The field of neuro-symbolic artificial intelligence (NeSy), which combines learning and reasoning, has recently experienced significant growth. There now are a wide variety of NeSy frameworks, each with its own specific language for expressing background knowledge and how to relate it to neural networks. This heterogeneity hinders accessibility for newcomers and makes comparing different NeSy frameworks challenging. We propose a unified language for NeSy, which we call ULLER, a Unified Language for LEarning and Reasoning. ULLER encompasses a wide variety of settings, while ensuring that knowledge described in it can be used in existing NeSy systems. ULLER has a neuro-symbolic first-order syntax for which we provide example semantics including classical, fuzzy, and probabilistic logics. We believe ULLER is a first step towards making NeSy research more accessible and comparable, paving the way for libraries that streamline training and evaluation across a multitude of semantics, knowledge bases, and NeSy systems.

For one to guarantee higher-quality software development processes, risk management is essential. Furthermore, risks are those that could negatively impact an organization's operations or a project's progress. The appropriate prioritisation of software project risks is a crucial factor in ascertaining the software project's performance features and eventual success. They can be used harmoniously with the same training samples and have good complement and compatibility. We carried out in-depth tests on four benchmark datasets to confirm the efficacy of our CIA approach in closed-world and open-world scenarios, with and without defence. We also present a sequential augmentation parameter optimisation technique that captures the interdependencies of the latest deep learning state-of-the-art WF attack models. To achieve precise software risk assessment, the enhanced crow search algorithm (ECSA) is used to modify the ANFIS settings. Solutions that very slightly alter the local optimum and stay inside it are extracted using the ECSA. ANFIS variable when utilising the ANFIS technique. An experimental validation with NASA 93 dataset and 93 software project values was performed. This method's output presents a clear image of the software risk elements that are essential to achieving project performance. The results of our experiments show that, when compared to other current methods, our integrative fuzzy techniques may perform more accurately and effectively in the evaluation of software project risks.

Mastering multiple tasks through exploration and learning in an environment poses a significant challenge in reinforcement learning (RL). Unsupervised RL has been introduced to address this challenge by training policies with intrinsic rewards rather than extrinsic rewards. However, current intrinsic reward designs and unsupervised RL algorithms often overlook the heterogeneous nature of collected samples, thereby diminishing their sample efficiency. To overcome this limitation, in this paper, we propose a reward-free RL algorithm called \alg. The key idea behind our algorithm is an uncertainty-aware intrinsic reward for exploring the environment and an uncertainty-weighted learning process to handle heterogeneous uncertainty in different samples. Theoretically, we show that in order to find an $\epsilon$-optimal policy, GFA-RFE needs to collect $\tilde{O} (H^2 \log N_{\mathcal F} (\epsilon) \mathrm{dim} (\mathcal F) / \epsilon^2 )$ number of episodes, where $\mathcal F$ is the value function class with covering number $N_{\mathcal F} (\epsilon)$ and generalized eluder dimension $\mathrm{dim} (\mathcal F)$. Such a result outperforms all existing reward-free RL algorithms. We further implement and evaluate GFA-RFE across various domains and tasks in the DeepMind Control Suite. Experiment results show that GFA-RFE outperforms or is comparable to the performance of state-of-the-art unsupervised RL algorithms.

Reinforcement Learning (RL) has gained significant attention across various domains. However, the increasing complexity of RL programs presents testing challenges, particularly the oracle problem: defining the correctness of the RL program. Conventional human oracles struggle to cope with the complexity, leading to inefficiencies and potential unreliability in RL testing. To alleviate this problem, we propose an automated oracle approach that leverages RL properties using fuzzy logic. Our oracle quantifies an agent's behavioral compliance with reward policies and analyzes its trend over training episodes. It labels an RL program as "Buggy" if the compliance trend violates expectations derived from RL characteristics. We evaluate our oracle on RL programs with varying complexities and compare it with human oracles. Results show that while human oracles perform well in simpler testing scenarios, our fuzzy oracle demonstrates superior performance in complex environments. The proposed approach shows promise in addressing the oracle problem for RL testing, particularly in complex cases where manual testing falls short. It offers a potential solution to improve the efficiency, reliability, and scalability of RL program testing. This research takes a step towards automated testing of RL programs and highlights the potential of fuzzy logic-based oracles in tackling the oracle problem.

Artificial intelligence systems often address fairness concerns by evaluating and mitigating measures of group discrimination, for example that indicate biases against certain genders or races. However, what constitutes group fairness depends on who is asked and the social context, whereas definitions are often relaxed to accept small deviations from the statistical constraints they set out to impose. Here we decouple definitions of group fairness both from the context and from relaxation-related uncertainty by expressing them in the axiomatic system of Basic fuzzy Logic (BL) with loosely understood predicates, like encountering group members. We then evaluate the definitions in subclasses of BL, such as Product or Lukasiewicz logics. Evaluation produces continuous instead of binary truth values by choosing the logic subclass and truth values for predicates that reflect uncertain context-specific beliefs, such as stakeholder opinions gathered through questionnaires. Internally, it follows logic-specific rules to compute the truth values of definitions. We show that commonly held propositions standardize the resulting mathematical formulas and we transcribe logic and truth value choices to layperson terms, so that anyone can answer them. We also use our framework to study several literature definitions of algorithmic fairness, for which we rationalize previous expedient practices that are non-probabilistic and show how to re-interpret their formulas and parameters in new contexts.

We study the finite-time convergence of TD learning with linear function approximation under Markovian sampling. Existing proofs for this setting either assume a projection step in the algorithm to simplify the analysis, or require a fairly intricate argument to ensure stability of the iterates. We ask: \textit{Is it possible to retain the simplicity of a projection-based analysis without actually performing a projection step in the algorithm?} Our main contribution is to show this is possible via a novel two-step argument. In the first step, we use induction to prove that under a standard choice of a constant step-size $\alpha$, the iterates generated by TD learning remain uniformly bounded in expectation. In the second step, we establish a recursion that mimics the steady-state dynamics of TD learning up to a bounded perturbation on the order of $O(\alpha^2)$ that captures the effect of Markovian sampling. Combining these pieces leads to an overall approach that considerably simplifies existing proofs. We conjecture that our inductive proof technique will find applications in the analyses of more complex stochastic approximation algorithms, and conclude by providing some examples of such applications.

We study model-based reinforcement learning with non-linear function approximation where the transition function of the underlying Markov decision process (MDP) is given by a multinomial logistic (MNL) model. In this paper, we develop two algorithms for the infinite-horizon average reward setting. Our first algorithm \texttt{UCRL2-MNL} applies to the class of communicating MDPs and achieves an $\tilde{\mathcal{O}}(dD\sqrt{T})$ regret, where $d$ is the dimension of feature mapping, $D$ is the diameter of the underlying MDP, and $T$ is the horizon. The second algorithm \texttt{OVIFH-MNL} is computationally more efficient and applies to the more general class of weakly communicating MDPs, for which we show a regret guarantee of $\tilde{\mathcal{O}}(d^{2/5} \mathrm{sp}(v^*)T^{4/5})$ where $\mathrm{sp}(v^*)$ is the span of the associated optimal bias function. We also prove a lower bound of $\Omega(d\sqrt{DT})$ for learning communicating MDPs with MNL transitions of diameter at most $D$. Furthermore, we show a regret lower bound of $\Omega(dH^{3/2}\sqrt{K})$ for learning $H$-horizon episodic MDPs with MNL function approximation where $K$ is the number of episodes, which improves upon the best-known lower bound for the finite-horizon setting.

In this paper, we generalize the Pearl and Neyman-Rubin methodologies in causal inference by introducing a generalized approach that incorporates fuzzy logic. Indeed, we introduce a fuzzy causal inference approach that consider both the vagueness and imprecision inherent in data, as well as the subjective human perspective characterized by fuzzy terms such as 'high', 'medium', and 'low'. To do so, we introduce two fuzzy causal effect formulas: the Fuzzy Average Treatment Effect (FATE) and the Generalized Fuzzy Average Treatment Effect (GFATE), together with their normalized versions: NFATE and NGFATE. When dealing with a binary treatment variable, our fuzzy causal effect formulas coincide with classical Average Treatment Effect (ATE) formula, that is a well-established and popular metric in causal inference. In FATE, all values of the treatment variable are considered equally important. In contrast, GFATE takes into account the rarity and frequency of these values. We show that for linear Structural Equation Models (SEMs), the normalized versions of our formulas, NFATE and NGFATE, are equivalent to ATE. Further, we provide identifiability criteria for these formulas and show their stability with respect to minor variations in the fuzzy subsets and the probability distributions involved. This ensures the robustness of our approach in handling small perturbations in the data. Finally, we provide several experimental examples to empirically validate and demonstrate the practical application of our proposed fuzzy causal inference methods.

Given a raw knowledge in the form of a data table/a decision system, one is facing two possible venues. One, to treat the system as closed, i.e., its universe does not admit new objects, or, to the contrary, its universe is open on admittance of new objects. In particular, one may obtain new objects whose sets of values of features are new to the system. In this case the problem is to assign a decision value to any such new object. This problem is somehow resolved in the rough set theory, e.g., on the basis of similarity of the value set of a new object to value sets of objects already assigned a decision value. It is crucial for online learning when each new object must have a predicted decision value.\ There is a vast literature on various methods for decision prediction for new yet unseen object. The approach we propose is founded in the theory of rough mereology and it requires a theory of sets/concepts, and, we root our theory in classical set theory of Syllogistic within which we recall the theory of parts known as Mereology. Then, we recall our theory of Rough Mereology along with the theory of weight assignment to the Tarski algebra of Mereology.\ This allows us to introduce the notion of a part to a degree. Once we have defined basics of Mereology and rough Mereology, we recall our theory of weight assignment to elements of the Boolean algebra within Mereology and this allows us to define the relation of parts to the degree and we apply this notion in a procedure to select a decision for new yet unseen objects.\ In selecting a plausible candidate which would pass its decision value to the new object, we employ the notion of Vapnik - Chervonenkis dimension in order to select at the first stage the candidate with the largest VC-dimension of the family of its $\varepsilon$-components for some choice of $\varepsilon$.

In the intricate field of medical diagnostics, capturing the subtle manifestations of diseases remains a challenge. Traditional methods, often binary in nature, may not encapsulate the nuanced variances that exist in real-world clinical scenarios. This paper introduces a novel approach by leveraging Fuzzy Logic Rules to derive disease classes based on expert domain knowledge from a medical practitioner. By recognizing that diseases do not always fit into neat categories, and that expert knowledge can guide the fuzzification of these boundaries, our methodology offers a more sophisticated and nuanced diagnostic tool. Using a dataset procured from a prominent hospital, containing detailed patient blood count records, we harness Fuzzy Logic Rules, a computational technique celebrated for its ability to handle ambiguity. This approach, moving through stages of fuzzification, rule application, inference, and ultimately defuzzification, produces refined diagnostic predictions. When combined with the Random Forest classifier, the system adeptly predicts hematological conditions using Complete Blood Count (CBC) parameters. Preliminary results showcase high accuracy levels, underscoring the advantages of integrating fuzzy logic into the diagnostic process. When juxtaposed with traditional diagnostic techniques, it becomes evident that Fuzzy Logic, especially when guided by medical expertise, offers significant advancements in the realm of hematological diagnostics. This paper not only paves the path for enhanced patient care but also beckons a deeper dive into the potentialities of fuzzy logic in various medical diagnostic applications.