In temporal extensions of answer set programming (ASP) based on linear time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. However, timing constraints are important in many applications like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time temporal equilibrium logic, in which temporal operators are constrained by intervals over natural numbers. The resulting Metric Equilibrium Logic (MEL) provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. To this end, we define a translation of metric formulas into monadic first-order formulas and give a correspondence between their models in MEL and Monadic Quantified Equilibrium Logic, respectively. Interestingly, our translation provides a blue print for implementation in terms of ASP modulo difference constraints.

The inexpressive Description Logic (DL) ${\cal F}{{\cal L}_0}$ , which has conjunction and value restriction as its only concept constructors, had fallen into disrepute when it turned out that reasoning in ${\cal F}{{\cal L}_0}$ w.r.t. general TBoxes is ExpTime-complete, that is, as hard as in the considerably more expressive logic ${\cal A}{\cal L}{\cal C}$ . In this paper, we rehabilitate ${\cal F}{{\cal L}_0}$ by presenting a dedicated subsumption algorithm for ${\cal F}{{\cal L}_0}$ , which is much simpler than the tableau-based algorithms employed by highly optimized DL reasoners. Our experiments show that the performance of our novel algorithm, as prototypically implemented in our ${\cal F}{{\cal L}_0}$ wer reasoner, compares very well with that of the highly optimized reasoners. ${\cal F}{{\cal L}_0}$ wer can also deal with ontologies written in the extension ${\cal F}{{\cal L}_ \bot }$ of ${\cal F}{{\cal L}_0}$ with the top and the bottom concept by employing a polynomial-time reduction, shown in this paper, which eliminates top and bottom. We also investigate the complexity of reasoning in DLs related to the Horn-fragments of ${\cal F}{{\cal L}_0}$ and ${\cal F}{{\cal L}_ \bot }$ .

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.

As the popularity of adhesive joints in industry increases, so does the need for tools to support the process of selecting a suitable adhesive. While some such tools already exist, they are either too limited in scope or offer too little flexibility in use. This work presents a more advanced tool, that was developed together with a team of adhesive experts. We first extract the experts’ knowledge about this domain and formalize it in a Knowledge Base (KB). The IDP-Z3 reasoning system can then be used to derive the necessary functionality from this KB. Together with a user-friendly interactive interface, this creates an easy-to-use tool capable of assisting the adhesive experts. To validate our approach, we performed user testing in the form of qualitative interviews. The experts are very positive about the tool, stating that, among others, it will help save time and find more suitable adhesives.

Constraint Handling Rules (CHR) is both an effective concurrent declarative programming language and a versatile computational logic formalism. In CHR, guarded reactive rules rewrite a multi-set of constraints. Concurrency is inherent, since rules can be applied to the constraints in parallel. In this comprehensive survey, we give an overview of the concurrent, parallel as well as distributed CHR semantics, standard and more exotic, that have been proposed over the years at various levels of refinement. These semantics range from the abstract to the concrete. They are related by formal soundness results. Their correctness is proven as a correspondence between parallel and sequential computations. On the more practical side, we present common concise example CHR programs that have been widely used in experiments and benchmarks. We review parallel and distributed CHR implementations in software as well as hardware. The experimental results obtained show a parallel speed-up for unmodified sequential CHR programs. The software implementations are available online for free download and we give the web links. Due to its high level of abstraction, the CHR formalism can also be used to implement and analyse models for concurrency. To this end, the Software Transaction Model, the Actor Model, Colored Petri Nets and the Join-Calculus have been faithfully encoded in CHR. Finally, we identify and discuss commonalities of the approaches surveyed and indicate what problems are left open for future research.

Goal-level Independent and-parallelism (IAP) is exploited by scheduling for simultaneous execution of two or more goals, which will not interfere with each other at run time. This can be done safely even if such goals can produce multiple answers. The most successful IAP implementations to date have used recomputation of answers and sequentially ordered backtracking. While in principle simplifying the implementation, recomputation can be very inefficient if the granularity of the parallel goals is large enough and they produce several answers, while sequentially ordered backtracking limits parallelism. And, despite the expected simplification, the implementation of the classic schemes has proved to involve complex engineering, with the consequent difficulty for system maintenance and extension, while still frequently running into the well-known trapped goal and garbage slot problems. This work presents an alternative parallel backtracking model for IAP and its implementation. The model features parallel out-of-order (i.e., nonchronological) backtracking and relies on answer memoization to reuse and combine answers. We show that this approach can bring significant performance advantages. Also, it can bring some simplification to the important engineering task involved in implementing the backtracking mechanism of previous approaches.

In this note, we use Kunen’s notion of a signing to establish two theorems about the well-founded semantics of logic programs, in the case where we are interested in only (say) the positive literals of a predicate p that are consequences of the program. The first theorem identifies a class of programs for which the well-founded and Fitting semantics coincide for the positive part of p. The second theorem shows that if a program has a signing, then computing the positive part of p under the well-founded semantics requires the computation of only one part of each predicate. This theorem suggests an analysis for query answering under the well-founded semantics. In the process of proving these results, we use an alternative formulation of the well-founded semantics of logic programs, which might be of independent interest.

Knowledge representation and reasoning (KRR) systems describe and reason with complex concepts and relations in the form of facts and rules. Unfortunately, wide deployment of KRR systems runs into the problem that domain experts have great difficulty constructing correct logical representations of their domain knowledge. Knowledge engineers can help with this construction process, but there is a deficit of such specialists. The earlier Knowledge Authoring Logic Machine (KALM) based on Controlled Natural Language (CNL) was shown to have very high accuracy for authoring facts and questions. More recently, KALMFL, a successor of KALM, replaced CNL with factual English, which is much less restrictive and requires very little training from users. However, KALMFL has limitations in representing certain types of knowledge, such as authoring rules for multi-step reasoning or understanding actions with timestamps. To address these limitations, we propose KALMRA to enable authoring of rules and actions. Our evaluation using the UTI guidelines benchmark shows that KALMRA achieves a high level of correctness (100%) on rule authoring. When used for authoring and reasoning with actions, KALMRA achieves more than 99.3% correctness on the bAbI benchmark, demonstrating its effectiveness in more sophisticated KRR jobs. Finally, we illustrate the logical reasoning capabilities of KALMRA by drawing attention to the problems faced by the recently made famous AI, ChatGPT.

Answer set programs used in real-world applications often require that the program is usable with different input data. This, however, can often lead to contradictory statements and consequently to an inconsistent program. Causes for potential contradictions in a program are conflicting rules. In this paper, we show how to ensure that a program $\mathcal{P}$ remains non-contradictory given any allowed set of such input data. For that, we introduce the notion of conflict-resolving ${\lambda}$-extensions. A conflict-resolving ${\lambda}$-extension for a conflicting rule r is a set ${\lambda}$ of (default) literals such that extending the body of r by ${\lambda}$ resolves all conflicts of r at once. We investigate the properties that suitable ${\lambda}$-extensions should possess and building on that, we develop a strategy to compute all such conflict-resolving ${\lambda}$-extensions for each conflicting rule in $\mathcal{P}$. We show that by implementing a conflict resolution process that successively resolves conflicts using ${\lambda}$-extensions eventually yields a program that remains non-contradictory given any allowed set of input data.

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.

We deal with a challenging scheduling problem on parallel machines with sequence-dependent setup times and release dates from a real-world application of semiconductor work-shop production. There, jobs can only be processed by dedicated machines, thus few machines can determine the makespan almost regardless of how jobs are scheduled on the remaining ones. This causes problems when machines fail and jobs need to be rescheduled. Instead of optimising only the makespan, we put the individual machine spans in non-ascending order and lexicographically minimise the resulting tuples. This achieves that all machines complete as early as possible and increases the robustness of the schedule. We study the application of answer-set programming (ASP) to solve this problem. While ASP eases modelling, the combination of timing constraints and the considered objective function challenges current solving technology. The former issue is addressed by using an extension of ASP by difference logic. For the latter, we devise different algorithms that use multi-shot solving. To tackle industrial-sized instances, we study different approximations and heuristics. Our experimental results show that ASP is indeed a promising knowledge representation and reasoning (KRR) paradigm for this problem and is competitive with state-of-the-art constraint programming (CP) and Mixed-Integer Programming (MIP) solvers.

Through the Internet and the World-Wide Web, a vast number of information sources has become available, which offer information on various subjects by different providers, often in heterogeneous formats. This calls for tools and methods for building an advanced information-processing infrastructure. One issue in this area is the selection of suitable information sources in query answering. In this paper, we present a knowledge-based approach to this problem, in the setting where one among a set of information sources (prototypically, data repositories) should be selected for evaluating a user query. We use extended logic programs (ELPs) to represent rich descriptions of the information sources, an underlying domain theory, and user queries in a formal query language (here, XML-QL, but other languages can be handled as well). Moreover, we use ELPs for declarative query analysis and generation of a query description. Central to our approach are declarative source-selection programs, for which we define syntax and semantics. Due to the structured nature of the considered data items, the semantics of such programs must carefully respect implicit context information in source-selection rules, and furthermore combine it with possible user preferences. A prototype implementation of our approach has been realized exploiting the DLV KR system and its PLP front-end for prioritized ELPs. We describe a representative example involving specific movie databases, and report about experimental results.

Researchers working on the automatic parallelization of programs have long known that too much parallelism can be even worse for performance than too little, because spawning a task to be run on another CPU incurs overheads. Autoparallelizing compilers have therefore long tried to use granularity analysis to ensure that they only spawn off computations whose cost will probably exceed the spawn-off cost by a comfortable margin. However, this is not enough to yield good results, because data dependencies may also limit the usefulness of running computations in parallel. If one computation blocks almost immediately and can resume only after another has completed its work, then the cost of parallelization again exceeds the benefit. We present a set of algorithms for recognizing places in a program where it is worthwhile to execute two or more computations in parallel that pay attention to the second of these issues as well as the first. Our system uses profiling information to compute the times at which a procedure call consumes the values of its input arguments and the times at which it produces the values of its output arguments. Given two calls that may be executed in parallel, our system uses the times of production and consumption of the variables they share to determine how much their executions would overlap if they were run in parallel, and therefore whether executing them in parallel is a good idea or not. We have implemented this technique for Mercury in the form of a tool that uses profiling data to generate recommendations about what to parallelize, for the Mercury compiler to apply on the next compilation of the program. We present preliminary results that show that this technique can yield useful parallelization speedups, while requiring nothing more from the programmer than representative input data for the profiling run.

Logic programming is a powerful paradigm for programming autonomous agents in dynamic domains as witnessed by languages such as Golog and Flux. In this work we present ALPprolog, an expressive, yet efficient, logic programming language for the online control of agents that have to reason about incomplete information and sensing actions.

Since the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new algorithm for finding the stable matchings. To address this issue, we propose an encoding of the SMP using answer set programming (ASP), which can straightforwardly be adapted and extended to suit the needs of specific applications. The use of ASP also means that we can take advantage of highly efficient off-the-shelf solvers. To illustrate the flexibility of our approach, we show how our ASP encoding naturally allows us to select optimal stable matchings, i.e. matchings that are optimal according to some user-specified criterion. To the best of our knowledge, our encoding offers the first exact implementation to find sex-equal, minimum regret, egalitarian or maximum cardinality stable matchings for SMP instances in which individuals may designate unacceptable partners and ties between preferences are allowed.

M. Bezem defined an extensional semantics for positive higher-order logic programs. Recently, it was demonstrated by Rondogiannis and Symeonidou that Bezem's technique can be extended to higher-order logic programs with negation, retaining its extensional properties, provided that it is interpreted under a logic with an infinite number of truth values. Rondogiannis and Symeonidou also demonstrated that Bezem's technique, when extended under the stable model semantics, does not in general lead to extensional stable models. In this paper, we consider the problem of extending Bezem's technique under the well-founded semantics. We demonstrate that the well-founded extension fails to retain extensionality in the general case. On the positive side, we demonstrate that for stratified higher-order logic programs, extensionality is indeed achieved. We analyze the reasons of the failure of extensionality in the general case, arguing that a three-valued setting cannot distinguish between certain predicates that appear to have a different behaviour inside a program context, but which happen to be identical as three-valued relations.

LogicWeb mobile code consists of Prolog-like rules embedded in Web pages, thereby adding logic programming behaviour to those pages. Since LogicWeb programs are downloaded from foreign hosts and executed locally, there is a need to protect the client from buggy or malicious code. A security model is crucial for making LogicWeb mobile code safe to execute. This paper presents such a model, which supports programs of varying trust levels by using different resource access policies. The implementation of the model derives from an extended operational semantics for the LogicWeb language, which provides a precise meaning of safety.

Describing complex objects by elementary ones is a common strategy in mathematics and science in general. In their seminal 1965 paper, Kenneth Krohn and John Rhodes showed that every finite deterministic automaton can be represented (or “emulated”) by a cascade product of very simple automata. This led to an elegant algebraic theory of automata based on finite semigroups (Krohn-Rhodes Theory). Surprisingly, by relating logic programs and automata, we can show in this paper that the Krohn-Rhodes Theory is applicable in Answer Set Programming (ASP). More precisely, we recast the concept of a cascade product to ASP, and prove that every program can be represented by a product of very simple programs, the reset and standard programs. Roughly, this implies that the reset and standard programs are the basic building blocks of ASP with respect to the cascade product. In a broader sense, this paper is a first step towards an algebraic theory of products and networks of nonmonotonic reasoning systems based on Krohn-Rhodes Theory, aiming at important open issues in ASP and AI in general.

This special issue marks the tenth anniversary of the LOPSTR workshop. LOPSTR started in 1991 as a workshop on Logic Program Synthesis and Transformation, but later it broadened its scope to logic-based Program Development in general.

The motivating force behind LOPSTR has been a belief that declarative paradigms such as logic programming are better suited to program development tasks than traditional non-declarative ones such as the imperative paradigm. Specification, synthesis, transformation or specialisation, analysis, verification and debugging can all be given logical foundations, thus providing a unifying framework for the whole development process.

In the past ten years or so, such a theoretical framework has indeed begun to emerge. Even tools have been implemented for analysis, verification and specialisation. However, it is fair to say that so far the focus has largely been on programming-in-the-small. So the future challenge is to apply or extend these techniques to programming-in-the-large, in order to tackle software engineering in the real world.