Related papers: Some Model Theory of Guarded Negation
We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…
Ontologies and automated reasoning are the building blocks of the Semantic Web initiative. Derivation rules can be included in an ontology to define derived concepts, based on base concepts. For example, rules allow to define the extension…
Most existing word embedding methods can be categorized into Neural Embedding Models and Matrix Factorization (MF)-based methods. However some models are opaque to probabilistic interpretation, and MF-based methods, typically solved using…
We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…
Subatomic logic is a recent innovation in structural proof theory where atoms are no longer the smallest entity in a logical formula, but are instead treated as binary connectives. As a consequence, we can give a subatomic proof system for…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional modal logics definable by the axioms D, T, B, 4, and 5 with varying, increasing, decreasing, and constant domains.…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
In ontology-based data access (OBDA), the classical database is enhanced with an ontology in the form of logical assertions generating new intensional knowledge. A powerful form of such logical assertions is the tuple-generating…
The Svenonius theorem describes the (first-order) definability in a structure in terms of permutations preserving the relations of elementary extensions of the structure. In the present paper we prove a version of this theorem using…
In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby…
We define a natural notion of standard translation for the formulas of conditional logic which is analogous to the standard translation of modal formulas into the first-order logic. We briefly show that this translation works (modulo a…
Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
By Fagin's Theorem, NP contains precisely those problems that can be described by formulas starting with an existential second-order quantifier, followed by only first-order quantifiers (ESO formulas). Subsequent research refined this…
The article investigates classes of queries maintainable by conjunctive queries (CQs) and their extensions and restrictions in the dynamic complexity framework of Patnaik and Immerman. Starting from the basic language of quantifier-free…
We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.
While Transformers have had significant success in paragraph generation, they treat sentences as linear sequences of tokens and often neglect their hierarchical information. Prior work has shown that decomposing the levels of…
This work lists and describes the main recent strategies for building fixed-length, dense and distributed representations for words, based on the distributional hypothesis. These representations are now commonly called word embeddings and,…
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…