Pre-trained language models (PLMs) have made significant advances in natural language inference (NLI) tasks, however their sensitivity to textual perturbations and dependence on large datasets indicate an over-reliance on shallow heuristics. In contrast, inductive logic programming (ILP) excels at inferring logical relationships across diverse, sparse and limited datasets, but its discrete nature requires the inputs to be precisely specified, which limits their application. This paper proposes a bridge between the two approaches: neuro-symbolic contrastive learning. This allows for smooth and differentiable optimisation that improves logical accuracy across an otherwise discrete, noisy, and sparse topological space of logical functions. We show that abstract logical relationships can be effectively embedded within a neuro-symbolic paradigm, by representing data as logic programs and sets of logic rules. The embedding space captures highly varied textual information with similar semantic logical relations, but can also separate similar textual relations that have dissimilar logical relations. Experimental results demonstrate that our approach significantly improves the inference capabilities of the models in terms of generalisation and reasoning.

Metamodeling helps in specifying conceptual modelling requirements with the notion of meta-classes (for instance, classes that are instances of other classes) and meta-properties (relations between metaconcepts). These notions can be expressed in OWL Full. However, OWL Full is so expressive for metamodeling that it leads to undecidability [13]. OWL 2 DL and its sub-profiles guarantee decidability, but they provide a very restricted form of metamodeling [7] and give no semantic support due to the prevalent Direct Semantics (DS). Consider an example adapted from [6], concerning the modeling of biological species, stating that all golden eagles are eagles, all eagles are birds, and Harry is an instance of GoldenEagle, which further can be inferred as an instance of Eagle and Bird. However, in the species domain one can not just express properties of and relationships among species, but also express properties of the species themselves. For example "GoldenEagle is listed in the IUCN Red List of endangered species" states that GoldenEagle as a whole class is an endangered species. Note that this is also not a subclass relation, as Harry is not an endangered species. To formally model this expression, we can declare GoldenEagle to be an instance of new class EndangeredSpecies.

In our daily lives and industrial settings, we often encounter dynamic problems that require reasoning over time and metric constraints. These include tasks such as scheduling, routing, and production sequencing. Dynamic logics have traditionally addressed these needs but often lack the flexibility and integration required for comprehensive problem modeling. This research aims to extend Answer Set Programming (ASP), a powerful declarative problem-solving approach, to handle dynamic domains effectively. By integrating concepts from dynamic, temporal, and metric logics into ASP, we seek to develop robust systems capable of modeling complex dynamic problems and performing efficient reasoning tasks, thereby enhancing ASPs applicability in industrial contexts.

Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy (especially, artificially intelligent) software systems. However, formally verifying ASP programs offers some unique challenges, such as 1. a lack of modularity (the meanings of rules are difficult to define in isolation from the enclosing program), 2. the ground-and-solve semantics (the meanings of rules are dependent on the input data with which the program is grounded), and 3. limitations of existing tools. My research agenda has been focused on addressing these three issues with the intention of making ASP verification an accessible, routine task that is regularly performed alongside program development. In this vein, I have investigated alternative semantics for ASP based on translations into the logic of here-and-there and many-sorted first-order logic. These semantics promote a modular understanding of logic programs, bypass grounding, and enable us to use automated theorem provers to automatically verify properties of programs.

Nowadays, sophisticated domains are emerging which require appropriate formalisms to be specified accurately in order to reason about them. One such domain is constituted of smart contracts that have emerged in cyber physical systems as a way of enforcing formal agreements between components of these systems. Smart contracts self-execute to run and share business processes through blockchain, in decentralized systems, with many different participants. Legal contracts are in many cases complex documents, with a number of exceptions, and many subcontracts. The implementation of smart contracts based on legal contracts is a long and laborious task, that needs to include all actions, procedures, and the effects of actions related to the execution of the contract. An ongoing open problem in this area is to formally account for smart contracts using a uniform and somewhat universal formalism. This thesis proposes logical foundations to smart contracts using the Situation Calculus, a logic for reasoning about actions. Situation Calculus is one of the prominent logic-based artificial intelligence approaches that provides enough logical mechanism to specify and implement dynamic and complex systems such as contracts. Situation Calculus is suitable to show how worlds dynamically change. Smart contracts are going to be implement with Golog (written en Prolog), a Situation Calculus-based programming language for modeling complex and dynamic behaviors.

We have focused on Answer Set Programming (ASP), more specifically, answer set counting, exploring both exact and approximate methodologies. We developed an exact ASP counter, sharpASP, which utilizes a compact encoding for propositional formulas, significantly enhancing efficiency compared to existing methods that often struggle with inefficient encodings. Our evaluations indicate that sharpASP outperforms current ASP counters on several benchmarks. In addition, we proposed an approximate ASP counter, named ApproxASP, a hashing-based counter integrating Gauss-Jordan elimination within the ASP solver, clingo. As a practical application, we employed ApproxASP for network reliability estimation, demonstrating superior performance over both traditional reliability estimators and #SAT-based methods.

Answer Set Programming (ASP) is a powerful tool for solving real-world problems. However, many problems involve numeric values and complex constraints beyond the capabilities of standard ASP solvers. Hybrid solvers like CLINGCON and CLINGO[DL] address this by using specialized methods for specific constraints. However, these solvers lack a strong theoretical foundation. This issue has first been addressed by introducing the Logic of Here-and-There with constraints (HT_c) as an extension of the Logic of Here-and-There (HT) and its non-monotone extension Equilibrium Logic. Nowadays, HT serves as a logical foundation for ASP and has facilitated a broader understanding of this paradigm. The idea is that HTC (and other extensions) play an analogous role for hybrid ASP. There remain many open questions about these logics regarding their fundamental characteristics as well as their practical use in solvers, ie. how they can guide the implementation. Having a formal understanding of these hybrid logics is also needed to better understand the inherent structure of the (real-world) problems they are applied to and to improve their representations in ASP. As an example of an application of ASP we use product configuration.

While the multi-step dialog model initiated by ChatGPT is now available from a few dozen online or locally run open source and closed source LLMs, it does not cover the need to efficiently extract salient information from an LLMs "parameter-memory" that encapsulates in a heavily compressed form the result of training the model on trillions of documents and multimodal data. Steps in this direction have been taken, relying on ground-truth involving additional information sources (e.g., collections of reference documents or use of web search queries). Among them, we mention work on improving performance of Retrieval Augmented Generation (RAG) systems [7] by recursively embedding, clustering, and summarizing chunks of text for better hierarchical LLM-assisted summarization [15], multi-agent hybrid LLM and local computation aggregators [3] and deductive verifiers of chain of thoughts reasoning [9]. A more direct approach is recursion on LLM queries, by chaining the LLM's distilled output as input to a next step and casting its content and interrelations in the form of logic programs, to automate and focus this information extraction with minimal human input [18, 20]. Like in the case of typical RAG architectures [7, 15], this process can rely on external ground truth but it can also use new LLM client instances as "oracles" deciding the validity of the synthesized rules or facts. With focus on automation of this unmediated salient knowledge extraction from the LLM's parameter memory and its encapsulation in the form of synthesized logic programming code, we will extend in this paper the work initiated in [18, 20] with: new LLM input-output chaining mechanisms new types of generated logic programs new relational representations elicited from LLM output steps 2 On LLM-generated Logic Programs and their Inference Execution Methods scalable execution mechanisms that accommodate very large logic programs at deeper recursion levels soft-unification based execution of LLM-generated logic programs as a principled encapsulation of the RAG retrieval process The rest of the paper is organized as follows. Section 2 overviews the DeepLLM architecture described in [20] and its new extensions supporting the results in this paper.

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.

The reviewers gave mixed scores and raised various issues with respect to the evaluation and the novelty compared to the ICLR 2018 workshop paper. However, I felt that accepting the paper at this time would be valuable to the NeurIPS community as it combines pre-existing components in a reasonable way, yielding both good performance improvement and providing useful insights about these models. I would encourage the authors to address the issues raised by the reviewers in the camera-ready.