Design activity -- constructing an artifact description satisfying given goals and constraints -- distinguishes humanity from other animals and traditional machines, and endowing machines with design abilities at the human level or beyond has been a long-term pursuit. Though machines have already demonstrated their abilities in designing new materials, proteins, and computer programs with advanced artificial intelligence (AI) techniques, the search space for designing such objects is relatively small, and thus, "Can machines design like humans?" remains an open question. To explore the boundary of machine design, here we present a new AI approach to automatically design a central processing unit (CPU), the brain of a computer, and one of the world's most intricate devices humanity have ever designed. This approach generates the circuit logic, which is represented by a graph structure called Binary Speculation Diagram (BSD), of the CPU design from only external input-output observations instead of formal program code. During the generation of BSD, Monte Carlo-based expansion and the distance of Boolean functions are used to guarantee accuracy and efficiency, respectively. By efficiently exploring a search space of unprecedented size 10^{10^{540}}, which is the largest one of all machine-designed objects to our best knowledge, and thus pushing the limits of machine design, our approach generates an industrial-scale RISC-V CPU within only 5 hours. The taped-out CPU successfully runs the Linux operating system and performs comparably against the human-designed Intel 80486SX CPU. In addition to learning the world's first CPU only from input-output observations, which may reform the semiconductor industry by significantly reducing the design cycle, our approach even autonomously discovers human knowledge of the von Neumann architecture.

Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical probability levels to WEP. For example, highly likely corresponds to a median chance of 0.90+-0.08 in Fagen-Ulmschneider (2015)'s survey. In this work, we measure the ability of neural language processing models to capture the consensual probability level associated to each WEP. Firstly, we use the UNLI dataset (Chen et al., 2020) which associates premises and hypotheses with their perceived joint probability p, to construct prompts, e.g. "[PREMISE]. [WEP], [HYPOTHESIS]." and assess whether language models can predict whether the WEP consensual probability level is close to p. Secondly, we construct a dataset of WEP-based probabilistic reasoning, to test whether language models can reason with WEP compositions. When prompted "[EVENTA] is likely. [EVENTB] is impossible.", a causal language model should not express that [EVENTA&B] is likely. We show that both tasks are unsolved by off-the-shelf English language models, but that fine-tuning leads to transferable improvement.

In recent years, neural systems have demonstrated highly effective learning ability and superior perception intelligence. However, they have been found to lack effective reasoning and cognitive ability. On the other hand, symbolic systems exhibit exceptional cognitive intelligence but suffer from poor learning capabilities when compared to neural systems. Recognizing the advantages and disadvantages of both methodologies, an ideal solution emerges: combining neural systems and symbolic systems to create neural-symbolic learning systems that possess powerful perception and cognition. The purpose of this paper is to survey the advancements in neural-symbolic learning systems from four distinct perspectives: challenges, methods, applications, and future directions. By doing so, this research aims to propel this emerging field forward, offering researchers a comprehensive and holistic overview. This overview will not only highlight the current state-of-the-art but also identify promising avenues for future research.

We consider a weakly supervised learning scenario where the supervision signal is generated by a transition function $\sigma$ of labels associated with multiple input instances. We formulate this problem as \emph{multi-instance Partial Label Learning (multi-instance PLL)}, which is an extension to the standard PLL problem. Our problem is met in different fields, including latent structural learning and neuro-symbolic integration. Despite the existence of many learning techniques, limited theoretical analysis has been dedicated to this problem. In this paper, we provide the first theoretical study of multi-instance PLL with possibly an unknown transition $\sigma$. Our main contributions are as follows. Firstly, we propose a necessary and sufficient condition for the learnability of the problem. This condition non-trivially generalizes and relaxes the existing small ambiguity degree in the PLL literature, since we allow the transition to be deterministic. Secondly, we derive Rademacher-style error bounds based on a top-$k$ surrogate loss that is widely used in the neuro-symbolic literature. Furthermore, we conclude with empirical experiments for learning under unknown transitions. The empirical results align with our theoretical findings; however, they also expose the issue of scalability in the weak supervision literature.

Wikidata is a knowledge graph increasingly adopted by many communities for diverse applications. Wikidata statements are annotated with qualifier-value pairs that are used to depict information, such as the validity context of the statement, its causality, provenances, etc. Handling the qualifiers in reasoning is a challenging problem. When defining inference rules (in particular, rules on ontological properties (x subclass of y, z instance of x, etc.)), one must consider the qualifiers, as most of them participate in the semantics of the statements. This poses a complex problem because a) there is a massive number of qualifiers, and b) the qualifiers of the inferred statement are often a combination of the qualifiers in the rule condition. In this work, we propose to address this problem by a) defining a categorization of the qualifiers b) formalizing the Wikidata model with a many-sorted logical language; the sorts of this language are the qualifier categories. We couple this logic with an algebraic specification that provides a means for effectively handling qualifiers in inference rules. Using Wikidata ontological properties, we show how to use the MSL and specification to reason on qualifiers. Finally, we discuss the methodology for practically implementing the work and present a prototype implementation. The work can be naturally extended, thanks to the extensibility of the many-sorted algebraic specification, to cover more qualifiers in the specification, such as uncertain time, recurring events, geographic locations, and others.

We motivate and formally define a new task for fine-tuning rule-like generalization in large language models. It is conjectured that the shortcomings of current LLMs are due to a lack of ability to generalize. It has been argued that, instead, humans are better at generalization because they have a tendency at extracting rules from complex data. We try to recreate this tendency to rule-based generalization. When exposed to tests of analytic intelligence, for example, the visual RAVEN IQ test, human problem-solvers identify the relevant objects in the picture and their relevant attributes and reason based on rules applied to these objects and attributes. Based on the induced rules, they are able to provide a solution to the test. We propose a task that translates this IQ task into language. In this paper, we provide the formal specification for the task and the generative process of its datasets.

Planning as theorem proving in situation calculus was abandoned 50 years ago as an impossible project. But we have developed a Theorem Proving Lifted Heuristic (TPLH) planner that searches for a plan in a tree of situations using the A* search algorithm. It is controlled by a delete relaxation-based domain independent heuristic. We compare TPLH with Fast Downward (FD) and Best First Width Search (BFWS) planners over several standard benchmarks. Since our implementation of the heuristic function is not optimized, TPLH is slower than FD and BFWS. But it computes shorter plans, and it explores fewer states. We discuss previous research on planning within KR\&R and identify related directions. Thus, we show that deductive lifted heuristic planning in situation calculus is actually doable.

Inference and prediction of routes have become of interest over the past decade owing to a dramatic increase in package delivery and ride-sharing services. Given the underlying combinatorial structure and the incorporation of probabilities, route prediction involves techniques from both formal methods and machine learning. One promising approach for predicting routes uses decision diagrams that are augmented with probability values. However, the effectiveness of this approach depends on the size of the compiled decision diagrams. The scalability of the approach is limited owing to its empirical runtime and space complexity. In this work, our contributions are two-fold: first, we introduce a relaxed encoding that uses a linear number of variables with respect to the number of vertices in a road network graph to significantly reduce the size of resultant decision diagrams. Secondly, instead of a stepwise sampling procedure, we propose a single pass sampling-based route prediction. In our evaluations arising from a real-world road network, we demonstrate that the resulting system achieves around twice the quality of suggested routes while being an order of magnitude faster compared to state-of-the-art.

This paper proposes a new AND-OR graph search framework for synthesis of Linear Temporal Logic on finite traces (\LTLf), that overcomes some limitations of previous approaches. Within such framework, we devise a procedure inspired by the Davis-Putnam-Logemann-Loveland (DPLL) algorithm to generate the next available agent-environment moves in a truly depth-first fashion, possibly avoiding exhaustive enumeration or costly compilations. We also propose a novel equivalence check for search nodes based on syntactic equivalence of state formulas. Since the resulting procedure is not guaranteed to terminate, we identify a stopping condition to abort execution and restart the search with state-equivalence checking based on Binary Decision Diagrams (BDD), which we show to be correct. The experimental results show that in many cases the proposed techniques outperform other state-of-the-art approaches. Our implementation Nike competed in the LTLf Realizability Track in the 2023 edition of SYNTCOMP, and won the competition.

The success of Computer Vision (CV) relies heavily on manually annotated data. However, it is prohibitively expensive to annotate images in key domains such as healthcare, where data labeling requires significant domain expertise and cannot be easily delegated to crowd workers. To address this challenge, we propose a neuro-symbolic approach called Rapid, which infers image labeling rules from a small amount of labeled data provided by domain experts and automatically labels unannotated data using the rules. Specifically, Rapid combines pre-trained CV models and inductive logic learning to infer the logic-based labeling rules. Rapid achieves a labeling accuracy of 83.33% to 88.33% on four image labeling tasks with only 12 to 39 labeled samples. In particular, Rapid significantly outperforms finetuned CV models in two highly specialized tasks. These results demonstrate the effectiveness of Rapid in learning from small data and its capability to generalize among different tasks. Code and our dataset are publicly available at https://github.com/Neural-Symbolic-Image-Labeling/