Verification of AI is a challenge that has engineering, algorithmic and programming language components. For example, AI planners are deployed to model actions of autonomous agents. They comprise a number of searching algorithms that, given a set of specified properties, find a sequence of actions that satisfy these properties. Although AI planners are mature tools from the algorithmic and engineering points of view, they have limitations as programming languages. Decidable and efficient automated search entails restrictions on the syntax of the language, prohibiting use of higher-order properties or recursion. This paper proposes a methodology for embedding plans produced by AI planners into dependently-typed language Agda, which enables users to reason about and verify more general and abstract properties of plans, and also provides a more holistic programming language infrastructure for modelling plan execution.

Recently Bonet and Geffner have shown that first-order representations for planning domains can be learned from the structure of the state space without any prior knowledge about the action schemas or domain predicates. For this, the learning problem is formulated as the search for a simplest first-order domain description D that along with information about instances I_i (number of objects and initial state) determine state space graphs G(P_i) that match the observed state graphs G_i where P_i = (D, I_i). The search is cast and solved approximately by means of a SAT solver that is called over a large family of propositional theories that differ just in the parameters encoding the possible number of action schemas and domain predicates, their arities, and the number of objects. In this work, we push the limits of these learners by moving to an answer set programming (ASP) encoding using the CLINGO system. The new encodings are more transparent and concise, extending the range of possible models while facilitating their exploration. We show that the domains introduced by Bonet and Geffner can be solved more efficiently in the new approach, often optimally, and furthermore, that the approach can be easily extended to handle partial information about the state graphs as well as noise that prevents some states from being distinguished.

We present a general technique for constructing Graph Neural Networks (GNNs) capable of using multi-relational domain knowledge. The technique is based on mode-directed inverse entailment (MDIE) developed in Inductive Logic Programming (ILP). Given a data instance $e$ and background knowledge $B$, MDIE identifies a most-specific logical formula $\bot_B(e)$ that contains all the relational information in $B$ that is related to $e$. We transform $\bot_B(e)$ into a corresponding "bottom-graph" that can be processed for use by standard GNN implementations. This transformation allows a principled way of incorporating generic background knowledge into GNNs: we use the term `BotGNN' for this form of graph neural networks. For several GNN variants, using real-world datasets with substantial background knowledge, we show that BotGNNs perform significantly better than both GNNs without background knowledge and a recently proposed simplified technique for including domain knowledge into GNNs. We also provide experimental evidence comparing BotGNNs favourably to multi-layer perceptrons (MLPs) that use features representing a "propositionalised" form of the background knowledge; and BotGNNs to a standard ILP based on the use of most-specific clauses. Taken together, these results point to BotGNNs as capable of combining the computational efficacy of GNNs with the representational versatility of ILP.

One of the things that always intrigues me is to look back at how a technology has evolved. Building programs to communicate with computers is something that has a particularly interesting history. Ada Lovelace is recognized as having written the first program to calculate Bernoulli numbers using Charles Babbage's Analytical Engine back in the mid-nineteenth century. Later in the following century came coding languages for lambda calculus and Turing machines making tape-based computations. Then assembly language, FORTRAN, LISP, COBOL, BASIC, C, and SQL came along with more general purpose and specialized programming languages leading up to the twenty-first century.

Given a specification $\varphi(X,Y)$ over inputs $X$ and output $Y$, defined over a background theory $\mathbb{T}$, the problem of program synthesis is to design a program $f$ such that $Y=f(X)$ satisfies the specification $\varphi$. Over the past decade, syntax-guided synthesis (SyGuS) has emerged as a dominant approach for program synthesis where in addition to the specification $\varphi$, the end-user also specifies a grammar $L$ to aid the underlying synthesis engine. This paper investigates the feasibility of synthesis techniques without grammar, a sub-class defined as $\mathbb{T}$-constrained synthesis. We show that $\mathbb{T}$-constrained synthesis can be reduced to DQF($\mathbb{T}$), i.e., to the problem of finding a witness of a Dependency Quantified Formula Modulo Theory. When the underlying theory is the theory of bitvectors, the corresponding DQF(BV) problem can be further reduced to Dependency Quantified Boolean Formulas (DQBF). We rely on the progress in DQBF solving to design DQBF-based synthesizers that outperform the domain-specific program synthesis techniques, thereby positioning DQBF as a core representation language for program synthesis. Our empirical analysis shows that $\mathbb{T}$-constrained synthesis can achieve significantly better performance than syntax-guided approaches. Furthermore, the general-purpose DQBF solvers perform on par with domain-specific synthesis techniques.

The application of Artificial Intelligence (AI) to synthetic biology will provide the foundation for the creation of a high throughput automated platform for genetic design, in which a learning machine is used to iteratively optimise the system through a design-build-test-learn (DBTL) cycle. However, mainstream machine learning techniques represented by deep learning lacks the capability to represent relational knowledge and requires prodigious amounts of annotated training data. These drawbacks strongly restrict AI's role in synthetic biology in which experimentation is inherently resource and time intensive. In this work, we propose an automated biodesign engineering framework empowered by Abductive Meta-Interpretive Learning ($Meta_{Abd}$), a novel machine learning approach that combines symbolic and sub-symbolic machine learning, to further enhance the DBTL cycle by enabling the learning machine to 1) exploit domain knowledge and learn human-interpretable models that are expressed by formal languages such as first-order logic; 2) simultaneously optimise the structure and parameters of the models to make accurate numerical predictions; 3) reduce the cost of experiments and effort on data annotation by actively generating hypotheses and examples. To verify the effectiveness of $Meta_{Abd}$, we have modelled a synthetic dataset for the production of proteins from a three gene operon in a microbial host, which represents a common synthetic biology problem.

In the meantime, a wide variety of terminologies, motivations, approaches and evaluation criteria have been developed within the scope of research on explainable artificial intelligence (XAI). Many taxonomies can be found in the literature, each with a different focus, but also showing many points of overlap. In this paper, we summarize the most cited and current taxonomies in a meta-analysis in order to highlight the essential aspects of the state-of-the-art in XAI. We also present and add terminologies as well as concepts from a large number of survey articles on the topic. Last but not least, we illustrate concepts from the higher-level taxonomy with more than 50 example methods, which we categorize accordingly, thus providing a wide-ranging overview of aspects of XAI and paving the way for use case-appropriate as well as context-specific subsequent research.

In this paper, we provide simplified semantics for the logic K45(G), i.e. the many-valued Godel counterpart of the classical modal logic K45. More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Godel Kripke Frames where W is a non-empty set of worlds and \pi: W \to [0, 1] is a possibility distribution on W.

Topological Spatial Model Checking is a recent paradigm that combines Model Checking with the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting spatial properties, such as "being near to" or "being surrounded by". SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images, interpreted as quasi discrete closure spaces. In particular, the spatial model checker VoxLogicA, that uses an extended version of SLCS, has been used successfully in the domain of medical imaging. However, SLCS is not restricted to discrete space. Following a recently developed geometric semantics of Modal Logic, we show that it is possible to assign an interpretation to SLCS in continuous space, admitting a model checking procedure, by resorting to models based on polyhedra. In medical imaging such representations of space are increasingly relevant, due to recent developments of 3D scanning and visualisation techniques that exploit mesh processing. We demonstrate feasibility of our approach via a new tool, PolyLogicA, aimed at efficient verification of SLCS formulas on polyhedra, while inheriting some well-established optimization techniques already adopted in VoxLogicA. Finally, we cater for a geometric definition of bisimilarity, proving that it characterises logical equivalence.

Recent work has unveiled a theory for reasoning about the decisions made by binary classifiers: a classifier describes a Boolean function, and the reasons behind an instance being classified as positive are the prime-implicants of the function that are satisfied by the instance. One drawback of these works is that they do not explicitly treat scenarios where the underlying data is known to be constrained, e.g., certain combinations of features may not exist, may not be observable, or may be required to be disregarded. We propose a more general theory, also based on prime-implicants, tailored to taking constraints into account. The main idea is to view classifiers in the presence of constraints as describing partial Boolean functions, i.e., that are undefined on instances that do not satisfy the constraints. We prove that this simple idea results in reasons that are no less (and sometimes more) succinct. That is, not taking constraints into account (e.g., ignored, or taken as negative instances) results in reasons that are subsumed by reasons that do take constraints into account. We illustrate this improved parsimony on synthetic classifiers and classifiers learned from real data.