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**Extensions of ASP**

10:45 | Constrained Default Logic Programming PRESENTER: Shutao Zhang ABSTRACT. This paper develops a new formalism CDLP by combining ASP and constrained default logic to facilitate modeling questions with incomplete information, such that both Reiter's defaults and constraint defaults can be represented directly. After that, a method to split the CDLP programs is proposed by extending the notion of splitting sets to accommodate its property of constraint nonmonotonicity. Finally, we design a primary algorithm for solving the CDLP programs. |

11:05 | On the generalization of learnt constraints in ASP solving for temporal domains PRESENTER: Klaus Strauch ABSTRACT. The representation of a dynamic problem in ASP usually boils down to using copies of variables and constraints, one for each time stamp, no matter whether it is directly encoded or via an action or temporal language. The multiplication of variables and constraints is commonly done during grounding and the solver is completely ignorant about the temporal relationship among the different instances. On the other hand, a key factor in the performance of today's ASP solvers is conflict-driven constraint learning. Our question is now whether a constraint learned for particular time steps can be generalized and reused at other time stamps, and ultimately whether this enhances the overall solver performance on dynamic problems. Knowing full well the domain of time, we study conditions under which learned dynamic constraints can be generalized and propose a simple translation of the original logic program such that, for the translated programs, all learned constraints can be generalized to other time points. Last but not least, we empirically evaluate the impact of adding the generalized constraints to the ASP solver. |

11:25 | PRESENTER: Konstantin Herud ABSTRACT. Product configuration is one of the most important industrial applications of artificial intelligence. To enable customers to individualize complex products, usually logical configuration models are necessary. One challenge that exists here is the communication of product knowledge to the customer. This work deals with the situation of invalid customer requirements under given logical constraints. The goal is to explain why configurations are invalid and how they can be minimally changed to become valid again. This involves computing all minimal subsets of both constraints and requirements that make the configuration unsatisfiable. For this, we present a novel approach based on the declarative paradigm of Answer Set Programming. We empirically demonstrate its suitability for real-time configurators with thousands of features and constraints. The approach thus fills the gap of an easy-to-implement as well as high-performing conflict resolution component. |

11:45 | Hard Variants of Stable Marriage Problems: An Empirical Comparison of ASP with Other Computing Paradigms |

Lunches will be held in Taub hall and in The Grand Water Research Institute.

**Counting/Probabilistic ASP & Synthesis **

14:00 | A Semantics For Probabilistic Answer Set Programs With Incomplete Stochastic Knowledge PRESENTER: David Tuckey ABSTRACT. Some probabilistic answer set programs (PASP) semantics assign probabilities to sets of answer sets and implicitly assumes these answer sets to be equiprobable. While this is a common choice in probability theory, it leads to unnatural behaviours with PASPs. We argue that the user should have a level of control over what assumption is used to obtain a probability distribution when the stochastic knowledge is incomplete. To this end, we introduce the Incomplete Knowledge Semantics (IKS) for probabilistic answer set programming. We take inspiration from the field of decision making under ignorance. Given a cost function, which is given by a user-defined ordering over answer sets through weak constraints, we use the notion of Ordered Weighted Averaging (OWA) operator, to distribute the probability over a set of answer sets accordingly to the user’s level of optimism. The more optimistic (or pessimistic) a user is, the more (or less) probability is assigned to the more (or less) optimal answer sets. We present an implementation and showcase the behaviour of this semantics on simple examples. We also highlight the impact that different OWA operators have on weight learning, showing that the equiprobability assumption isn't always the best option. |

14:20 | PRESENTER: Nicolas Ruehling ABSTRACT. We present plingo, an extension of the ASP system clingo with various probabilistic reasoning modes. Plingo is centered upon LPMLN, a probabilistic extension of ASP based upon a weight scheme from Markov Logic. This choice is motivated by the fact that the core probabilistic reasoning modes can be mapped onto optimization problems and that LPMLN may serve as a middle-ground formalism connecting to other probabilistic approaches. As a result, plingo offers three alternative front-ends, one for LPMLN, PLOG, and PROBLOG. The corresponding input languages and reasoning modes are implemented by means of clingo's multi-shot and theory solving capabilities. Although plingo's core amounts to a re-implementation of LPMLN in terms of modern ASP technology, it integrates various probabilistic reasoning modes with the full modeling language and reasoning spectrum of clingo. |

14:40 | Automatic Synthesis of Boolean Networks from Biological Knowledge and Data PRESENTER: Athénaïs Vaginay ABSTRACT. Boolean Networks (BNs) are a simple formalism used to study complex biological systems when the prediction of exact reaction times is not of interest. They play a key role to understand the dynamics of the studied systems and to predict their disruption in case of complex human diseases. BNs are generally built from experimental data and knowledge from the literature, either manually or with the aid of programs. The automatic synthesis of BNs is still a challenge for which several approaches have been proposed. In this paper, we propose ASKeD-BN, a new approach based on Answer-Set Programming to synthesise BNs constrained in their structure and dynamics. By applying our method on several well-known biological systems, we provide empirical evidence that our approach can construct BNs in line with the provided constraints. We compare our approach with three existing methods (REVEAL, Best-Fit and caspo-TS) and show that our approach synthesises a small number of BNs which are covering a good proportion of the dynamical constraints, and that the variance of this coverage is low. ------- This work was published at the conference OLA2021. https://www.springerprofessional.de/en/automatic-synthesis-of-boolean-networks-from-biological-knowledg/19574476 |

15:00 | ASP in Industry, here and there ABSTRACT. Answer Set Programming (ASP) has become a popular paradigm for declarativeproblem solving and is about to find its way into industry. This is dueto its expressive yet easy knowledge representation language powered by highlyperformant (Boolean) solving technology. As with many other such paradigmsbefore, the transition from academia to industry calls for more versatility.Hence, many real-world applications are not tackled by pure ASP but ratherhybrid ASP. The corresponding ASP systems are usually augmented by foreignlanguage constructs from which additional inferences can be drawn. Examplesinclude linear equations or temporal formulas. For the design of "sound"systems, however, it is indispensable to provide semantic underpinningsright from the start. To this end, we will discuss the vital role of ASP'slogical foundations, the logic of Here-and-There and its non-monotonic extension,Equilibrium Logic, in designing hybrid ASP systems and highlight some of theresulting industrial applications. |

**Modelling and Applications**

16:00 | PRESENTER: Nicolas Lecomte ABSTRACT. An H-partition of a finite undirected simple graph G is a labeling of G's vertices such that the constraints expressed by the model graph H are satisfied. For every model graph H, it can be decided in non-deterministic polynomial time whether a given input graph G admits an H-partition. Moreover, it has been shown by Dantas et al. that for most model graphs, this decision problem is in deterministic polynomial time. In this paper, we show that these polynomial-time algorithms for finding H-partitions can be expressed in Datalog with stratified negation. Moreover, using the answer set solver Clingo, we have conducted experiments to compare straightforward guess-and-check programs with Datalog programs. Our experiments indicate that in Clingo, guess-and check programs run faster than their equivalent Datalog programs. |

16:20 | Translating Definitions into the Language of Logic Programming: A Case Study ABSTRACT. In the process of creating a declarative program, the programmer transforms a problem specification expressed in a natural language into an executable specification. We study the case when the given specification is expressed by a mathematically precise definition, and the goal is to write a program for an answer set solver. |

16:40 | A normative model of explanation for binary classification legal AI and its implementation on causal explanations of Answer Set Programming ABSTRACT. In this paper, I provide a normative model of explanation for the output of AI algorithms used in legal practice. I focus on binary classification algorithms due to their extensive use in the field. In the last part of the paper, I examine the model’s compatibility with causal explanations provided by Answer Set Programming (ASP) causal models. The motivation for proposing this model is the necessity for providing explanations for the output of legal AI. From the multiplicity of arguments supporting that necessity, the proposed model addresses the argument that legal AI’s output should be objectionable. That can be achieved only if the explanation of the output has a form that makes it amenable to evaluation by legal practitioners. Hence, I firstly provide a normative model for the explanations used by legal practitioners in their practice (CLM_LP) and then I provide the normative model for the explanations of legal AI’s outputs (EXP_BC) that I base on CLP_LP. CLP_LP in its turn is based on the Classical Model of Science (CMS) which is the normative model of explanations that every “proper” science should follow according to philosophers throughout history. Following the introduction of EXP_BC, I propose three degrees of explainability regarding binary classification explanations according to their fidelity to EXPBC. I further argue that machine learning can not satisfy even the lowest degree of explainability, while rule-based AI - like ASP-based AI - can satisfy the highest degree. Concluding, I propose an ASP methodology in-progress that can use EXP_BC to provide causal explanations. In the proposed ASP methodology, I am using causal graphs as models of causal inference as well as a metaphysically neutral interventionist account of causation. CMS_LP and EXP_BC are normative models that are based on the derivation relation of subsumptive-deductive inference among norms and propositions. On the other hand, the proposed ASP methodology is based on causal - and hence non-subsumptive-deductive - relations among norms and propositions that supervene on the subsumptive-deductive ones. Consequently, the motivation behind proposing this specific ASP methodology is to establish a precedent for a unification of different types of explanations (e.g., deductive and causal explanations) as well as to bridge the gaps among computational modelling, actual practice, and the philosophical underpinnings of a domain of expertise (law in this case). |

17:00 | Assumable Answer Set Programming ABSTRACT. For modeling the assumption-based intelligent agents who make assumptions and use them to construct their belief sets, this paper proposes a logic programming language AASP (Assumable Answer Set Programming) by extending ASP (Answer Set Programming). Rational principles of assumption-based reasoning are given to define the semantics of the AASP program. The relation of AASP to some existing default formalism implies that AASP can be used to model and solve some interesting problems with incomplete information in the framework of assumption-based reasoning. |

**CAUSAL and EELP**

17:30 | Correct Causal Inference in Probabilistic Logic Programming |

17:50 | A Casual Perspective on AI Deception |

18:10 | Epistemic Logic Programs: a Novel Perspective and some Extensions PRESENTER: Stefania Costantini |