We propose Dr.Aid, a logic-based AI framework for automated compliance checking of data governance rules over data-flow graphs. The rules are modelled using a formal language based on situation calculus and are suitable for decentralized contexts with multi-input-multi-output (MIMO) processes. Dr.Aid models data rules and flow rules and checks compliance by reasoning about the propagation, combination, modification and application of data rules over the data flow graphs. Our approach is driven and evaluated by real-world datasets using provenance graphs from data-intensive research.

As robots begin to interact closely with humans, we need to build systems worthy of trust regarding both the safety and the quality of the interaction. To do so, we have to be able to formalize what a "good" interaction is, and we need algorithms that can check that a given system produces good interactions or can even synthesize such systems. To make progress, we must first acknowledge that a human is not another dynamic physical element in the environment, but has beliefs, goals, social norms, desires, and preferences. To address these complexities, we must develop models, specifications, and algorithms that use our knowledge about human behavior to create demonstrably trustworthy systems. In this article, we identified a number of promising research directions and we encourage the HRI and formal methods communities to create strong collaborations to tackle these and other questions toward the goal of trustworthy HRI.

Analogy-making is at the core of human intelligence and creativity with applications to such diverse tasks as commonsense reasoning, learning, language acquisition, and story telling. This paper studies analogical proportions between booleans of the form `$a$ is to $b$ what $c$ is to $d$' called boolean proportions. Technically, we instantiate an abstract algebraic framework of analogical proportions -- recently introduced by the author -- in the boolean domain consisting of the truth values true and false together with boolean functions. It turns out that our notion of boolean proportions has appealing mathematical properties and that it coincides with a prominent model of boolean proportions in the general case. In a broader sense, this paper is a further step towards a theory of analogical reasoning and learning systems with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity.

Abstract argumentation provides us with methods such as gradual and Dung semantics with which to evaluate arguments after potential attacks by other arguments. Some of these methods can take intrinsic strengths of arguments as input, with which to modulate the effects of attacks between arguments. Coming from abstract argumentation, these methods look only at the relations between arguments and not at the structure of the arguments themselves. In structured argumentation the way an argument is constructed, by chaining inference rules starting from premises, is taken into consideration. In this paper we study methods for assigning an argument its intrinsic strength, based on the strengths of the premises and inference rules used to form said argument. We first define a set of principles, which are properties that strength assigning methods might satisfy. We then propose two such methods and analyse which principles they satisfy. Finally, we present a generalised system for creating novel strength assigning methods and speak to the properties of this system regarding the proposed principles.

Shared benchmarks and datasets have historically played a crucial role in driving advances in large-scale applications of deep learning, e.g. in computer vision ([6]) and natural language processing ([19, 13, 11]). Neural theorem proving is a rapidly developing area which aims to apply techniques from deep learning to interactive theorem proving. To date, most contributions in this area have focused on individual theorem proving systems, each with a separately-implemented mathematics library and with results reported on a dataset-specific test split; examples include the HOList [2], CoqGym [24] and LeanStep [7] theorem proving environments and benchmarks. However, benchmarks from this paradigm are not ideal for measuring the mathematical reasoning ability of neural theorem provers for several reasons. Library-specific train/test splits are siloed by construction, dependent on how theorems and lemmas are split in these libraries, and as such are not directly comparable across systems. Moreover, formal mathematics libraries are closer to software repositories than informal mathematical exposition, and many lemmas are implementation-specific artifacts without precise informal mathematical or cross-system translations. To date, the neural theorem proving community has not organized its efforts around a cross-system benchmark. To address this need and to provide a common resource to research groups working on formal theorem proving, we present miniF2F, a unified cross-system benchmark of formal mathematics of progressively increasing difficulty, centering around Olympiad-level problem statements (AMC, AIME, IMO) as well as high-school and undergraduate maths classes.

The Shapes Constraint Language (SHACL) is the recent W3C recommendation language for validating RDF data, by verifying certain shapes on graphs. Previous work has largely focused on the validation problem and the standard decision problems of satisfiability and containment, crucial for design and optimisation purposes, have only been investigated for simplified versions of SHACL. Moreover, the SHACL specification does not define the semantics of recursively-defined constraints, which led to several alternative recursive semantics being proposed in the literature. The interaction between these different semantics and important decision problems has not been investigated yet. In this article we provide a comprehensive study of the different features of SHACL, by providing a translation to a new first-order language, called SCL, that precisely captures the semantics of SHACL. We also present MSCL, a second-order extension of SCL, which allows us to define, in a single formal logic framework, the main recursive semantics of SHACL. Within this language we also provide an effective treatment of filter constraints which are often neglected in the related literature. Using this logic we provide a detailed map of (un)decidability and complexity results for the satisfiability and containment decision problems for different SHACL fragments. Notably, we prove that both problems are undecidable for the full language, but we present decidable combinations of interesting features, even in the face of recursion.

In this paper, we address the problem of handling inconsistent data in Temporal Description Logic (TDL) knowledge bases. Considering the data part of the knowledge base as the source of inconsistency over time, we propose an ABox repair approach. This is the first work handling the repair in TDL Knowledge bases. To do so, our goal is twofold: 1) detect temporal inconsistencies and 2) propose a data temporal reparation. For the inconsistency detection, we propose a reduction approach from TDL to DL which allows to provide a tight NP-complete upper bound for TDL concept satisfiability and to use highly optimised DL reasoners that can bring precise explanation (the set of inconsistent data assertions). Thereafter, from the obtained explanation, we propose a method for automatically computing the best repair in the temporal setting based on the allowed rigid predicates and the time order of assertions.

The integration of learning and reasoning is one of the key challenges in artificial intelligence and machine learning today, and various communities have been addressing it. That is especially true for the field of neural-symbolic computation (NeSy) [10, 21], where the goal is to integrate symbolic reasoning and neural networks. NeSy already has a long tradition, and it has recently attracted a lot of attention from various communities (cf. the keynotes of Y. Bengio and H. Kautz on this topic at AAAI 2020, the AI Debate [9] between Y. Bengio and G. Marcus). Another domain that has a rich tradition in integrating learning and reasoning is that of statistical relational learning and artificial intelligence (StarAI) [39, 85]. But rather than focusing on integrating logic and neural networks, it is centred around the question of integrating logic with probabilistic reasoning, more specifically probabilistic graphical models. Despite the common interest in combining symbolic reasoning with a basic paradigm for learning, i.e., probabilistic graphical models or neural networks, it is surprising that there are not more interactions between these two fields.

There are some recent approaches and results about the use of answer-set programming for specifying counterfactual interventions on entities under classification, and reasoning about them. These approaches are flexible and modular in that they allow the seamless addition of domain knowledge. Reasoning is enabled by query answering from the answer-set program. The programs can be used to specify and compute responsibility-based numerical scores as attributive explanations for classification results.

This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the decades. The existential quantification of literals (variable states) and its applications have also been studied in the literature. In this paper, we complement this by studying universal literal quantification and its applications, particularly to explainable AI. We also provide a novel semantics for quantification, discuss the interplay between variable/literal and existential/universal quantification. We further identify some classes of Boolean formulas and circuits on which quantification can be done efficiently. Literal quantification is more fine-grained than variable quantification as the latter can be defined in terms of the former. This leads to a refinement of quantified Boolean logic with literal quantification as its primitive.