There has been a longstanding dispute over which formalism is the best for representing knowledge in AI. The well-known “declarative vs. procedural controversy” is concerned with the choice of utilizing declarations or procedures as the primary mode of knowledge representation. The ongoing debate between symbolic AI and connectionist AI also revolves around the question of whether knowledge should be represented implicitly (e.g., as parametric knowledge in deep learning and large language models) or explicitly (e.g., as logical theories in traditional knowledge representation and reasoning). To address these issues, we propose a general framework to capture various knowledge representation formalisms in which we are interested. Within the framework, we find a family of universal knowledge representation formalisms, and prove that all universal formalisms are recursively isomorphic. Moreover, we show that all pairwise intertranslatable formalisms that admit the padding property are also recursively isomorphic. These imply that, up to an offline compilation, all universal (or natural and equally expressive) representation formalisms are in fact the same, which thus provides a partial answer to the aforementioned dispute.

Due to its wide application, deep reinforcement learning (DRL) has been extensively studied in the motion planning community in recent years. However, in the current DRL research, regardless of task completion, the state information of the agent will be reset afterward. This leads to a low sample utilization rate and hinders further explorations of the environment. Moreover, in the initial training stage, the agent has a weak learning ability in general, which affects the training efficiency in complex tasks. In this study, a new hierarchical reinforcement learning (HRL) framework dubbed hierarchical learning based on game playing with state relay (HGR) is proposed. In particular, we introduce an auxiliary penalty to regulate task difficulty, and one training mechanism, the state relay mechanism, is designed. The relay mechanism can make full use of the intermediate states of the agent and expand the environment exploration of low-level policy. Our algorithm can improve the sample utilization rate, reduce the sparse reward problem, and thereby enhance the training performance in complex environments. Simulation tests are carried out on two public experiment platforms, i.e., MazeBase and MuJoCo, to verify the effectiveness of the proposed method. The results show that HGR significantly benefits the reinforcement learning (RL) area.

General Game Playing (GGP), a research field aimed at developing agents that master different games in a unified way, is regarded as a necessary step towards creating artificial general intelligence. With the success of deep reinforcement learning (DRL) in games like Go, chess, and shogi, it has been recently introduced to GGP and is regarded as a promising technique to achieve the goal of GGP. However, the current work uses fully connected neural networks and is thus unable to efficiently exploit the topological structure of game states. In this paper, we propose an approach to applying general-purposed convolutional neural networks to GGP and implement a DRL-based GGP player. Experiments indicate that the built player not only outperforms the previous algorithm and UCT benchmark in a variety of games but also requires less training time.

Abstract Bisimulations are a key notion to study the expressive power of a modal language. This paper studies the expressivity of Game Description Language (GDL) and its epistemic extension Epistemic GDL (EGDL) through a bisimulation approach. We first define a notion of bisimulation for GDL and prove that it coincides with the indistinguishability of GDL formulas. Based on it, we establish a characterization of the definability of GDL in terms of $k$-bisimulations. Then we design novel notions of bisimulation for EGDL and obtain characterizations of the expressive power of EGDL in terms of them. These characterizations provide a powerful tool to identify the expressive power of game description languages. Finally, we demonstrate with real games that bisimulation can be generalized to capture a wide range of game equivalence.

Existential rule languages are a family of ontology languages that have been widely used in ontology-mediated query answering (OMQA). However, for most of them, the expressive power of representing domain knowledge for OMQA, known as the program expressive power, is not well-understood yet. In this paper, we establish a number of novel characterizations for the program expressive power of several important existential rule languages, including tuple-generating dependencies (TGDs), linear TGDs, as well as disjunctive TGDs. The characterizations employ natural model-theoretic properties, and automata-theoretic properties sometimes, which thus provide powerful tools for identifying the definability of domain knowledge for OMQA in these languages.

Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep understanding of these languages in model theory, we establish model-theoretic characterizations for a number of existential rule languages such as (disjunctive) embedded dependencies, tuple-generating dependencies (TGDs), (frontier-)guarded TGDs and linear TGDs. All these characterizations hold for the class of arbitrary structures, and most of them also work on the class of finite structures. As a natural application of these results, complexity bounds for the rewritability of above languages are also identified.

Judgment aggregation deals with the problem of how collective judgments on logically connected propositions can be formed based on individual judgments on the same propositions. The existing literature on judgment aggregation mainly focuses on the anonymity condition requiring that individual judgments be treated equally. However, in many real‐world situations, a group making collective judgments may assign individual members or subgroups different priorities to determine the collective judgment. Based on this consideration, this article relaxes the anonymity condition by giving a hierarchy over individuals so as to investigate how the judgment from each individual affects the group judgment in such a hierarchical environment. Moreover, we assume that an individual can abstain from voting on a proposition and the collective judgment on a proposition can be undetermined, which means that we do not require completeness at both individual and collective levels. In this new setting, we first identify an impossibility result and explore a set of plausible conditions in terms of abstentions. Secondly, we develop an aggregation rule based on the hierarchy of individuals and show that the aggregation rule satisfies those plausible conditions. The computational complexity of this rule is also investigated. Finally, we show that the proposed rule is (weakly) oligarchic over a subset of agenda. This is by no means a negative result. In fact, our result reveals that with abstentions, oligarchic aggregation is not necessary to be a single‐level determination but can be a multiple‐level collective decision making, which partially explains its ubiquity in the real world.

We propose a modal logic that supports reasoning about trust-based belief change. The term trust-based belief change refers to belief change that depends on the degree of trust the receiver has in the source of information.