In the study of logic programming, notions of equivalence play a significant role. This is due to the fact that under common nonmonotonic semantics, like answer-set programming, two programs sharing the same models (answer sets) does not necessarily yield that they are equivalent in all contexts. Whether this context concerns other program modules or just different data, distinguishes strong from uniform equivalence. We introduce a new notion of equivalence for logic programs under the answer-set semantics that allows to precisely compare and simplify programs that receive input from different sources (i.e., over different alphabets); a setting that previous equivalence notions have not considered, but has some interesting use cases, like data integration or belief merging. Our notion further generalizes relativized equivalence, where equivalence is only required over a parameterized context, and has the core concepts of strong and uniform equivalence as corner cases. We provide a model-theoretic characterization in the spirit of SE-models and establish some theoretical properties including a thorough complexity analysis. Furthermore, using our notion, we can pinpoint the known complexity gap between strong and uniform equivalence, giving insight into why the latter is harder than the former.

Answer Set Programming (ASP) is a popular nonmonotonic formalism used for common-sense reasoning and problem-solving based on stable model semantics. Equilibrium logic is a generalisation of ASP for arbitrary propositional theories and thus provides a logical characterisation of the nonmonotonic stable model semantics. In difference to classical logic, which can be defined via proof or model theory, nonmonotonic reasoning formalisms are defined via their models exclusively. Equilibrium logic is no exception here, as it has no proper proof-theoretic axiomatisation. Besides this being a theoretical imbalance, it also has consequences regarding notions of justification and explainability. In this work, we fill this gap by providing a sequent calculus for answer set entailment. Our calculus builds upon ideas from existing calculi for other nonmonotonic formalisms and utilises calculi for the logic of here and there, which is the underlying base logic of equilibrium logic. We show that the calculus is sound and complete and discuss pitfalls as well as alternative axiomatisations. Finally, we address how our approach can be of use for explainability in ASP.

We define several canonical problems related to contrastive explanations, each answering a question of the form “Why P but not Q?”. The problems compute causes for both P and Q, explicitly comparing their differences. We investigate the basic properties of our definitions in the setting of propositional logic. We show, inter alia, that our framework captures a cardinality-minimal version of existing contrastive explanations in the literature. Furthermore, we provide an extensive analysis of the computational complexities of the problems. We also implement the problems for CNF-formulas using answer set programming and present several examples demonstrating how they work in practice.

Abstract We present the solver asp-fzn for Constraint Answer Set Programming (CASP), which extends ASP with linear constraints. Our approach is based on translating CASP programs into the solver-independent FlatZinc language that supports several Constraint Programming and Integer Programming backend solvers. Our solver supports a rich language of linear constraints, including some common global constraints. As for evaluation, we show that asp-fzn is competitive with state-of-the-art ASP solvers on benchmarks taken from past ASP competitions. Furthermore, we evaluate it on several CASP problems from the literature and compare its performance with clingcon, which is a prominent CASP solver that supports most of the asp-fzn language. The performance of asp-fzn is very promising as it is already competitive on plain ASP and even outperforms clingcon on some CASP benchmarks.

Computational evaluations are crucial in modern problem-solving when we surpass theoretical algorithms or bounds. These experiments frequently take much work, and the sheer amount of needed resources makes it impossible to execute them on a single personal computer or laptop. Cluster schedulers allow for automatizing these tasks and scale to many computers. But, when we evaluate implementations of combinatorial algorithms, we depend on stable runtime results. Common approaches either limit parallelism or suffer from unstable runtime measurements due to interference among jobs on modern hardware. The former is inefficient and not sustainable. The latter results in unreplicable experiments. In this work, we address this issue and offer an acceptable balance between efficiency, software, hardware complexity, reliability, and replicability. We investigate effects towards replicability stability and illustrate how to efficiently use widely employed cluster resources for parallel evaluations. Furthermore, we present solutions which mitigate issues that emerge from the concurrent execution of benchmark jobs. Our experimental evaluation shows that – despite parallel execution – our approach reduces the runtime instability on the majority of instances to one second.

Answer-set programming (ASP) is a prominent approach to declarative problem solving that is increasingly used to tackle challenging optimisation problems. We present an approach to leverage ASP optimisation by using large-neighbourhood search (LNS), which is a meta-heuristic where parts of a solution are iteratively destroyed and reconstructed in an attempt to improve an overall objective. In our LNS framework, neighbourhoods can be specified either declaratively as part of the ASP encoding or automatically generated by code. Furthermore, our framework is self-adaptive, i.e., it also incorporates portfolios for the LNS operators along with selection strategies to adjust search parameters on the fly. The implementation of our framework, the system ALASPO, currently supports the ASP solver clingo, as well as its extensions clingo-dl and clingcon that allow for difference and full integer constraints, respectively. It utilises multi-shot solving to efficiently realise the LNS loop and in this way avoids program regrounding. We describe our LNS framework for ASP as well as its implementation, discuss methodological aspects, and demonstrate the effectiveness of the adaptive LNS approach for ASP on different optimisation benchmarks, some of which are notoriously difficult, as well as real-world applications for shift planning, configuration of railway-safety systems, parallel machine scheduling, and test laboratory scheduling.

Answer-Set Programming (ASP) is a popular declarative reasoning and problem solving formalism. Due to the increasing interest in explainabilty, several explanation approaches have been developed for ASP. However, support for commonly used advanced language features of ASP, as for example aggregates or choice rules, is still mostly lacking. We deal with explaining ASP programs containing Abstract Constraint Atoms, which encompass the above features and others. We provide justifications for the presence, or absence, of an atom in a given answer-set. To this end, we introduce several formal notions of justification in this setting based on the one hand on a semantic characterisation utilising minimal partial models, and on the other hand on a more ruled-guided approach. We provide complexity results for checking and computing such justifications, and discuss how the semantic and syntactic approaches relate and can be jointly used to offer more insight. Our results contribute to a basis for explaining commonly used language features and thus increase accessibility and usability of ASP as an AI tool.

Visual Question Answering (VQA) is a well-known problem for which deep-learning is key. This poses a challenge for explaining answers to questions, the more if advanced notions like contrastive explanations (CEs) should be provided. The latter explain why an answer has been reached in contrast to a different one and are attractive as they focus on reasons necessary to flip a query answer. We present a CE framework for VQA that uses a neurosymbolic VQA architecture which disentangles perception from reasoning. Once the reasoning part is provided as logical theory, we use answer-set programming, in which CE generation can be framed as an abduction problem. We validate our approach on the CLEVR dataset, which we extend by more sophisticated questions to further demonstrate the robustness of the modular architecture. While we achieve top performance compared to related approaches, we can also produce CEs for explanation, model debugging, and validation tasks, showing the versatility of the declarative approach to reasoning.

Automated scheduling solutions are tremendously important for the efficient operation of industrial laboratories. The Test Laboratory Scheduling Problem (TLSP) is an extension of the well-known Resource Constrained Project Scheduling Problem (RCPSP) and captures the specific requirements of such laboratories. In addition to several new scheduling constraints, it features a grouping phase, where the jobs to be scheduled are assembled from smaller units. In this work, we introduce an innovative scheduling system that allows the efficient and flexible generation of schedules for TLSP. It features a new Constraint Programming model that covers both the grouping and the scheduling aspect, as well as a hybrid Very Large Neighborhood Search that internally uses the CP model. Our experimental results on generated and real-world benchmark instances show that good results can be obtained even compared to settings which have a good grouping already provided, including several new best known solutions for these instances. Our algorithms for TLSP have been successfully implemented in a real-world industrial test laboratory. We provide a detailed description of the deployed system as well as additional useful soft constraints supported by the solvers and general lessons learned. This includes a discussion of the choice of soft constraint weights, with an analysis on the impact and relation of different objectives to each other. Our experiments show that some soft constraints complement each other well, while others require explicit trade-offs via their relative weights.

Abstract 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.

While Answer-Set Programming (ASP) is a prominent approach to declarative problem solving, optimisation problems can still be a challenge for it. Large-Neighbourhood Search (LNS) is a metaheuristic for optimisation where parts of a solution are alternately destroyed and reconstructed that has high but untapped potential for ASP solving. We present a framework for LNS optimisation in answer-set solving, in which neighbourhoods can be specified either declaratively as part of the ASP encoding, or automatically generated by code. To effectively explore different neighbourhoods, we focus on multi-shot solving as it allows to avoid program regrounding. We illustrate the framework on different optimisation problems, some of which are notoriously difficult, including shift planning and a parallel machine scheduling problem from semi-conductor production which demonstrate the effectiveness of the LNS approach.

The Test Laboratory Scheduling Problem (TLSP) and its subproblem TLSP-S are real-world industrial scheduling problems that are extensions of the Resource-Constrained Project Scheduling Problem (RCPSP). Besides several additional constraints, TLSP includes a grouping phase where the jobs to be scheduled have to be assembled from smaller tasks and derive their properties from this grouping. For TLSP-S such a grouping is already part of the input. In this work, we show how TLSP-S can be solved by Answer-set Programming extended with ideas from other constraint solving paradigms. We propose a novel and efficient encoding and apply an answer-set solver for constraint logic programs called clingcon. Additionally, we utilize our encoding in a Very Large Neighborhood Search framework and compare our methods with the state of the art approaches. Our approach provides new upper bounds and optimality proofs for several existing benchmark instances in the literature.

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 KRR paradigm for this problem and is competitive with state-of-the-art CP and MIP solvers.