Complex Event Recognition (CER) systems detect event occurrences in streaming time-stamped input using predefined event patterns. Logic-based approaches are of special interest in CER, since, via Statistical Relational AI, they combine uncertainty-resilient reasoning with time and change, with machine learning, thus alleviating the cost of manual event pattern authoring. We present a system based on Answer Set Programming (ASP), capable of probabilistic reasoning with complex event patterns in the form of weighted rules in the Event Calculus, whose structure and weights are learnt online. We compare our ASP-based implementation with a Markov Logic-based one and with a number of state-of-the-art batch learning algorithms on CER data sets for activity recognition, maritime surveillance and fleet management. Our results demonstrate the superiority of our novel approach, both in terms of efficiency and predictive performance. This paper is under consideration for publication in Theory and Practice of Logic Programming (TPLP).

The development of complex software requires tools promoting fail-fast approaches, so that bugs and unexpected behavior can be quickly identified and fixed. Tools for data validation may save the day of computer programmers. In fact, processing invalid data is a waste of resources at best, and a drama at worst if the problem remains unnoticed and wrong results are used for business. Answer Set Programming (ASP) is not an exception, but the quest for better and better performance resulted in systems that essentially do not validate data. Even under the simplistic assumption that input/output data are eventually validated by external tools, invalid data may appear in other portions of the program, and go undetected until some other module of the designed software suddenly breaks. This paper formalizes the problem of data validation for ASP programs, introduces a language to specify data validation, and presents valasp, a tool to inject data validation in ordinary programs. The proposed approach promotes fail-fast techniques at coding time without imposing any lag on the deployed system if data are pretended to be valid. Validation can be specified in terms of statements using YAML, ASP and Python. Additionally, the proposed approach opens the possibility to use ASP for validating data of imperative programming languages.

We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP’s modeling language, we introduce a formal characterization of grounding algorithms in terms of (fixed point) operators. A major role is played by dedicated well-founded operators whose associated models provide semantic guidance for delineating the result of grounding along with on-the-fly simplifications. We address an expressive class of logic programs that incorporates recursive aggregates and thus amounts to the scope of existing ASP modeling languages. This is accompanied with a plain algorithmic framework detailing the grounding of recursive aggregates. The given algorithms correspond essentially to the ones used in the ASP grounder gringo.

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, that is, operators whose range are sets of elements rather than single elements. In this paper, we make three further contributions to non-deterministic AFT: (1) we define and study ultimate approximations of non-deterministic operators, (2) we give an algebraic formulation of the semi-equilibrium semantics by Amendola et al., and (3) we generalize the characterizations of disjunctive logic programs to disjunctive logic programs with aggregates.

We address the problem of compiling defeasible theories to Datalog¬ programs. We prove the correctness of this compilation, for the defeasible logic DL(∂||), but the techniques we use apply to many other defeasible logics. Structural properties of DL(∂||) are identified that support efficient implementation and/or approximation of the conclusions of defeasible theories in the logic, compared with other defeasible logics. We also use previously well-studied structural properties of logic programs to adapt to incomplete Datalog¬ implementations.

We provide a framework for probabilistic reasoning in Vadalog-based Knowledge Graphs (KGs), satisfying the requirements of ontological reasoning: full recursion, powerful existential quantification, expression of inductive definitions. Vadalog is a Knowledge Representation and Reasoning (KRR) language based on Warded Datalog+/–, a logical core language of existential rules, with a good balance between computational complexity and expressive power. Handling uncertainty is essential for reasoning with KGs. Yet Vadalog and Warded Datalog+/– are not covered by the existing probabilistic logic programming and statistical relational learning approaches for several reasons, including insufficient support for recursion with existential quantification and the impossibility to express inductive definitions. In this work, we introduce Soft Vadalog, a probabilistic extension to Vadalog, satisfying these desiderata. A Soft Vadalog program induces what we call a Probabilistic Knowledge Graph (PKG), which consists of a probability distribution on a network of chase instances, structures obtained by grounding the rules over a database using the chase procedure. We exploit PKGs for probabilistic marginal inference. We discuss the theory and present MCMC-chase, a Monte Carlo method to use Soft Vadalog in practice. We apply our framework to solve data management and industrial problems and experimentally evaluate it in the Vadalog system.

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 modeling tools to account for it. The first contribution of this paper is a novel interpretation of probabilistic argumentation frameworks as probabilistic logic programs. Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. We show that the programs representing probabilistic argumentation frameworks do not satisfy a common assumption in probabilistic logic programming (PLP) semantics, which is, that probabilistic facts fully capture the uncertainty in the domain under investigation. The second contribution of this paper is then a novel PLP semantics for programs where a choice of probabilistic facts does not uniquely determine the truth assignment of the logical atoms. The third contribution of this paper is the implementation of a PLP system supporting this semantics: smProbLog. smProbLog is a novel PLP framework based on the PLP language ProbLog. smProbLog supports many inference and learning tasks typical of PLP, which, together with our first contribution, provide novel reasoning tools for probabilistic argumentation. We evaluate our approach with experiments analyzing the computational cost of the proposed algorithms and their application to a dataset of argumentation problems.

In this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.

The goal of inductive logic programming (ILP) is to learn a program that explains a set of examples. Until recently, most research on ILP targeted learning Prolog programs. The ILASP system instead learns answer set programs (ASP). Learning such expressive programs widens the applicability of ILP considerably; for example, enabling preference learning, learning common-sense knowledge, including defaults and exceptions, and learning non-deterministic theories. Early versions of ILASP can be considered meta-level ILP approaches, which encode a learning task as a logic program and delegate the search to an ASP solver. More recently, ILASP has shifted towards a new method, inspired by conflict-driven SAT and ASP solvers. The fundamental idea of the approach, called Conflict-driven ILP (CDILP), is to iteratively interleave the search for a hypothesis with the generation of constraints which explain why the current hypothesis does not cover a particular example. These coverage constraints allow ILASP to rule out not just the current hypothesis, but an entire class of hypotheses that do not satisfy the coverage constraint. This article formalises the CDILP approach and presents the ILASP3 and ILASP4 systems for CDILP, which are demonstrated to be more scalable than previous ILASP systems, particularly in the presence of noise.

Many practical problems can be understood as the search for a state of affairs that extends a fixed partial state of affairs, the environment, while satisfying certain conditions that are formally specified. Such problems are found in, for example, engineering, law or economics. We study this class of problems in a context where some of the relevant information about the environment is not known by the user at the start of the search. During the search, the user may consider tentative solutions that make implicit hypotheses about these unknowns. To ensure that the solution is appropriate, these hypotheses must be verified by observing the environment. Furthermore, we assume that, in addition to knowledge of what constitutes a solution, knowledge of general laws of the environment is also present. We formally define partial solutions with enough verified facts to guarantee the existence of complete and appropriate solutions. Additionally, we propose an interactive system to assist the user in their search by determining (1) which hypotheses implicit in a tentative solution must be verified in the environment, and (2) which observations can bring useful information for the search. We present an efficient method to over-approximate the set of relevant information, and evaluate our implementation.

The decoupling between the representation of a certain problem, that is, its knowledge model, and the reasoning side is one of main strong points of model-based artificial intelligence (AI). This allows, for example, to focus on improving the reasoning side by having advantages on the whole solving process. Further, it is also well known that many solvers are very sensitive to even syntactic changes in the input. In this paper, we focus on improving the reasoning side by taking advantages of such sensitivity. We consider two well-known model-based AI methodologies, SAT and ASP, define a number of syntactic features that may characterise their inputs, and use automated configuration tools to reformulate the input formula or program. Results of a wide experimental analysis involving SAT and ASP domains, taken from respective competitions, show the different advantages that can be obtained by using input reformulation and configuration.

Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence (AI) has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling search-optimization problems. Automated reasoning and knowledge representation are the subfields of AI that are particularly vested in these developments. Many popular automated reasoning paradigms provide users with languages supporting optimization statements. Recall integer linear programming, MaxSAT, optimization satisfiability modulo theory, (constraint) answer set programming. These paradigms vary significantly in their languages in ways they express quality conditions on computed solutions. Here we propose a unifying framework of so-called extended weight systems that eliminates syntactic distinctions between paradigms. They allow us to see essential similarities and differences between optimization statements provided by distinct automated reasoning languages. We also study formal properties of the proposed systems that immediately translate into formal properties of paradigms that can be captured within our framework.

Knowledge-based AI typically depends on a knowledge engineer to construct a formal model of domain knowledge – but what if domain experts could do this themselves? This paper describes an extension to the Decision Model and Notation (DMN) standard, called Constraint Decision Model and Notation (cDMN). DMN is a user-friendly, table-based notation for decision logic, which allows domain experts to model simple decision procedures without the help of IT staff. cDMN aims to enlarge the expressiveness of DMN in order to model more complex domain knowledge, while retaining DMNs goal of being understandable by domain experts. We test cDMN by solving the most complex challenges posted on the DM Community website. We compare our own cDMN solutions to the solutions that have been submitted to the website and find that our approach is competitive. Moreover, cDMN is able to solve more challenges than any other approach.

This paper introduces a formal definition of a Cyber-Physical System (CPS) in the spirit of the CPS Framework proposed by the National Institute of Standards and Technology (NIST). It shows that using this definition, various problems related to concerns in a CPS can be precisely formalized and implemented using Answer Set Programming (ASP). These include problems related to the dependency or conflicts between concerns, how to mitigate an issue, and what the most suitable mitigation strategy for a given issue would be. It then shows how ASP can be used to develop an implementation that addresses the aforementioned problems. The paper concludes with a discussion of the potentials of the proposed methodologies.

Over the last couple of decades, there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the result of bringing up-to-date a logic program when the world it describes changes. Whereas the state-of-the-art approaches are guided by the same basic intuitions and aspirations as belief updates in the context of classical logic, they build upon fundamentally different principles and methods, which have prevented a unifying framework that could embrace both belief and rule updates. In this paper, we will overview some of the main approaches and results related to answer-set programming updates, while pointing out some of the main challenges that research in this topic has faced.

In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson’s constructive logic N4. We do so by formalising, in this logic, two principles that we call noncontradictory inference and strengthened closed world assumption: the first states that no belief can be held based on contradictory evidence while the latter forces both unknown and contradictory evidence to be regarded as false. Using these principles, both logic programming and abstract argumentation frameworks are translated into constructive logic in a modular way and using the object language. Logic programming implication and abstract argumentation supports become, in the translation, a new implication connective following the noncontradictory inference principle. Attacks are then represented by combining this new implication with strong negation. Under consideration in Theory and Practice of Logic Programming (TPLP).

Forgetting – or variable elimination – is an operation that allows the removal, from a knowledge base, of middle variables no longer deemed relevant. In recent years, many different approaches for forgetting in Answer Set Programming have been proposed, in the form of specific operators, or classes of such operators, commonly following different principles and obeying different properties. Each such approach was developed to address some particular view on forgetting, aimed at obeying a specific set of properties deemed desirable in such view, but a comprehensive and uniform overview of all the existing operators and properties is missing. In this article, we thoroughly examine existing properties and (classes of) operators for forgetting in Answer Set Programming, drawing a complete picture of the landscape of these classes of forgetting operators, which includes many novel results on relations between properties and operators, including considerations on concrete operators to compute results of forgetting and computational complexity. Our goal is to provide guidance to help users in choosing the operator most adequate for their application requirements.