Related papers: Extensional Denotational Semantics of Higher-Order…
Ehrhard, Pagani and Tasson proposed a model of probabilistic functional programming in a category of normed positive cones and stable measurable cone maps, which can be seen as a coordinate-free generalization of probabilistic coherence…
We show that intuitionistic propositional logic is \emph{Carnap categorical}: the only interpretation of the connectives consistent with the intuitionistic consequence relation is the standard interpretation. This holds relative to the most…
Different semantic interpretation tasks such as text entailment and question answering require the classification of semantic relations between terms or entities within text. However, in most cases it is not possible to assign a direct…
We examine the meaning and the complexity of probabilistic logic programs that consist of a set of rules and a set of independent probabilistic facts (that is, programs based on Sato's distribution semantics). We focus on two semantics,…
In recent years, the development of large pretrained language models, such as BERT and GPT, significantly improved information extraction systems on various tasks, including relation classification. State-of-the-art systems are highly…
We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued…
The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its…
A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidability of the diagonal problem for schemes. This…
Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for…
A standard intensional account of probabilistic computation represents a randomized program as a deterministic computation that consumes an explicit random tape. This yields a two-layer perspective: an intensional layer that makes reuse of…
We present an elaboration of inductive definitions down to a universe of datatypes. The universe of datatypes is an internal presentation of strictly positive families within type theory. By elaborating an inductive definition -- a…
Probabilistic sentential decision diagrams are a class of structured-decomposable probabilistic circuits especially designed to embed logical constraints. To adapt the classical LearnSPN scheme to learn the structure of these models, we…
The characterization of PSPACE-queries over ordered structures as exactly those expressible in first-order logic with partial fixpoints (Vardi'82) is one of the classical results in the field of descriptive complexity. In this paper, we…
This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies.…
Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…
We introduce DeepProbLog, a neural probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques of the underlying probabilistic logic…
Probabilistic extensions of logic programming languages, such as ProbLog, integrate logical reasoning with probabilistic inference to evaluate probabilities of output relations; however, prior work does not account for potential statistical…
We design a predictive layer for structured-output prediction (SOP) that can be plugged into any neural network guaranteeing its predictions are consistent with a set of predefined symbolic constraints. Our Semantic Probabilistic Layer…
Bayesian networks are a canonical formalism for representing probabilistic dependencies, yet their integration within logic programming frameworks remains a nontrivial challenge, mainly due to the complex structure of these networks. In…
Choice constructs are an important part of the language of logic programming, yet the study of their semantics has been a challenging task. So far, only two-valued semantics have been studied, and the different proposals for such semantics…