Abstract Answer set programming is a well-understood and established problem-solving and knowledge representation paradigm. It has become more prominent amongst a wider audience due to its multiple applications in science and industry. The constant development of advanced programming and modeling techniques extends the toolset for developers and users regularly. This paper compiles and demonstrates different techniques to reuse logic program parts (multi-shot) by solving the arcade game snake. This game is particularly interesting because a victory can be assured by solving the NP-hard problem of Hamiltonian Cycles. We will demonstrate five hands-on implementations in clingo and compare their performance in an empirical evaluation. In addition, our implementation utilizes clingraph to generate a simple yet informative image representation of the game’s progress.

Ontology-based query answering with existential rules is well understood and implemented for positive queries, in particular conjunctive queries. For queries with negation, however, there is no agreed-upon semantics or standard implementation. This problem is unknown for simpler rule languages, such as Datalog, where it is intuitive and practical to evaluate negative queries over the least model. This fails for existential rules, which instead of a single least model have multiple universal models that may not lead to the same results for negative queries. We therefore propose universal core models as a basis for a meaningful (non-monotonic) semantics for queries with negation. Since cores are hard to compute, we identify syntactic conditions (on rules and queries) under which our core-based semantics can equivalently be obtained for other universal models, such as those produced by practical chase algorithms. Finally, we use our findings to propose a semantics for a broad class of existential rules with negation.

Dialectical Frameworks [1] (ADF) are a generalisation of Dung's Argumentation frameworks [2].Multiple approaches for reasoning under various semantics have been proposed over the last decade [3,4,5,6].We present "Abstract Dialectical Frameworks solved by Binary Decision Diagrams, developed in Dresden" (ADF-BDD) 2 , a novel approach that relies on the translation of the acceptance conditions of a given ADF into reduced ordered binary decision diagrams (roBDD) [7].Our system is based on the consideration that many otherwise hard to decide problems in ADF semantics (e. g., answering SAT-questions) can be solved in polynomial time on roBDDs (see [8] for an in-depth analysis).Our novel approach differs to the currently used systems, like the SAT-based approach K++ADF [5] or the wide spectrum of answer set programming (ASP) focused approaches like the DIAMOND family (e.g., DIAMOND [3] or GODIA-MOND [4]) and YADF [6].ADF-BDD is written in RUST [9] to provide good performance while enforcing a high amount of memory-and type-safety.In addition the rust-compiler produces highly optimised machine code, while keeping the whole tech stack simple.ADF-BDD accepts the established input format, introduced first in [10].There statements are unary predicates s, defining the labels and the acceptance conditions are binary predicates ac, relating the label to a formula.It allows to enumerate the grounded and complete interpretations, and stable models of the given input instance.The set of statements is the shared signature of all acceptance conditions, hence our implementation uses a single structure to store the nodes of all the roBDDs, which represent each acceptance condition.This allows for efficient caching of nodes and to eliminate duplicate node candidates.Another side-effect is that shared sub-BDDs are computed only once.ADF-BDD provides the explained implementation of roBDDs as the representation of the acceptance conditions.As the instantiation of roBDDs is a computational hard task, it is possible to utilise another state-of-the art competitive library called Biodivine/LibBDD 3 .It is part of the Biodivine software in the AEON project [11].While LibBDD is faster in 1 This work is partly supported by the BMBF, Grant 01IS20056 NAVAS, by the Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), and by the DFG through the Collaborative Research Center, Grant TRR 248 project ID 389792660.2

With the rise of machine learning, and more recently the overwhelming interest in deep learning, knowledge representation and reasoning (KRR) approaches struggle to maintain their position within the wider Artificial Intelligence (AI) community. Often considered as part of thegood old-fashioned AI(Haugeland 1985) – like a memory of glorious old days that have come to an end – many consider KRR as no longer applicable (on its own) to the problems faced by AI today (Blackwell 2015; Garneloet al.2016). What they see are logical languages with symbols incomprehensible by most, inference mechanisms that even experts have difficulties tracing and debugging, and the incapability to process unstructured data like text.

We present a reimplementation of the DIAMOND system for computing with abstract dialectical frameworks. The original DIAMOND was a script-based tool that called an external ASP solver. This reimplementation uses the clingo library in a native C++ environment and thus avoids communication overhead.

We present DIAMOND, an implementation of Brewka and Woltran's abstract dialectical frameworks (ADFs). The system uses answer set programming encodings to compute interpretations of ADFs according to various semantics. We evaluate the performance of the system using an actual reasoning problem as opposed to using randomly generated frameworks.

We show in this paper how managed multi-context systems (mMCS) can be turned into a reactive formalism suitable for continuous reasoning in dynamic environments. We extend mMCS with (abstract) sensors and define the notion of a run of the extended systems. We then show how typical problems arising in online reasoning can be addressed: handling potentially inconsistent sensor input, modeling intelligent forms of forgetting, and controlling the reasoning effort spent by contexts. We also investigate the complexity of some important related decision problems.