Finite-state abstractions (a.k.a. symbolic models) present a promising avenue for the formal verification and synthesis of controllers in continuous-space control systems. These abstractions provide simplified models that capture the fundamental behaviors of the original systems. However, the creation of such abstractions typically relies on the availability of precise knowledge concerning system dynamics, which might not be available in many real-world applications. In this work, we introduce an innovative, data-driven, and compositional approach to generate finite abstractions for interconnected systems that consist of discrete-time control subsystems with unknown dynamics. These subsystems interact through an unknown static interconnection map. Our methodology for abstracting the interconnected system involves constructing abstractions for individual subsystems and incorporating an abstraction of the interconnection map.

Neural probabilistic logic systems follow the neuro-symbolic (NeSy) paradigm by combining the perceptive and learning capabilities of neural networks with the robustness of probabilistic logic. Learning corresponds to likelihood optimization of the neural networks. However, to obtain the likelihood exactly, expensive probabilistic logic inference is required. To scale learning to more complex systems, we therefore propose to instead optimize a sampling based objective. We prove that the objective has a bounded error with respect to the likelihood, which vanishes when increasing the sample count. Furthermore, the error vanishes faster by exploiting a new concept of sample diversity. We then develop the EXPLAIN, AGREE, LEARN (EXAL) method that uses this objective. EXPLAIN samples explanations for the data. AGREE reweighs each explanation in concordance with the neural component. LEARN uses the reweighed explanations as a signal for learning. In contrast to previous NeSy methods, EXAL can scale to larger problem sizes while retaining theoretical guarantees on the error. Experimentally, our theoretical claims are verified and EXAL outperforms recent NeSy methods when scaling up the MNIST addition and Warcraft pathfinding problems.

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.

When we want to compute the probability of a query from a Probabilistic Answer Set Program, some parts of a program may not influence the probability of a query, but they impact on the size of the grounding. Identifying and removing them is crucial to speed up the computation. Algorithms for SLG resolution offer the possibility of returning the residual program which can be used for computing answer sets for normal programs that do have a total well-founded model. The residual program does not contain the parts of the program that do not influence the probability. In this paper, we propose to exploit the residual program for performing inference. Empirical results on graph datasets show that the approach leads to significantly faster inference. The paper has been accepted at the ICLP2024 conference and under consideration in Theory and Practice of Logic Programming (TPLP).

The dominating set reconfiguration problem is defined as determining, for a given dominating set problem and two among its feasible solutions, whether one is reachable from the other via a sequence of feasible solutions subject to a certain adjacency relation. This problem is PSPACE-complete in general. The concept of the dominating set is known to be quite useful for analyzing wireless networks, social networks, and sensor networks. We develop an approach to solve the dominating set reconfiguration problem based on Answer Set Programming (ASP). Our declarative approach relies on a high-level ASP encoding, and both the grounding and solving tasks are delegated to an ASP-based combinatorial reconfiguration solver. To evaluate the effectiveness of our approach, we conduct experiments on a newly created benchmark set.

Answer Set Programming (asp) has demonstrated its potential as an effective tool for concisely representing and reasoning about real-world problems. In this paper, we present an application in which asp has been successfully used in the context of dynamic traffic distribution for urban networks, within a more general framework devised for solving such a real-world problem. In particular, asp has been employed for the computation of the "optimal" routes for all the vehicles in the network. We also provide an empirical analysis of the performance of the whole framework, and of its part in which asp is employed, on two European urban areas, which shows the viability of the framework and the contribution asp can give.

We present an on-the-fly synthesis framework for Linear Temporal Logic over finite traces (LTLf) based on top-down deterministic automata construction. Existing approaches rely on constructing a complete Deterministic Finite Automaton (DFA) corresponding to the LTLf specification, a process with doubly exponential complexity relative to the formula size in the worst case. In this case, the synthesis procedure cannot be conducted until the entire DFA is constructed. This inefficiency is the main bottleneck of existing approaches. To address this challenge, we first present a method for converting LTLf into Transition-based DFA (TDFA) by directly leveraging LTLf semantics, incorporating intermediate results as direct components of the final automaton to enable parallelized synthesis and automata construction. We then explore the relationship between LTLf synthesis and TDFA games and subsequently develop an algorithm for performing LTLf synthesis using on-the-fly TDFA game solving. This algorithm traverses the state space in a global forward manner combined with a local backward method, along with the detection of strongly connected components. Moreover, we introduce two optimization techniques -- model-guided synthesis and state entailment -- to enhance the practical efficiency of our approach. Experimental results demonstrate that our on-the-fly approach achieves the best performance on the tested benchmarks and effectively complements existing tools and approaches.

Formal languages are essential for computer programming and are constructed to be easily processed by computers. In contrast, natural languages are much more challenging and instigated the field of Natural Language Processing (NLP). One major obstacle is the ubiquity of ambiguities. Recent advances in NLP have led to the development of large language models, which can resolve ambiguities with high accuracy. At the same time, quantum computers have gained much attention in recent years as they can solve some computational problems faster than classical computers. This new computing paradigm has reached the fields of machine learning and NLP, where hybrid classical-quantum learning algorithms have emerged. However, more research is needed to identify which NLP tasks could benefit from a genuine quantum advantage. In this thesis, we applied formalisms arising from foundational quantum mechanics, such as contextuality and causality, to study ambiguities arising from linguistics. By doing so, we also reproduced psycholinguistic results relating to the human disambiguation process. These results were subsequently used to predict human behaviour and outperformed current NLP methods.

Answer Set Programming with Quantifiers (ASP(Q)) has been introduced to provide a natural extension of ASP modeling to problems in the polynomial hierarchy (PH). However, ASP(Q) lacks a method for encoding in an elegant and compact way problems requiring a polynomial number of calls to an oracle in $\Sigma_n^p$ (that is, problems in $\Delta_{n+1}^p$). Such problems include, in particular, optimization problems. In this paper we propose an extension of ASP(Q), in which component programs may contain weak constraints. Weak constraints can be used both for expressing local optimization within quantified component programs and for modeling global optimization criteria. We showcase the modeling capabilities of the new formalism through various application scenarios. Further, we study its computational properties obtaining complexity results and unveiling non-obvious characteristics of ASP(Q) programs with weak constraints.

Model counting is a fundamental problem in automated reasoning with applications in probabilistic inference, network reliability, neural network verification, and more. Although model counting is computationally intractable from a theoretical perspective due to its #P-completeness, the past decade has seen significant progress in developing state-of-the-art model counters to address scalability challenges. In this work, we conduct a rigorous assessment of the scalability of model counters in the wild. To this end, we surveyed 11 application domains and collected an aggregate of 2262 benchmarks from these domains. We then evaluated six state-of-the-art model counters on these instances to assess scalability and runtime performance. Our empirical evaluation demonstrates that the performance of model counters varies significantly across different application domains, underscoring the need for careful selection by the end user. Additionally, we investigated the behavior of different counters with respect to two parameters suggested by the model counting community, finding only a weak correlation. Our analysis highlights the challenges and opportunities for portfolio-based approaches in model counting.