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Motivated by applications in declarative data analysis, we study $\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two…

We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…

Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…

The programming language Prolog makes declarative programming possible, at least to a substantial extent. Programs may be written and reasoned about in terms of their declarative semantics. All the advantages of declarative programming are…

Datalog has become a popular language for writing static analyses. Because Datalog is very limited, some implementations of Datalog for static analysis have extended it with new language features. However, even with these features it is…

In this work, which is done in the context of a (moded) logic programming language, we devise a data-flow analysis dedicated to computing what we call argument profiles. Such a profile essentially describes, for each argument of a…

Fact-checking real-world claims often requires collecting multiple pieces of evidence and applying complex multi-step reasoning. In this paper, we present Program-Guided Fact-Checking (ProgramFC), a novel fact-checking model that decomposes…

We consider a simple extension of logic programming where variables may range over goals and goals may be arguments of predicates. In this language we can write logic programs which use goals as data. We give practical evidence that, by…

Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…

In recent years, various machine and deep learning architectures have been successfully introduced to the field of predictive process analytics. Nevertheless, the inherent opacity of these algorithms poses a significant challenge for human…

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…

There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing…

The explication and the generation of explanations are prominent topics in artificial intelligence and data science, in order to make methods and systems more transparent and understandable for humans. This paper investigates the problem of…

Datalog is a popular logic programming language for deductive reasoning tasks in a wide array of applications, including business analytics, program analysis, and ontological reasoning. However, Datalog's restriction to flat facts over…

Building explainable systems is a critical problem in the field of Natural Language Processing (NLP), since most machine learning models provide no explanations for the predictions. Existing approaches for explainable machine learning…

Language models are increasingly being used in important decision pipelines, so ensuring the correctness of their outputs is crucial. Recent work has proposed evaluating the "factuality" of claims decomposed from a language model generation…

Arguing for the need to combine declarative and probabilistic programming, B\'ar\'any et al. (TODS 2017) recently introduced a probabilistic extension of Datalog as a "purely declarative probabilistic programming language." We revisit this…

Recent studies have adopted pre-trained language models, such as CodeT5 and CodeGPT, for automated program generation tasks like code generation, repair, and translation. Numerous language model-based approaches have been proposed and…

Many tools used to process programs, like compilers, analyzers, or verifiers, perform transformations on their intermediate program representation, like abstract syntax trees. Implementing such program transformations is a non-trivial task,…

Training on verifiable symbolic data is a promising way to expand the reasoning frontier of language models beyond what standard pre-training corpora provide. Yet existing procedural generators often rely on fixed puzzles or templates and…