Neural-symbolic learning, an intersection of neural networks and symbolic reasoning, aims to blend neural networks' learning capabilities with symbolic AI's interpretability and reasoning. This paper introduces an approach designed to improve the performance of neural models in learning reasoning tasks. It achieves this by integrating Answer Set Programming (ASP) solvers and domain-specific expertise, which is an approach that diverges from traditional complex neural-symbolic models. In this paper, a shallow artificial neural network (ANN) is specifically trained to solve Sudoku puzzles with minimal training data. The model has a unique loss function that integrates losses calculated using the ASP solver outputs, effectively enhancing its training efficiency. Most notably, the model shows a significant improvement in solving Sudoku puzzles using only 12 puzzles for training and testing without hyperparameter tuning. This advancement indicates that the model's enhanced reasoning capabilities have practical applications, extending well beyond Sudoku puzzles to potentially include a variety of other domains. The code can be found on GitHub: https://github.com/Fadi2200/ASPEN.

Substantial efforts have been made in developing various Decision Modeling formalisms, both from industry and academia. A challenging problem is that of expressing decision knowledge in the context of incomplete knowledge. In such contexts, decisions depend on what is known or not known. We argue that none of the existing formalisms for modeling decisions are capable of correctly capturing the epistemic nature of such decisions, inevitably causing issues in situations of uncertainty. This paper presents a new language for modeling decisions with incomplete knowledge. It combines three principles: stratification, autoepistemic logic, and definitions. A knowledge base in this language is a hierarchy of epistemic theories, where each component theory may epistemically reason on the knowledge in lower theories, and decisions are made using definitions with epistemic conditions.

In the article, within the framework of the Boolean Satisfiability problem (SAT), the problem of estimating the hardness of specific Boolean formulas w.r.t. a specific complete SAT solving algorithm is considered. Based on the well-known Strong Backdoor Set (SBS) concept, we introduce the notion of decomposition hardness (d-hardness). If $B$ is an arbitrary subset of the set of variables occurring in a SAT formula $C$, and $A$ is an arbitrary complete SAT solver , then the d-hardness expresses an estimate of the hardness of $C$ w.r.t. $A$ and $B$. We show that the d-hardness of $C$ w.r.t. a particular $B$ can be expressed in terms of the expected value of a special random variable associated with $A$, $B$, and $C$. For its computational evaluation, algorithms based on the Monte Carlo method can be used. The problem of finding $B$ with the minimum value of d-hardness is formulated as an optimization problem for a pseudo-Boolean function whose values are calculated as a result of a probabilistic experiment. To minimize this function, we use evolutionary algorithms. In the experimental part, we demonstrate the applicability of the concept of d-hardness and the methods of its estimation to solving hard unsatisfiable SAT instances.

This work presents insights gained by investigating the relationship between algorithmic fairness and the concept of secure information flow. The problem of enforcing secure information flow is well-studied in the context of information security: If secret information may "flow" through an algorithm or program in such a way that it can influence the program's output, then that is considered insecure information flow as attackers could potentially observe (parts of) the secret. There is a strong correspondence between secure information flow and algorithmic fairness: if protected attributes such as race, gender, or age are treated as secret program inputs, then secure information flow means that these ``secret'' attributes cannot influence the result of a program. While most research in algorithmic fairness evaluation concentrates on studying the impact of algorithms (often treating the algorithm as a black-box), the concepts derived from information flow can be used both for the analysis of disparate treatment as well as disparate impact w.r.t. a structural causal model. In this paper, we examine the relationship between quantitative as well as qualitative information-flow properties and fairness. Moreover, based on this duality, we derive a new quantitative notion of fairness called fairness spread, which can be easily analyzed using quantitative information flow and which strongly relates to counterfactual fairness. We demonstrate that off-the-shelf tools for information-flow properties can be used in order to formally analyze a program's algorithmic fairness properties, including the new notion of fairness spread as well as established notions such as demographic parity.

The rise of AI-based and autonomous systems is raising concerns and apprehension due to potential negative repercussions stemming from their behavior or decisions. These systems must be designed to comply with the human contexts in which they will operate. To this extent, Townsend et al. (2022) introduce the concept of SLEEC (social, legal, ethical, empathetic, or cultural) rules that aim to facilitate the formulation, verification, and enforcement of the rules AI-based and autonomous systems should obey. They lay out a methodology to elicit them and to let philosophers, lawyers, domain experts, and others to formulate them in natural language. To enable their effective use in AI systems, it is necessary to translate these rules systematically into a formal language that supports automated reasoning. In this study, we first conduct a linguistic analysis of the SLEEC rules pattern, which justifies the translation of SLEEC rules into classical logic. Then we investigate the computational complexity of reasoning about SLEEC rules and show how logical programming frameworks can be employed to implement SLEEC rules in practical scenarios. The result is a readily applicable strategy for implementing AI systems that conform to norms expressed as SLEEC rules.

Deep neural learning uses an increasing amount of computation and data to solve very specific problems. By stark contrast, human minds solve a wide range of problems using a fixed amount of computation and limited experience. One ability that seems crucial to this kind of general intelligence is meta-reasoning, i.e., our ability to reason about reasoning. To make deep learning do more from less, we propose the first neural meta-symbolic system (NEMESYS) for reasoning and learning: meta programming using differentiable forward-chaining reasoning in first-order logic. Differentiable meta programming naturally allows NEMESYS to reason and learn several tasks efficiently. This is different from performing object-level deep reasoning and learning, which refers in some way to entities external to the system. In contrast, NEMESYS enables self-introspection, lifting from object- to meta-level reasoning and vice versa. In our extensive experiments, we demonstrate that NEMESYS can solve different kinds of tasks by adapting the meta-level programs without modifying the internal reasoning system. Moreover, we show that NEMESYS can learn meta-level programs given examples. This is difficult, if not impossible, for standard differentiable logic programming

The synthesis of string transformation programs from input-output examples utilizes various techniques, all based on an inductive bias that comprises a restricted set of basic operators to be combined. A new algorithm, Transduce, is proposed, which is founded on the construction of abstract transduction grammars and their generalization. We experimentally demonstrate that Transduce can learn positional transformations efficiently from one or two positive examples without inductive bias, achieving a success rate higher than the current state of the art.

We analyze how symmetries can be used to compress structures (also known as interpretations) onto a smaller domain without loss of information. This analysis suggests the possibility to solve satisfiability problems in the compressed domain for better performance. Thus, we propose a 2-step novel method: (i) the sentence to be satisfied is automatically translated into an equisatisfiable sentence over a ``lifted'' vocabulary that allows domain compression; (ii) satisfiability of the lifted sentence is checked by growing the (initially unknown) compressed domain until a satisfying structure is found. The key issue is to ensure that this satisfying structure can always be expanded into an uncompressed structure that satisfies the original sentence to be satisfied. We present an adequate translation for sentences in typed first-order logic extended with aggregates. Our experimental evaluation shows large speedups for generative configuration problems. The method also has applications in the verification of software operating on complex data structures. Our results justify further research in automatic translation of sentences for symmetry reduction.

Regular decision processes (RDPs) are a subclass of non-Markovian decision processes where the transition and reward functions are guarded by some regular property of the past (a lookback). While RDPs enable intuitive and succinct representation of non-Markovian decision processes, their expressive power coincides with finite-state Markov decision processes (MDPs). We introduce omega-regular decision processes (ODPs) where the non-Markovian aspect of the transition and reward functions are extended to an omega-regular lookahead over the system evolution. Semantically, these lookaheads can be considered as promises made by the decision maker or the learning agent about her future behavior. In particular, we assume that, if the promised lookaheads are not met, then the payoff to the decision maker is $\bot$ (least desirable payoff), overriding any rewards collected by the decision maker. We enable optimization and learning for ODPs under the discounted-reward objective by reducing them to lexicographic optimization and learning over finite MDPs. We present experimental results demonstrating the effectiveness of the proposed reduction.

Program synthesis aims to automatically generate an executable program that conforms to the given specification. Recent advancements have demonstrated that deep neural methodologies and large-scale pretrained language models are highly proficient in capturing program semantics. For robot programming, prior works have facilitated program synthesis by incorporating global environments. However, the assumption of acquiring a comprehensive understanding of the entire environment is often excessively challenging to achieve. In this work, we present a framework that learns to synthesize a program by rectifying potentially erroneous code segments, with the aid of partially observed environments. To tackle the issue of inadequate attention to partial observations, we propose to first learn an environment embedding space that can implicitly evaluate the impacts of each program token based on the precondition. Furthermore, by employing a graph structure, the model can aggregate both environmental and syntactic information flow and furnish smooth program rectification guidance. Extensive experimental evaluations and ablation studies on the partially observed VizDoom domain authenticate that our method offers superior generalization capability across various tasks and greater robustness when encountering noises.