We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge (programs/proofs), but also appropriate ways of reasoning (logics/type systems). We draw on the frameworks of cubical type theory and dependent typed metagraphs to formalize our approach. In doing so, we show that specific constructions within the meta-language can be related via bisimulation (implying path equivalence) to the type systems they correspond. This allows our approach to provide a convenient means of deriving synthetic denotational semantics for various type systems. Particularly, we derive bisimulations for pure type systems (PTS), and probabilistic dependent type systems (PDTS). We discuss further the relationship of PTS to non-well-founded set theory, and demonstrate the feasibility of our approach with an implementation of a bisimulation proof in a Guarded Cubical Type Theory type checker.

"Simply Logical -- Intelligent Reasoning by Example" by Peter Flach was first published by John Wiley in 1994. It could be purchased as book-only or with a 3.5 inch diskette containing the SWI-Prolog programmes printed in the book (for various operating systems). In 2007 the copyright reverted back to the author at which point the book and programmes were made freely available online; the print version is no longer distributed through John Wiley publishers. In 2015, as a pilot, we ported most of the original book into an online, interactive website using SWI-Prolog's SWISH platform. Since then, we launched the Simply Logical open source organisation committed to maintaining a suite of freely available interactive online educational resources about Artificial Intelligence and Logic Programming with Prolog. With the advent of new educational technologies we were inspired to rebuild the book from the ground up using the Jupyter Book platform enhanced with a collection of bespoke plugins that implement, among other things, interactive SWI-Prolog code blocks that can be executed directly in a web browser. This new version is more modular, easier to maintain, and can be split into custom teaching modules, in addition to being modern-looking, visually appealing, and compatible with a range of (mobile) devices of varying screen sizes.

In the hospital world there are several complex combinatory problems, and solving these problems is important to increase the degree of patients' satisfaction and the quality of care offered. The problems in the healthcare are complex since to solve them several constraints and different type of resources should be taken into account. Moreover, the solutions must be evaluated in a small amount of time to ensure the usability in real scenarios. We plan to propose solutions to these kind of problems both expanding already tested solutions and by modelling solutions for new problems, taking into account the literature and by using real data when available. Solving these kind of problems is important but, since the European Commission established with the General Data Protection Regulation that each person has the right to ask for explanation of the decision taken by an AI, without developing Explainability methodologies the usage of AI based solvers e.g. those based on Answer Set programming will be limited. Thus, another part of the research will be devoted to study and propose new methodologies for explaining the solutions obtained.

Avoiding congestion and controlling traffic in urban scenarios is becoming nowadays of paramount importance due to the rapid growth of our cities' population and vehicles. The effective control of urban traffic as a means to mitigate congestion can be beneficial in an economic, environmental and health way. In this paper, a framework which allows to efficiently simulate and optimize traffic flow in a large roads' network with hundreds of vehicles is presented. The framework leverages on an Answer Set Programming (ASP) encoding to formally describe the movements of vehicles inside a network. Taking advantage of the ability to specify optimization constraints in ASP and the off-the-shelf solver Clingo, it is then possible to optimize the routes of vehicles inside the network to reduce a range of relevant metrics (e.g., travel times or emissions). Finally, an analysis on real-world traffic data is performed, utilizing the state-of-the-art Urban Mobility Simulator (SUMO) to keep track of the state of the network, test the correctness of the solution and to prove the efficiency and capabilities of the presented solution.

When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for each given problem instance. However, the application of such approaches to large-scale instances or advanced problem encodings might be problematic since the computed SBCs are propositional and, therefore, can neither be meaningfully interpreted nor transferred to other instances. As a result, a time-consuming recomputation of SBCs must be done before every invocation of a solver. To overcome these limitations, we introduce a new model-oriented approach for Answer Set Programming that lifts the SBCs of small problem instances into a set of interpretable first-order constraints using a form of machine learning called Inductive Logic Programming. After targeting simple combinatorial problems, we aim to extend our method to be applied also for advanced decision and optimization problems.

The notion of covariant-contravariant refinement (CC-refinement, for short) is a generalization of the notions of bisimulation, simulation and refinement. This paper introduces CC-refinement modal $\mu$-calculus (CCRML$^{\mu}$) obtained from the modal $\mu$-calculus system K$^{\mu}$ by adding CC-refinement quantifiers, establishes an axiom system for CCRML$^{\mu}$ and explores the important properties: soundness, completeness and decidability of this axiom system. The language of CCRML$^{\mu}$ may be considered as a specification language for describing the properties of a system referring to reactive and generative actions. It may be used to formalize some interesting problems in the field of formal methods.

The Model Reconciliation Problem (MRP) was introduced to address issues in explainable AI planning. A solution to a MRP is an explanation for the differences between the models of the human and the planning agent (robot). Most approaches to solving MRPs assume that the robot, who needs to provide explanations, knows the human model. This assumption is not always realistic in several situations (e.g., the human might decide to update her model and the robot is unaware of the updates). In this paper, we propose a dialog-based approach for computing explanations of MRPs under the assumptions that (i) the robot does not know the human model; (ii) the human and the robot share the set of predicates of the planning domain and their exchanges are about action descriptions and fluents' values; (iii) communication between the parties is perfect; and (iv) the parties are truthful. A solution of a MRP is computed through a dialog, defined as a sequence of rounds of exchanges, between the robot and the human. In each round, the robot sends a potential explanation, called proposal, to the human who replies with her evaluation of the proposal, called response. We develop algorithms for computing proposals by the robot and responses by the human and implement these algorithms in a system that combines imperative means with answer set programming using the multi-shot feature of clingo.

Graph Neural Networks share with Logic Programming several key relational inference mechanisms. The datasets on which they are trained and evaluated can be seen as database facts containing ground terms. This makes possible modeling their inference mechanisms with equivalent logic programs, to better understand not just how they propagate information between the entities involved in the machine learning process but also to infer limits on what can be learned from a given dataset and how well that might generalize to unseen test data. This leads us to the key idea of this paper: modeling with the help of a logic program the information flows involved in learning to infer from the link structure of a graph and the information content of its nodes properties of new nodes, given their known connections to nodes with possibly similar properties. The problem is known as graph node property prediction and our approach will consist in emulating with help of a Prolog program the key information propagation steps of a Graph Neural Network's training and inference stages. We test our a approach on the ogbn-arxiv node property inference benchmark. To infer class labels for nodes representing papers in a citation network, we distill the dependency trees of the text associated to each node into directed acyclic graphs that we encode as ground Prolog terms. Together with the set of their references to other papers, they become facts in a database on which we reason with help of a Prolog program that mimics the information propagation in graph neural networks predicting node properties. In the process, we invent ground term similarity relations that help infer labels in the test set by propagating node properties from similar nodes in the training set and we evaluate their effectiveness in comparison with that of the graph's link structure. Finally, we implement explanation generators that unveil performance upper bounds inherent to the dataset. As a practical outcome, we obtain a logic program, that, when seen as machine learning algorithm, performs close to the state of the art on the node property prediction benchmark.

Answer Set Programming (ASP) is a powerful declarative programming paradigm commonly used for solving challenging search and optimization problems. The modeling languages of ASP are supported by sophisticated solving algorithms (solvers) that make the solution search efficient while enabling the programmer to model the problem at a high level of abstraction. As an approach to Knowledge Representation and Reasoning, ASP benefits from its simplicity, conciseness and rigorously defined semantics. These characteristics make ASP a straightforward way to develop formally verifiable programs. In the context of artificial intelligence (AI), the clarity of ASP programs lends itself to the construction of explainable, trustworthy AI. In support of these goals, my research is concerned with extending the theory and tools supporting the verification of ASP progams.

The logic of hybrid MKNF (minimal knowledge and negation as failure) is a powerful knowledge representation language that elegantly pairs ASP (answer set programming) with ontologies. Disjunctive rules are a desirable extension to normal rule-based reasoning and typically semantic frameworks designed for normal knowledge bases need substantial restructuring to support disjunctive rules. Alternatively, one may lift characterizations of normal rules to support disjunctive rules by inducing a collection of normal knowledge bases, each with the same body and a single atom in its head. In this work, we refer to a set of such normal knowledge bases as a head-cut of a disjunctive knowledge base. The question arises as to whether the semantics of disjunctive hybrid MKNF knowledge bases can be characterized using fixpoint constructions with head-cuts. Earlier, we have shown that head-cuts can be paired with fixpoint operators to capture the two-valued MKNF models of disjunctive hybrid MKNF knowledge bases. Three-valued semantics extends two-valued semantics with the ability to express partial information. In this work, we present a fixpoint construction that leverages head-cuts using an operator that iteratively captures three-valued models of hybrid MKNF knowledge bases with disjunctive rules. This characterization also captures partial stable models of disjunctive logic programs since a program can be expressed as a disjunctive hybrid MKNF knowledge base with an empty ontology. We elaborate on a relationship between this characterization and approximators in AFT (approximation fixpoint theory) for normal hybrid MKNF knowledge bases.