Artificial Intelligence (cs.AI)

Abstract: The recommendation system is not only a problem of inductive statistics from data but also a cognitive task that requires reasoning ability. The most advanced graph neural networks have been widely used in recommendation systems because they can capture implicit structured information from graph-structured data. However, like most neural network algorithms, they only learn matching patterns from a perception perspective. Some researchers use user behavior for logic reasoning to achieve recommendation prediction from the perspective of cognitive reasoning, but this kind of reasoning is a local one and ignores implicit information on a global scale. In this work, we combine the advantages of graph neural networks and propositional logic operations to construct a neuro-symbolic recommendation model with both global implicit reasoning ability and local explicit logic reasoning ability. We first build an item-item graph based on the principle of adjacent interaction and use graph neural networks to capture implicit information in global data. Then we transform user behavior into propositional logic expressions to achieve recommendations from the perspective of cognitive reasoning. Extensive experiments on five public datasets show that our proposed model outperforms several state-of-the-art methods, source code is avaliable at [https://github.com/hanzo2020/GNNLR].

Abstract: Aristotle's discussions on modal syllogistic have often been viewed as error-prone and have garnered significant attention in the literature due to historical and philosophical interests. However, from a contemporary standpoint, they also introduced natural fragments of first-order modal logic, warranting a comprehensive technical analysis. In this paper, drawing inspiration from the natural logic program, we propose and examine several variants of modal syllogistic within the epistemic context, thereby coining the term Epistemic Syllogistic. Specifically, we concentrate on the de re interpretation of epistemic syllogisms containing non-trivial yet natural expressions such as "all things known to be A are also known to be not B." We explore the epistemic apodeictic syllogistic and its extensions, which accommodate more complex terms. Our main contributions include several axiomatizations of these logics, with completeness proofs that may be of independent interest.

Abstract: The dominant theories of rational choice assume logical omniscience. That is, they assume that when facing a decision problem, an agent can perform all relevant computations and determine the truth value of all relevant logical/mathematical claims. This assumption is unrealistic when, for example, we offer bets on remote digits of pi or when an agent faces a computationally intractable planning problem. Furthermore, the assumption of logical omniscience creates contradictions in cases where the environment can contain descriptions of the agent itself. Importantly, strategic interactions as studied in game theory are decision problems in which a rational agent is predicted by its environment (the other players). In this paper, we develop a theory of rational decision making that does not assume logical omniscience. We consider agents who repeatedly face decision problems (including ones like betting on digits of pi or games against other agents). The main contribution of this paper is to provide a sensible theory of rationality for such agents. Roughly, we require that a boundedly rational inductive agent tests each efficiently computable hypothesis infinitely often and follows those hypotheses that keep their promises of high rewards. We then prove that agents that are rational in this sense have other desirable properties. For example, they learn to value random and pseudo-random lotteries at their expected reward. Finally, we consider strategic interactions between different agents and prove a folk theorem for what strategies bounded rational inductive agents can converge to.

Abstract: Unknown unknowns are future relevant contingencies that lack an ex ante description. While there are numerous retrospective accounts showing that significant gains or losses might have been achieved or avoided had such contingencies been previously uncovered, getting hold of unknown unknowns still remains elusive, both in practice and conceptually. Using Formal Concept Analysis (FCA) - a subfield of lattice theory which is increasingly applied for mining and organizing data - this paper introduces a simple framework to systematically think out of the box and direct the search for unknown unknowns.

Abstract: Binarizing belief aggregation addresses how to rationally aggregate individual probabilistic beliefs into collective binary beliefs. Similar to the development of judgment aggregation theory, formulating axiomatic requirements, proving impossibility theorems, and identifying exact agenda conditions of impossibility theorems are natural and important research topics in binarizing belief aggregation. Building on our previous research on impossibility theorems, we use an agenda-theoretic approach to generalize the results and to determine the necessary and sufficient level of logical interconnection between the issues in an agenda for the impossibility theorems to arise. We demonstrate that (1) path-connectedness and even-negatability constitute the exact agenda condition for the oligarchy result stating that binarizing belief aggregation satisfying proposition-wise independence and deductive closure of collective beliefs yields the oligarchies under minor conditions; (2) negation-connectedness is the condition for the triviality result obtained by adding anonymity to the oligarchy result; and (3) blockedness is the condition for the impossibility result, which follows by adding completeness and consistency of collective beliefs. Moreover, we compare these novel findings with existing agenda-theoretic characterization theorems in judgment aggregation and belief binarization.

Abstract: This research presents a comprehensive methodology for utilizing an ontology-driven structured prompts system in interplay with ChatGPT, a widely used large language model (LLM). The study develops formal models, both information and functional, and establishes the methodological foundations for integrating ontology-driven prompts with ChatGPT's meta-learning capabilities. The resulting productive triad comprises the methodological foundations, advanced information technology, and the OntoChatGPT system, which collectively enhance the effectiveness and performance of chatbot systems. The implementation of this technology is demonstrated using the Ukrainian language within the domain of rehabilitation. By applying the proposed methodology, the OntoChatGPT system effectively extracts entities from contexts, classifies them, and generates relevant responses. The study highlights the versatility of the methodology, emphasizing its applicability not only to ChatGPT but also to other chatbot systems based on LLMs, such as Google's Bard utilizing the PaLM 2 LLM. The underlying principles of meta-learning, structured prompts, and ontology-driven information retrieval form the core of the proposed methodology, enabling their adaptation and utilization in various LLM-based systems. This versatile approach opens up new possibilities for NLP and dialogue systems, empowering developers to enhance the performance and functionality of chatbot systems across different domains and languages.

Abstract: In this paper, we propose a modal logic in which counting modalities appear in linear inequalities. We show that each formula can be transformed into an equivalent graph neural network (GNN). We also show that each GNN can be transformed into a formula. We show that the satisfiability problem is decidable. We also discuss some variants that are in PSPACE.

Abstract: This paper examines how a notion of stable explanation developed elsewhere in Defeasible Logic can be expressed in the context of formal argumentation. With this done, we discuss the deontic meaning of this reconstruction and show how to build from argumentation neighborhood structures for deontic logic where this notion of explanation can be characterised. Some direct complexity results are offered.

Abstract: Recent studies show that deep reinforcement learning (DRL) agents tend to overfit to the task on which they were trained and fail to adapt to minor environment changes. To expedite learning when transferring to unseen tasks, we propose a novel approach to representing the current task using reward machines (RM), state machine abstractions that induce subtasks based on the current task's rewards and dynamics. Our method provides agents with symbolic representations of optimal transitions from their current abstract state and rewards them for achieving these transitions. These representations are shared across tasks, allowing agents to exploit knowledge of previously encountered symbols and transitions, thus enhancing transfer. Our empirical evaluation shows that our representations improve sample efficiency and few-shot transfer in a variety of domains.

Abstract: Efficient planning of scarce resources in hospitals is a challenging task for which a large variety of Operations Research and Management Science approaches have been developed since the 1950s. While efficient planning of single resources such as operating rooms, beds, or specific types of staff can already lead to enormous efficiency gains, integrated planning of several resources has been shown to hold even greater potential, and a large number of integrated planning approaches have been presented in the literature over the past decades. This paper provides the first literature review that focuses specifically on the Operations Research and Management Science literature related to integrated planning of different resources in hospitals. We collect the relevant literature and analyze it regarding different aspects such as uncertainty modeling and the use of real-life data. Several cross comparisons reveal interesting insights concerning, e.g., relations between the modeling and solution methods used and the practical implementation of the approaches developed. Moreover, we provide a high-level taxonomy for classifying different resource-focused integration approaches and point out gaps in the literature as well as promising directions for future research.

Abstract: Human intelligence thrives on the concept of cognitive synergy, where collaboration and information integration among different cognitive processes yield superior outcomes compared to individual cognitive processes in isolation. Although Large Language Models (LLMs) have demonstrated promising performance as general task-solving agents, they still struggle with tasks that require intensive domain knowledge and complex reasoning. In this work, we propose Solo Performance Prompting (SPP), which transforms a single LLM into a cognitive synergist by engaging in multi-turn self-collaboration with multiple personas. A cognitive synergist refers to an intelligent agent that collaborates with multiple minds, combining their individual strengths and knowledge, to enhance problem-solving and overall performance in complex tasks. By dynamically identifying and simulating different personas based on task inputs, SPP unleashes the potential of cognitive synergy in LLMs. We have discovered that assigning multiple, fine-grained personas in LLMs elicits better problem-solving abilities compared to using a single or fixed number of personas. We evaluate SPP on three challenging tasks: Trivia Creative Writing, Codenames Collaborative, and Logic Grid Puzzle, encompassing both knowledge-intensive and reasoning-intensive types. Unlike previous works, such as Chain-of-Thought, that solely enhance the reasoning abilities in LLMs, SPP effectively elicits internal knowledge acquisition abilities, reduces hallucination, and maintains strong reasoning capabilities. Code, data, and prompts can be found at: https://github.com/MikeWangWZHL/Solo-Performance-Prompting.git.