Thomas Eiter

Thomas Eiter, Nelson Higuera Ruiz, Johannes Oetsch

Visual Question Answering (VQA) is the task of answering questions about images, requiring the integration of multimodal input and reasoning. Modular approaches that incorporate logic-based representations into the reasoning component offer clear advantages over end-to-end trained systems, particularly in terms of interpretability. However, adapting or extending these representations when task requirements change can place a significant burden on developers. To address this challenge, we present an approach for distilling rules from Large Language Models (LLMs). Our method prompts an LLM to extend an initial VQA reasoning theory, expressed as an answer-set program, to meet new requirements of the task. Examples from VQA datasets guide the LLM, validate the results, and help correct erroneous rules by leveraging feedback from the ASP solver. We demonstrate that our approach is effective across diverse VQA datasets. Notably, only a few examples are needed to elicit correct rules from LLMs. Our experiments suggest that rule distillation from LLMs is a promising alternative to traditional data-driven rule learning approaches. Under consideration in Theory and Practice of Logic Programming (TPLP).

Thomas Eiter, Nelson Higuera, Johannes Oetsch et al.

We present a neuro-symbolic visual question answering (VQA) pipeline for CLEVR, which is a well-known dataset that consists of pictures showing scenes with objects and questions related to them. Our pipeline covers (i) training neural networks for object classification and bounding-box prediction of the CLEVR scenes, (ii) statistical analysis on the distribution of prediction values of the neural networks to determine a threshold for high-confidence predictions, and (iii) a translation of CLEVR questions and network predictions that pass confidence thresholds into logic programs so that we can compute the answers using an ASP solver. By exploiting choice rules, we consider deterministic and non-deterministic scene encodings. Our experiments show that the non-deterministic scene encoding achieves good results even if the neural networks are trained rather poorly in comparison with the deterministic approach. This is important for building robust VQA systems if network predictions are less-than perfect. Furthermore, we show that restricting non-determinism to reasonable choices allows for more efficient implementations in comparison with related neuro-symbolic approaches without loosing much accuracy. This work is under consideration for acceptance in TPLP.

Thomas Eiter, Tobias Geibinger, Nysret Musliu et al.

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. Under consideration in Theory and Practice of Logic Programming (TPLP).

Jacopo Urbani, Markus Krötzsch, Thomas Eiter

We study reasoning with existential rules to perform query answering over streams of data. On static databases, this problem has been widely studied, but its extension to rapidly changing data has not yet been considered. To bridge this gap, we extend LARS, a well-known framework for rule-based stream reasoning, to support existential rules. For that, we show how to translate LARS with existentials into a semantics-preserving set of existential rules. As query answering with such rules is undecidable in general, we describe how to leverage the temporal nature of streams and present suitable notions of acyclicity that ensure decidability.

Christian Hatschka, Agata Ciabattoni, Thomas Eiter

The rise of powerful AI technology for a range of applications that are sensitive to legal, social, and ethical norms demands decision-making support in presence of norms and regulations. Normative reasoning is the realm of deontic logics, that are challenged by well-known benchmark problems (deontic paradoxes), and lack efficient computational tools. In this paper, we use Answer Set Programming (ASP) for addressing these shortcomings and showcase how to encode and resolve several well-known deontic paradoxes utilizing weak constraints. By abstracting and generalizing this encoding, we present a methodology for translating normative systems in ASP with weak constraints. This methodology is applied to "ethical" versions of Pac-man, where we obtain a comparable performance with related works, but ethically preferable results.

Rafael Bankosegger, Thomas Eiter, Johannes Oetsch

Reinforcement Learning (RL) enables autonomous agents to learn policies from experience, but realistic problems often involve enormous state spaces, making learning and generalisation challenging. Abstraction and approximation are therefore essential. Relational Reinforcement Learning (RRL) offers a way to reason about objects and their relations, and the CARCASS framework by Martijn van Otterlo demonstrates how logical representations can model Markov Decision Processes (MDPs) in first-order domains. Originally implemented in Prolog, CARCASS leverages domain knowledge to create powerful abstractions. We explore Answer-Set Programming (ASP), which is a rich and, contrary to Prolog, fully declarative modelling language, to realise CARCASS abstractions. We evaluate our ASP-based implementation in case studies of two domains, viz. Blocks World and Minigrid. Our results indicate that CARCASS with ASP provides a promising approach to constructing abstractions for RL, especially when domain knowledge is available.

Guillermo Badia, Manfred Droste, Thomas Eiter et al.

In recent years, quantitative complexity over semirings has been intensively investigated. In this context, Eiter and Kiesel (Semiring Reasoning Frameworks in AI and Their Computational Complexity, J. Artif. Intell. Res., 2023) introduced non-deterministic Turing Machines with semiring-weighted transitions (SRTMs) to capture the complexity of a manifold of semiring frameworks. Beyond computational complexity, they posed the question of how we can relate the computational power of SRTMs to logical expressiveness. While this question was partially addressed for a more limited machine model by Badia et al.\ (Logical characterizations of weighted complexity classes, MFCS, 2024), the full question remained open. To answer it, we present an improved version of Eiter and Kiesel's SRTM model of computation. First and foremost, this enables us to prove a Fagin Theorem for the SRTM model, i.e., we show that the quantitative complexity class $\text{NP}_\infty(R)$, which comprises non-deterministic polynomial time computability in the improved SRTM model over a commutative semiring $R$, is captured by a version of weighted existential second-order logic that allows for predicates interpreted as semiring-annotated relations over $R$. Furthermore, we argue that the new SRTM model is preferable over the original one and show that it reclaims some important results from Eiter and Kiesel (2023) that were flawed with respect to the latter.

Thomas Eiter, Tobias Geibinger, Zeynep G. Saribatur

Answer Set Programming (ASP) is a popular declarative reasoning and problem solving approach in symbolic AI. Its rule-based formalism makes it inherently attractive for explainable and interpretive reasoning, which is gaining importance with the surge of Explainable AI (XAI). A number of explanation approaches and tools for ASP have been developed, which often tackle specific explanatory settings and may not cover all scenarios that ASP users encounter. In this survey, we provide, guided by an XAI perspective, an overview of types of ASP explanations in connection with user questions for explanation, and describe how their coverage by current theory and tools. Furthermore, we pinpoint gaps in existing ASP explanations approaches and identify research directions for future work.

Thomas Eiter, Katsumi Inoue, Sota Moriyama

Integration of Answer Set Programming (ASP) with neural networks has emerged as a promising tool in Neuro-symbolic AI. While existing approaches extend the capabilities of ASP to real world domains, their reasoning pipelines depend on classical solvers, which is a bottleneck for scalability. To tackle this problem, we propose a new method to compute stable models, called decision-propagation (DProp), which alternates falsity decisions and truth propagations. Successful DProp computations are shown to capture the stable model semantics. We then develop Neural DProp (NDProp), a differentiable extension of DProp with neural computation for decisions and fuzzy evaluation for propagations. We evaluate the capabilities of NDProp for learning decision heuristics as well as neuro-symbolic integration, and compare it with existing neuro-symbolic approaches. The results show that NDProp can learn to efficiently compute stable models, and it improves accuracy and scalability on neuro-symbolic benchmarks.

Thomas Eiter, Johannes K. Fichte, Markus Hecher et al.

Answer Set Programming (ASP) is a prominent problem-modeling and solving framework, whose solutions are called answer sets. Epistemic logic programs (ELP) extend ASP to reason about all or some answer sets. Solutions to an ELP can be seen as consequences over multiple collections of answer sets, known as world views. While the complexity of propositional programs is well studied, the non-ground case remains open. This paper establishes the complexity of non-ground ELPs. We provide a comprehensive picture for well-known program fragments, which turns out to be complete for the class NEXPTIME with access to oracles up to Σ^P_2. In the quantitative setting, we establish complexity results for counting complexity beyond #EXP. To mitigate high complexity, we establish results in case of bounded predicate arity, reaching up to the fourth level of the polynomial hierarchy. Finally, we provide ETH-tight runtime results for the parameter treewidth, which has applications in quantitative reasoning, where we reason on (marginal) probabilities of epistemic literals.

Thomas Eiter, Jan Giesselmann, Robert Lasarzik et al.

We consider a structure-preserving finite-volume scheme for the Euler-Korteweg (EK) and Navier-Stokes-Korteweg (NSK) equations. We prove that its numerical solutions converge to energy-variational solutions of EK or NSK under mesh refinement. Energy-variational solutions constitute a novel solution concept that has recently been introduced for hyperbolic conservation laws, including the EK system, and which we extend to the NSK model. Our proof is based on establishing uniform estimates following from the properties of the structure-preserving scheme, and using the stability of the energy-variational formulation under weak convergence in the natural energy spaces.

Kun Gao, Davide SoldÃ, Thomas Eiter et al.

Learning rules plays a crucial role in deep learning, particularly in explainable artificial intelligence and enhancing the reasoning capabilities of large language models. While existing rule learning methods are primarily designed for symbolic data, learning rules from image data without supporting image labels and automatically inventing predicates remains a challenge. In this paper, we tackle these inductive rule learning problems from images with a framework called γILP, which provides a fully differentiable pipeline from image constant substitution to rule structure induction. Extensive experiments demonstrate that γILP achieves strong performance not only on classical symbolic relational datasets but also on relational image data and pure image datasets, such as Kandinsky patterns.

Thomas Eiter, Tobias Geibinger, Tobias Kaminski et al.

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.

Yi-Dong Shen, Thomas Eiter

Non-monotonic logic programming is the basis for a declarative problem solving paradigm known as answer set programming (ASP). Departing from the seminal definition by Gelfond and Lifschitz in 1988 for simple normal logic programs, various answer set semantics have been proposed for extensions. We consider two important questions: (1) Should the minimal model property, constraint monotonicity and foundedness as defined in the literature be mandatory conditions for an answer set semantics in general? (2) If not, what other properties could be considered as general principles for answer set semantics? We address the two questions. First, it seems that the three aforementioned conditions may sometimes be too strong, and we illustrate with examples that enforcing them may exclude expected answer sets. Second, we evolve the Gelfond answer set (GAS) principles for answer set construction by refining the Gelfond's rationality principle to well-supportedness, minimality w.r.t. negation by default and minimality w.r.t. epistemic negation. The principle of well-supportedness guarantees that every answer set is constructible from if-then rules obeying a level mapping and is thus free of circular justification, while the two minimality principles ensure that the formalism minimizes knowledge both at the level of answer sets and of world views. Third, to embody the refined GAS principles, we extend the notion of well-supportedness substantially to answer sets and world views, respectively. Fourth, we define new answer set semantics in terms of the refined GAS principles. Fifth, we use the refined GAS principles as an alternative baseline to intuitively assess the existing answer set semantics. Finally, we analyze the computational complexity.

Jakob Johannes Bauer, Thomas Eiter, Nelson Higuera Ruiz et al.

Visual Question Answering (VQA) is a challenging problem that requires to process multimodal input. Answer-Set Programming (ASP) has shown great potential in this regard to add interpretability and explainability to modular VQA architectures. In this work, we address the problem of how to integrate ASP with modules for vision and natural language processing to solve a new and demanding VQA variant that is concerned with images of graphs (not graphs in symbolic form). Images containing graph-based structures are an ubiquitous and popular form of visualisation. Here, we deal with the particular problem of graphs inspired by transit networks, and we introduce a novel dataset that amends an existing one by adding images of graphs that resemble metro lines. Our modular neuro-symbolic approach combines optical graph recognition for graph parsing, a pretrained optical character recognition neural network for parsing labels, Large Language Models (LLMs) for language processing, and ASP for reasoning. This method serves as a first baseline and achieves an overall average accuracy of 73% on the dataset. Our evaluation provides further evidence of the potential of modular neuro-symbolic systems, in particular with pretrained models that do not involve any further training and logic programming for reasoning, to solve complex VQA tasks.

Thomas Eiter, Jan Hadl, Nelson Higuera et al.

Visual Question Answering (VQA) is the task of answering a question about an image and requires processing multimodal input and reasoning to obtain the answer. Modular solutions that use declarative representations within the reasoning component have a clear advantage over end-to-end trained systems regarding interpretability. The downside is that crafting the rules for such a component can be an additional burden on the developer. We address this challenge by presenting an approach for declarative knowledge distillation from Large Language Models (LLMs). Our method is to prompt an LLM to extend an initial theory on VQA reasoning, given as an answer-set program, to meet the requirements of the VQA task. Examples from the VQA dataset are used to guide the LLM, validate the results, and mend rules if they are not correct by using feedback from the ASP solver. We demonstrate that our approach works on the prominent CLEVR and GQA datasets. Our results confirm that distilling knowledge from LLMs is in fact a promising direction besides data-driven rule learning approaches.

Loris Bozzato, Thomas Eiter, Rafael Kiesel et al.

We present a continuation to our previous work, in which we developed the MR-CKR framework to reason with knowledge overriding across contexts organized in multi-relational hierarchies. Reasoning is realized via ASP with algebraic measures, allowing for flexible definitions of preferences. In this paper, we show how to apply our theoretical work to real autonomous-vehicle scene data. Goal of this work is to apply MR-CKR to the problem of generating challenging scenes for autonomous vehicle learning. In practice, most of the scene data for AV learning models common situations, thus it might be difficult to capture cases where a particular situation occurs (e.g. partial occlusions of a crossing pedestrian). The MR-CKR model allows for data organization exploiting the multi-dimensionality of such data (e.g., temporal and spatial). Reasoning over multiple contexts enables the verification and configuration of scenes, using the combination of different scene ontologies. We describe a framework for semantically guided data generation, based on a combination of MR-CKR and Algebraic Measures. The framework is implemented in a proof-of-concept prototype exemplifying some cases of scene generation.

Anh Le-Tuan, Manh Nguyen-Duc, Chien-Quang Le et al.

We present CQELS 2.0, the second version of Continuous Query Evaluation over Linked Streams. CQELS 2.0 is a platform-agnostic federated execution framework towards semantic stream fusion. In this version, we introduce a novel neural-symbolic stream reasoning component that enables specifying deep neural network (DNN) based data fusion pipelines via logic rules with learnable probabilistic degrees as weights. As a platform-agnostic framework, CQELS 2.0 can be implemented for devices with different hardware architectures (from embedded devices to cloud infrastructures). Moreover, this version also includes an adaptive federator that allows CQELS instances on different nodes in a network to coordinate their resources to distribute processing pipelines by delegating partial workloads to their peers via subscribing continuous queries

Loris Bozzato, Thomas Eiter, Rafael Kiesel

Dealing with context dependent knowledge has led to different formalizations of the notion of context. Among them is the Contextualized Knowledge Repository (CKR) framework, which is rooted in description logics but links on the reasoning side strongly to logic programs and Answer Set Programming (ASP) in particular. The CKR framework caters for reasoning with defeasible axioms and exceptions in contexts, which was extended to knowledge inheritance across contexts in a coverage (specificity) hierarchy. However, the approach supports only this single type of contextual relation and the reasoning procedures work only for restricted hierarchies, due to non-trivial issues with model preference under exceptions. In this paper, we overcome these limitations and present a generalization of CKR hierarchies to multiple contextual relations, along with their interpretation of defeasible axioms and preference. To support reasoning, we use ASP with algebraic measures, which is a recent extension of ASP with weighted formulas over semirings that allows one to associate quantities with interpretations depending on the truth values of propositional atoms. Notably, we show that for a relevant fragment of CKR hierarchies with multiple contextual relations, query answering can be realized with the popular asprin framework. The algebraic measures approach is more powerful and enables e.g. reasoning with epistemic queries over CKRs, which opens interesting perspectives for the use of quantitative ASP extensions in other applications.

Loris Bozzato, Thomas Eiter, Luciano Serafini

Reasoning on defeasible knowledge is a topic of interest in the area of description logics, as it is related to the need of representing exceptional instances in knowledge bases. In this direction, in our previous works we presented a framework for representing (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms: reasoning in such framework is realized by a translation into ASP programs. The resulting reasoning process for OWL RL, however, introduces a complex encoding in order to capture reasoning on the negative information needed for reasoning on exceptions. In this paper, we apply the justified exception approach to knowledge bases in $\textit{DL-Lite}_{\cal R}$, i.e., the language underlying OWL QL. We provide a definition for $\textit{DL-Lite}_{\cal R}$ knowledge bases with defeasible axioms and study their semantic and computational properties. In particular, we study the effects of exceptions over unnamed individuals. The limited form of $\textit{DL-Lite}_{\cal R}$ axioms allows us to formulate a simpler ASP encoding, where reasoning on negative information is managed by direct rules. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in $\textit{DL-Lite}_{\cal R}$ with defeasible axioms. Under consideration in Theory and Practice of Logic Programming (TPLP).

Yi-Dong Shen, Thomas Eiter

Recently, the notions of subjective constraint monotonicity, epistemic splitting, and foundedness have been introduced for epistemic logic programs, with the aim to use them as main criteria respectively intuitions to compare different answer set semantics proposed in the literature on how they comply with these intuitions. In this note, we consider these three notions and demonstrate on some examples that they may be too strong in general and may exclude some desired answer sets respectively world views. In conclusion, these properties should not be regarded as mandatory properties that every answer set semantics must satisfy in general.

Thomas Eiter, Rafael Kiesel

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(AC)), 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(AC) can be exploited for effective problem-solving in a rich framework. This work is under consideration for acceptance in Theory and Practice of Logic Programming.

Carmine Dodaro, Thomas Eiter, Paul Ogris et al.

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. Under consideration for acceptance in TPLP.

Thomas Eiter, Zeynep G. Saribatur, Peter Schüller

Humans are capable of abstracting away irrelevant details when studying problems. This is especially noticeable for problems over grid-cells, as humans are able to disregard certain parts of the grid and focus on the key elements important for the problem. Recently, the notion of abstraction has been introduced for Answer Set Programming (ASP), a knowledge representation and reasoning paradigm widely used in problem solving, with the potential to understand the key elements of a program that play a role in finding a solution. The present paper takes this further and empowers abstraction to deal with structural aspects, and in particular with hierarchical abstraction over the domain. We focus on obtaining the reasons for unsolvability of problems on grids, and show the possibility to automatically achieve human-like abstractions that distinguish only the relevant part of the grid. A user study on abstract explanations confirms the similarity of the focus points in machine vs. human explanations and reaffirms the challenge of employing abstraction to obtain machine explanations.

Thomas Eiter, Paul Ogris, Konstantin Schekotihin

Stream reasoning systems are designed for complex decision-making from possibly infinite, dynamic streams of data. Modern approaches to stream reasoning are usually performing their computations using stand-alone solvers, which incrementally update their internal state and return results as the new portions of data streams are pushed. However, the performance of such approaches degrades quickly as the rates of the input data and the complexity of decision problems are growing. This problem was already recognized in the area of stream processing, where systems became distributed in order to allocate vast computing resources provided by clouds. In this paper we propose a distributed approach to stream reasoning that can efficiently split computations among different solvers communicating their results over data streams. Moreover, in order to increase the throughput of the distributed system, we suggest an interval-based semantics for the LARS language, which enables significant reductions of network traffic. Performed evaluations indicate that the distributed stream reasoning significantly outperforms existing stand-alone LARS solvers when the complexity of decision problems and the rate of incoming data are increasing. Under consideration for acceptance in Theory and Practice of Logic Programming.

Loris Bozzato, Thomas Eiter, Luciano Serafini

Representation of defeasible information is of interest in description logics, as it is related to the need of accommodating exceptional instances in knowledge bases. In this direction, in our previous works we presented a datalog translation for reasoning on (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms. While it covers a relevant fragment of OWL, the resulting reasoning process needs a complex encoding in order to capture reasoning on negative information. In this paper, we consider the case of knowledge bases in $\textit{DL-Lite}_{\cal R}$, i.e. the language underlying OWL QL. We provide a definition for $\textit{DL-Lite}_{\cal R}$ knowledge bases with defeasible axioms and study their properties. The limited form of $\textit{DL-Lite}_{\cal R}$ axioms allows us to formulate a simpler encoding into datalog (under answer set semantics) with direct rules for reasoning on negative information. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in $\textit{DL-Lite}_{\cal R}$ with defeasible axioms.

Zeynep G. Saribatur, Thomas Eiter

ASP programs are a convenient tool for problem solving, whereas with large problem instances the size of the state space can be prohibitive. We consider abstraction as a means of over-approximation and introduce a method to automatically abstract (possibly non-ground) ASP programs that preserves their structure, while reducing the size of the problem. One particular application case is the problem of defining declarative policies for reactive agents and reasoning about them, which we illustrate on examples.

Loris Bozzato, Luciano Serafini, Thomas Eiter

This paper is an appendix to the paper "Reasoning with Justifiable Exceptions in Contextual Hierarchies" by Bozzato, Serafini and Eiter, 2018. It provides further details on the language, the complexity results and the datalog translation introduced in the main paper.

Harald Beck, Bruno Bierbaumer, Minh Dao-Tran et al.

Content-Centric Networking (CCN) research addresses the mismatch between the modern usage of the Internet and its outdated architecture. Importantly, CCN routers may locally cache frequently requested content in order to speed up delivery to end users. Thus, the issue of caching strategies arises, i.e., which content shall be stored and when it should be replaced. In this work, we employ novel techniques towards intelligent administration of CCN routers that autonomously switch between existing strategies in response to changing content request patterns. In particular, we present a router architecture for CCN networks that is controlled by rule-based stream reasoning, following the recent formal framework LARS which extends Answer Set Programming for streams. The obtained possibility for flexible router configuration at runtime allows for faster experimentation and may thus help to advance the further development of CCN. Moreover, the empirical evaluation of our feasibility study shows that the resulting caching agent may give significant performance gains.

Zeynep G. Saribatur, Thomas Eiter

We describe a representation in a high-level transition system for policies that express a reactive behavior for the agent. We consider a target decision component that figures out what to do next and an (online) planning capability to compute the plans needed to reach these targets. Our representation allows one to analyze the flow of executing the given reactive policy, and to determine whether it works as expected. Additionally, the flexibility of the representation opens a range of possibilities for designing behaviors.

Thomas Eiter, Michael Fink, Giovambattista Ianni et al.

As software systems are getting increasingly connected, there is a need for equipping nonmonotonic logic programs with access to external sources that are possibly remote and may contain information in heterogeneous formats. To cater for this need, HEX programs were designed as a generalization of answer set programs with an API style interface that allows to access arbitrary external sources, providing great flexibility. Efficient evaluation of such programs however is challenging, and it requires to interleave external computation and model building; to decide when to switch between these tasks is difficult, and existing approaches have limited scalability in many real-world application scenarios. We present a new approach for the evaluation of logic programs with external source access, which is based on a configurable framework for dividing the non-ground program into possibly overlapping smaller parts called evaluation units. The latter will be processed by interleaving external evaluation and model building using an evaluation graph and a model graph, respectively, and by combining intermediate results. Experiments with our prototype implementation show a significant improvement compared to previous approaches. While designed for HEX-programs, the new evaluation approach may be deployed to related rule-based formalisms as well.

Harald Beck, Minh Dao-Tran, Thomas Eiter et al.

The rise of smart applications has drawn interest to logical reasoning over data streams. Recently, different query languages and stream processing/reasoning engines were proposed in different communities. However, due to a lack of theoretical foundations, the expressivity and semantics of these diverse approaches are given only informally. Towards clear specifications and means for analytic study, a formal framework is needed to define their semantics in precise terms. To this end, we present a first step towards an ideal semantics that allows for exact descriptions and comparisons of stream reasoning systems.

Thomas Eiter, Michael Fink, Thomas Krennwallner et al.

HEX-programs are an extension of the Answer Set Programming (ASP) paradigm incorporating external means of computation into the declarative programming language through so-called external atoms. Their semantics is defined in terms of minimal models of the Faber-Leone-Pfeifer (FLP) reduct. Developing native solvers for HEX-programs based on an appropriate notion of unfounded sets has been subject to recent research for reasons of efficiency. Although this has lead to an improvement over naive minimality checking using the FLP reduct, testing for foundedness remains a computationally expensive task. In this work we improve on HEX-program evaluation in this respect by identifying a syntactic class of programs, that can be efficiently recognized and allows to entirely skip the foundedness check. Moreover, we develop criteria for decomposing a program into components, such that the search for unfounded sets can be restricted. Observing that our results apply to many HEX-program applications provides analytic evidence for the significance and effectiveness of our approach, which is complemented by a brief discussion of preliminary experimental validation.

Thomas Eiter, Thomas Lukasiewicz

We present the language {m P}{cal C}+ for probabilistic reasoning about actions, which is a generalization of the action language {cal C}+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics of {m P}{cal C}+ in terms of probabilistic transitions between sets of states. Using a concept of a history and its belief state, we then show how several important problems in reasoning about actions can be concisely formulated in our formalism.

Thomas Eiter, Michael Fink, Thomas Krennwallner et al.

Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs and efficient solvers. To enable access to external information, HEX-programs extend programs with external atoms, which allow for a bidirectional communication between the logic program and external sources of computation (e.g., description logic reasoners and Web resources). Current solvers evaluate HEX-programs by a translation to ASP itself, in which values of external atoms are guessed and verified after the ordinary answer set computation. This elegant approach does not scale with the number of external accesses in general, in particular in presence of nondeterminism (which is instrumental for ASP). In this paper, we present a novel, native algorithm for evaluating HEX-programs which uses learning techniques. In particular, we extend conflict-driven ASP solving techniques, which prevent the solver from running into the same conflict again, from ordinary to HEX-programs. We show how to gain additional knowledge from external source evaluations and how to use it in a conflict-driven algorithm. We first target the uninformed case, i.e., when we have no extra information on external sources, and then extend our approach to the case where additional meta-information is available. Experiments show that learning from external sources can significantly decrease both the runtime and the number of considered candidate compatible sets.