix…

We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This…

Graded modal logic is the formal language obtained from ordinary (propositional) modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive…

Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments, and the GRAPPA framework which…

Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…

We study the expressive power of the LARA language -- a recently proposed unified model for expressing relational and linear algebra operations -- both in terms of traditional database query languages and some analytic tasks often performed…

In this paper, we explore the finite difference approximation of the fractional Laplace operator in conjunction with a neural network method for solving it. We discretized the fractional Laplace operator using the Riemann-Liouville formula…