In a recent line of research, two familiar concepts from logic programming semantics (unfounded sets and splitting) were extrapolated to the case of epistemic logic programs. The property of epistemic splitting provides a natural and modular way to understand programs without epistemic cycles but, surprisingly, was only fulfilled by Gelfond's original semantics (G91), among the many proposals in the literature. On the other hand, G91 may suffer from a kind of self-supported, unfounded derivations when epistemic cycles come into play. Recently, the absence of these derivations was also formalised as a property of epistemic semantics called foundedness. Moreover, a first semantics proved to satisfy foundedness was also proposed, the so-called Founded Autoepistemic Equilibrium Logic (FAEEL). In this paper, we prove that FAEEL also satisfies the epistemic splitting property something that, together with foundedness, was not fulfilled by any other approach up to date. To prove this result, we provide an alternative characterisation of FAEEL as a combination of G91 with a simpler logic we called Founded Epistemic Equilibrium Logic (FEEL), which is somehow an extrapolation of the stable model semantics to the modal logic S5.

Repeated executions of reasoning tasks for varying inputs are necessary in many applicative settings, such as stream reasoning. In this context, we propose an incremental grounding approach for the answer set semantics. We focus on the possibility of generating incrementally larger ground logic programs equivalent to a given non-ground one; so called overgrounded programs can be reused in combination with deliberately many different sets of inputs. Updating overgrounded programs requires a small effort, thus making the instantiation of logic programs considerably faster when grounding is repeated on a series of inputs similar to each other. Notably, the proposed approach works "under the hood", relieving designers of logic programs from controlling technical aspects of grounding engines and answer set systems. In this work we present the theoretical basis of the proposed incremental grounding technique, we illustrate the consequent repeated evaluation strategy and report about our experiments. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).

Knowledge can be represented compactly in multiple ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a database modelled as a first-order relational structure. In the presence of integrity constraints, we identify classes of aggregators that respect them in the aggregated database, provided these are satisfied in all individual databases. We also characterise languages for first-order queries on which the answer to a query on the aggregated database coincides with the aggregation of the answers to the query obtained on each individual database. This contribution is meant to be a first step on the application of techniques from social choice theory to knowledge representation in databases.

We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the proposed semantics they are non-primitive but are defined from the concept of belief base. We show that this semantics allows us to define the universal epistemic model in a simpler and more compact way than existing inductive constructions of it. We provide (i) a number of semantic equivalence results for both the basic epistemic language with "individual belief" operators and its extension by the notion of "only believing", and (ii) a lower bound complexity result for epistemic logic model checking relative to the universal epistemic model.

Tremendous research effort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the different approaches is much called for. In this paper, we present an algebraic graded logic we refer to as LogAG capable of encompassing a wide variety of non-monotonic formalisms. We build on Lin and Shoham's argument systems first developed to formalize non-monotonic commonsense reasoning. We show how to encode argument systems as LogAG theories, and prove that LogAG captures the notion of belief spaces in argument systems. Since argument systems capture default logic, autoepistemic logic, the principle of negation as failure, and circumscription, our results show that LogAG captures the before-mentioned non-monotonic logical formalisms as well. Previous results show that LogAG subsumes possibilistic logic and any non-monotonic inference relation satisfying Makinson's rationality postulates. In this way, LogAG provides a powerful unified framework for non-monotonicity.

Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the rewriting may introduce new recursive definitions, which can involve even negation and aggregations, and may slow down program evaluation. This paper enhances the magic set technique by preventing the creation of (new) recursive definitions in the rewritten program. It turns out that the new version of magic sets is closed for Datalog programs with stratified negation and aggregations, which is very convenient to obtain efficient computation of the stable model of the rewritten program. Moreover, the rewritten program is further optimized by the elimination of subsumed rules and by the efficient handling of the cases where binding propagation is lost. The research was stimulated by a challenge on the exploitation of Datalog/\textsc{dlv} for efficient reasoning on large ontologies. All proposed techniques have been hence implemented in the \textsc{dlv} system, and tested for ontological reasoning, confirming their effectiveness. Under consideration for publication in Theory and Practice of Logic Programming.

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 programming language ProbLog can be adapted for the new language. We theoretically and experimentally demonstrate that DeepProbLog supports (i) both symbolic and subsymbolic representations and inference, (ii) program induction, (iii) probabilistic (logic) programming, and (iv) (deep) learning from examples. To the best of our knowledge, this work is the first to propose a framework where general-purpose neural networks and expressive probabilistic-logical modeling and reasoning are integrated in a way that exploits the full expressiveness and strengths of both worlds and can be trained end-to-end based on examples.

We propose symbolic learning as extensions to standard inductive learning models such as neural nets as a means to solve few shot learning problems. We device a class of visual discrimination puzzles that calls for recognizing objects and object relationships as well learning higher-level concepts from very few images. We propose a two-phase learning framework that combines models learned from large data sets using neural nets and symbolic first-order logic formulas learned from a few shot learning instance. We develop first-order logic synthesis techniques for discriminating images by using symbolic search and logic constraint solvers. By augmenting neural nets with them, we develop and evaluate a tool that can solve few shot visual discrimination puzzles with interpretable concepts.

In Multi-Agent Path Finding (MAPF), a team of agents needs to find collision-free paths from their starting locations to their respective targets. Combined Target Assignment and Path Finding (TAPF) extends MAPF by including the problem of assigning targets to agents as a precursor to the MAPF problem. A limitation of both models is their assumption that the number of agents and targets are equal, which is invalid in some applications. We address this limitation by generalizing TAPF to allow for (1) unequal number of agents and tasks; (2) tasks to have deadlines by which they must be completed; (3) ordering of groups of tasks to be completed; and (4) tasks that are composed of a sequence of checkpoints that must be visited in a specific order. Further, we model the problem using answer set programming (ASP) to show that customizing the desired variant of the problem is simple -- one only needs to choose the appropriate combination of ASP rules to enforce it. We also demonstrate experimentally that if problem specific information can be incorporated into the ASP encoding then ASP based methods can be efficient and can scale up to solve practical applications.

An important step in the development of value alignment (VA) systems in AI is understanding how values can interrelate with facts. Designers of future VA systems will need to utilize a hybrid approach in which ethical reasoning and empirical observation interrelate successfully in machine behavior. In this article we identify two problems about this interrelation that have been overlooked by AI discussants and designers. The first problem is that many AI designers commit inadvertently a version of what has been called by moral philosophers the "naturalistic fallacy," that is, they attempt to derive an "ought" from an "is." We illustrate when and why this occurs. The second problem is that AI designers adopt training routines that fail fully to simulate human ethical reasoning in the integration of ethical principles and facts. Using concepts of quantified modal logic, we proceed to offer an approach that promises to simulate ethical reasoning in humans by connecting ethical principles on the one hand and propositions about states of affairs on the other.