Thom Frühwirth presented a short, elegant, and efficient Prolog program for the n queens problem. However, the program may be seen as rather tricky and one may not be convinced about its correctness. This paper explains the program in a declarative way and provides proofs of its correctness and completeness. The specification and the proofs are declarative, that is they abstract from any operational semantics. The specification is approximate, it is unnecessary to describe the program’s semantics exactly. Despite the program works on non-ground terms, this work employs the standard semantics, based on logical consequence and Herbrand interpretations. Another purpose of the paper is to present an example of precise declarative reasoning about the semantics of a logic program.

In the context of planning and reasoning about actions and change, we call an action reversible when its effects can be reverted by applying other actions, returning to the original state. Renewed interest in this area has led to several results in the context of the PDDL language, widely used for describing planning tasks. In this paper, we propose several solutions to the computational problem of deciding the reversibility of an action. In particular, we leverage an existing translation from PDDL to Answer Set Programming (ASP), and then use several different encodings to tackle the problem of action reversibility for the STRIPS fragment of PDDL. For these, we use ASP, as well as Epistemic Logic Programming (ELP), an extension of ASP with epistemic operators, and compare and contrast their strengths and weaknesses.

The Stable Roommates problem with Ties and Incomplete lists (SRTI) is a matching problem characterized by the preferences of agents over other agents as roommates, where the preferences may have ties or be incomplete. SRTI asks for a matching that is stable and, sometimes, optimizes a domain-independent fairness criterion (e.g. Egalitarian). However, in real-world applications (e.g. assigning students as roommates at a dormitory), we usually consider a variety of domain-specific criteria depending on preferences over the habits and desires of the agents. With this motivation, we introduce a knowledge-based method to SRTI considering domain-specific knowledge and investigate its real-world application for assigning students as roommates at a university dormitory.

We present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.

In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of here-and-there allows us to establish strong equivalence by deriving rules of each group from rules of the other. In the process, rules are rewritten as propositional formulas. We extend this method of proving strong equivalence to an answer set programming language that includes operations on integers. The formula representing a rule in this language is a first-order formula that may contain comparison symbols among its predicate constants, and symbols for arithmetic operations among its function constants. The paper is under consideration for acceptance in TPLP.

Logic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational meaning of ordered disjunction is clear, there exists an important open issue regarding its semantics. In particular, there does not exist a purely model-theoretic approach for determining the most preferred models of an LPOD. At present, the selection of the most preferred models is performed using a technique that is not based exclusively on the models of the program and in certain cases produces counterintuitive results. We provide a novel, model-theoretic semantics for LPODs, which uses an additional truth value in order to identify the most preferred models of a program. We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs. Moreover, the new approach can be used to define the semantics of a natural class of logic programs that can have both ordered and classical disjunctions in the heads of clauses. This allows programs that can express not only strict levels of preferences but also alternatives that are equally preferred.

Given a combinatorial search problem, it may be highly useful to enumerate its (all) solutions besides just finding one solution, or showing that none exists. The same can be stated about optimal solutions if an objective function is provided. This work goes beyond the bare enumeration of optimal solutions and addresses the computational task of solution enumeration by optimality (SEO). This task is studied in the context of answer set programming (ASP) where (optimal) solutions of a problem are captured with the answer sets of a logic program encoding the problem. Existing answer set solvers already support the enumeration of all (optimal) answer sets. However, in this work, we generalize the enumeration of optimal answer sets beyond strictly optimal ones, giving rise to the idea of answer set enumeration in the order of optimality (ASEO). This approach is applicable up to the best k answer sets or in an unlimited setting, which amounts to a process of sorting answer sets based on the objective function. As the main contribution of this work, we present the first general algorithms for the aforementioned tasks of answer set enumeration. Moreover, we illustrate the potential use cases of ASEO. First, we study how efficiently access to the next-best solutions can be achieved in a number of optimization problems that have been formalized and solved in ASP. Second, we show that ASEO provides us with an effective sampling technique for Bayesian networks.

Approximation fixpoint theory (AFT) provides an algebraic framework for the study of fixpoints of operators on bilattices and has found its applications in characterizing semantics for various classes of logic programs and nonmonotonic languages. In this paper, we show one more application of this kind: the alternating fixpoint operator by Knorr et al. for the study of the well-founded semantics for hybrid minimal knowledge and negation as failure (MKNF) knowledge bases is in fact an approximator of AFT in disguise, which, thanks to the abstraction power of AFT, characterizes not only the well-founded semantics but also two-valued as well as three-valued semantics for hybrid MKNF knowledge bases. Furthermore, we show an improved approximator for these knowledge bases, of which the least stable fixpoint is information richer than the one formulated from Knorr et al.’s construction. This leads to an improved computation for the well-founded semantics. This work is built on an extension of AFT that supports consistent as well as inconsistent pairs in the induced product bilattice, to deal with inconsistencies that arise in the context of hybrid MKNF knowledge bases. This part of the work can be considered generalizing the original AFT from symmetric approximators to arbitrary approximators.

Relational autocompletion is the problem of automatically filling out some missing values in multi-relational data. We tackle this problem within the probabilistic logic programming framework of Distributional Clauses (DCs), which supports both discrete and continuous probability distributions. Within this framework, we introduce DiceML – an approach to learn both the structure and the parameters of DC programs from relational data (with possibly missing data). To realize this, DiceML integrates statistical modeling and DCs with rule learning. The distinguishing features of DiceML are that it (1) tackles autocompletion in relational data, (2) learns DCs extended with statistical models, (3) deals with both discrete and continuous distributions, (4) can exploit background knowledge, and (5) uses an expectation–maximization-based (EM) algorithm to cope with missing data. The empirical results show the promise of the approach, even when there is missing data.

Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption and, therefore, are not suited to deal with the anonymous objects that are common in ontological reasoning. Many real-world applications, like processing electronic health records, also contain a temporal dimension and require efficient reasoning algorithms. Moreover, since medical data are not recorded on a regular basis, reasoners must deal with sparse data with potentially large temporal gaps. Our contribution consists of two main parts: In the first part, we introduce a new closed-world semantics for answering conjunctive queries (CQs) with negation over ontologies formulated in the description logic $${\mathcal E}{\mathcal L}{{\mathcal H}_ \bot }$$ , which is based on the minimal canonical model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity. In the second part, we extend this minimal-world semantics for answering metric temporal CQs with negation over the lightweight temporal logic and obtain similar rewritability and complexity results.

A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames has already been established. By “traditional” classes of frames, we mean those characterized by any positive combination of reflexivity, seriality, symmetry, transitivity, and the Euclidean property. In this paper, we fill the gaps remaining in an analogous classification of the graded modal language with graded converse modalities. In particular, we show its NExpTime-completeness over the class of Euclidean frames, demonstrating this way that over this class the considered language is harder than the language without graded modalities or without converse modalities. We also consider its variation disallowing graded converse modalities, but still admitting basic converse modalities. Our most important result for this variation is confirming an earlier conjecture that it is decidable over transitive frames. This contrasts with the undecidability of the language with graded converse modalities.

Deploying Internet of Things (IoT)-enabled virtual network function (VNF) chains to Cloud-Edge infrastructures requires determining a placement for each VNF that satisfies all set deployment requirements as well as a software-defined routing of traffic flows between consecutive functions that meets all set communication requirements. In this article, we present a declarative solution, EdgeUsher, to the problem of how to best place VNF chains to Cloud-Edge infrastructures. EdgeUsher can determine all eligible placements for a set of VNF chains to a Cloud-Edge infrastructure so to satisfy all of their hardware, IoT, security, bandwidth, and latency requirements. It exploits probability distributions to model the dynamic variations in the available Cloud-Edge infrastructure and to assess output eligible placements against those variations.

ISO Prolog provides catch and throw to realize the control flow of exception handling. This pearl demonstrates that catch and throw are inconspicuously amenable to the implementation of backjumping. In fact, they have precisely the semantics required: rewinding the search to a specific point and carrying of a preserved term to that point. The utility of these properties is demonstrated through an implementation of graph coloring with backjumping and a backjumping SAT solver that applies conflict-driven clause learning.

Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on intuitionistic grounds, we introduce Answer Set Programming with Algebraic Constraints (ASP($\mathcal A \mathcal C$)), where rules may contain constraints that compare semiring values to weighted formula evaluations. Such constraints provide streamlined access to a manifold of constructs available in ASP, like aggregates, choice constraints, and arithmetic operators. They extend some of them and provide a generic framework for defining programs with algebraic computation, which can be fruitfully used e.g. for provenance semantics of datalog programs. While undecidable in general, expressive fragments of ASP($\mathcal A \mathcal C$) can be exploited for effective problem solving in a rich framework.

The Stable Roommates problem (SR) is characterized by the preferences of agents over other agents as roommates: each agent ranks all others in strict order of preference. A solution to SR is then a partition of the agents into pairs so that each pair shares a room, and there is no pair of agents that would block this matching (i.e., who prefers the other to their roommate in the matching). There are interesting variations of SR that are motivated by applications (e.g., the preference lists may be incomplete (SRI) and involve ties (SRTI)), and that try to find a more fair solution (e.g., Egalitarian SR). Unlike the Stable Marriage problem, every SR instance is not guaranteed to have a solution. For that reason, there are also variations of SR that try to find a good-enough solution (e.g., Almost SR). Most of these variations are NP-hard. We introduce a formal framework, called SRTI-ASP, utilizing the logic programming paradigm Answer Set Programming, that is provable and general enough to solve many of such variations of SR. Our empirical analysis shows that SRTI-ASP is also promising for applications.

Answer-Set Programming (ASP) is a powerful and expressive knowledge representation paradigm with a significant number of applications in logic-based AI. The traditional ground-and-solve approach, however, requires ASP programs to be grounded upfront and thus suffers from the so-called grounding bottleneck (i.e., ASP programs easily exhaust all available memory and thus become unsolvable). As a remedy, lazy-grounding ASP solvers have been developed, but many state-of-the-art techniques for grounded ASP solving have not been available to them yet. In this work we present, for the first time, adaptions to the lazy-grounding setting for many important techniques, like restarts, phase saving, domain-independent heuristics, and learned-clause deletion. Furthermore, we investigate their effects and in general observe a large improvement in solving capabilities and also uncover negative effects in certain cases, indicating the need for portfolio solving as known from other solvers.

Generalising and re-using knowledge learned while solving one problem instance has been neglected by state-of-the-art answer set solvers. We suggest a new approach that generalises learned nogoods for re-use to speed-up the solving of future problem instances. Our solution combines well-known ASP solving techniques with deductive logic-based machine learning. Solving performance can be improved by adding learned non-ground constraints to the original program. We demonstrate the effects of our method by means of realistic examples, showing that our approach requires low computational cost to learn constraints that yield significant performance benefits in our test cases. These benefits can be seen with ground-and-solve systems as well as lazy-grounding systems. However, ground-and-solve systems suffer from additional grounding overheads, induced by the additional constraints in some cases. By means of conflict minimization, non-minimal learned constraints can be reduced. This can result in significant reductions of grounding and solving efforts, as our experiments show.

Efficient decision-making over continuously changing data is essential for many application domains such as cyber-physical systems, industry digitalization, etc. Modern stream reasoning frameworks allow one to model and solve various real-world problems using incremental and continuous evaluation of programs as new data arrives in the stream. Applied techniques use, e.g., Datalog-like materialization or truth maintenance algorithms to avoid costly re-computations, thus ensuring low latency and high throughput of a stream reasoner. However, the expressiveness of existing approaches is quite limited and, e.g., they cannot be used to encode problems with constraints, which often appear in practice. In this paper, we suggest a novel approach that uses the Conflict-Driven Constraint Learning (CDCL) to efficiently update legacy solutions by using intelligent management of learned constraints. In particular, we study the applicability of reinforcement learning to continuously assess the utility of learned constraints computed in previous invocations of the solving algorithm for the current one. Evaluations conducted on real-world reconfiguration problems show that providing a CDCL algorithm with relevant learned constraints from previous iterations results in significant performance improvements of the algorithm in stream reasoning scenarios.

In this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible concept inclusions. Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated. The construction of the concept-aware multipreference semantics is related to Brewka’s framework for qualitative preferences. We exploit Answer Set Programming (in particular, asprin) to achieve defeasible reasoning under the multipreference approach for the lightweight description logic ξ$\mathcal L_ \bot ^ + $.