Logic-Based Analogical Reasoning and Learning

Analogy-making is at the core of human intelligence and creativity with applications to such diverse tasks as commonsense reasoning, learning, language acquisition, and story telling. This paper contributes to the foundations of artificial general intelligence by developing an abstract algebraic framework for logic-based analogical reasoning and learning in the setting of logic programming. The main idea is to define analogy in terms of modularity and to derive abstract forms of concrete programs from a `known' source domain which can then be instantiated in an `unknown' target domain to obtain analogous programs. To this end, we introduce algebraic operations for syntactic program composition and concatenation and illustrate, by giving numerous examples, that programs have nice decompositions. Moreover, we show how composition gives rise to a qualitative notion of syntactic program similarity. We then argue that reasoning and learning by analogy is the task of solving analogical proportions between logic programs. Interestingly, our work suggests a close relationship between modularity, generalization, and analogy which we believe should be explored further in the future. In a broader sense, this paper is a first step towards an algebraic and mainly syntactic theory of logic-based analogical reasoning and learning in knowledge representation and reasoning systems, with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity

Driving a car with custom-designed fuzzy inferencing VLSI chips and boards

Vehicle control in a-priori unknown, unpredictable, and dynamic environments requires many calculational and reasoning schemes to operate on the basis of very imprecise, incomplete, or unreliable data. For such systems, in which all the uncertainties can not be engineered away, approximate reasoning may provide an alternative to the complexity and computational requirements of conventional uncertainty analysis and propagation techniques. Two types of computer boards including custom-designed VLSI chips were developed to add a fuzzy inferencing capability to real-time control systems. All inferencing rules on a chip are processed in parallel, allowing execution of the entire rule base in about 30 microseconds, and therefore, making control of 'reflex-type' of motions envisionable. The use of these boards and the approach using superposition of elemental sensor-based behaviors for the development of qualitative reasoning schemes emulating human-like navigation in a-priori unknown environments are first discussed. Then how the human-like navigation scheme implemented on one of the qualitative inferencing boards was installed on a test-bed platform to investigate two control modes for driving a car in a-priori unknown environments on the basis of sparse and imprecise sensor data is described. In the first mode, the car navigates fully autonomously, while in the second mode, the system acts as a driver's aid providing the driver with linguistic (fuzzy) commands to turn left or right and speed up or slow down depending on the obstacles perceived by the sensors. Experiments with both modes of control are described in which the system uses only three acoustic range (sonar) sensor channels to perceive the environment. Simulation results as well as indoors and outdoors experiments are presented and discussed to illustrate the feasibility and robustness of autonomous navigation and/or safety enhancing driver's aid using the new fuzzy inferencing hardware system and some human-like reasoning schemes which may include as little as six elemental behaviors embodied in fourteen qualitative rules

Dexterous manipulation of unknown objects using virtual contact points

The manipulation of unknown objects is a problem of special interest in robotics since it is not always possible to have exact models of the objects with which the robot interacts. This paper presents a simple strategy to manipulate unknown objects using a robotic hand equipped with tactile sensors. The hand configurations that allow the rotation of an unknown object are computed using only tactile and kinematic information, obtained during the manipulation process and reasoning about the desired and real positions of the fingertips during the manipulation. This is done taking into account that the desired positions of the fingertips are not physically reachable since they are located in the interior of the manipulated object and therefore they are virtual positions with associated virtual contact points. The proposed approach was satisfactorily validated using three fingers of an anthropomorphic robotic hand (Allegro Hand), with the original fingertips replaced by tactile sensors (WTS-FT). In the experimental validation, several everyday objects with different shapes were successfully manipulated, rotating them without the need of knowing their shape or any other physical property.Peer ReviewedPostprint (author's final draft

Ask One More Time: Self-Agreement Improves Reasoning of Language Models in (Almost) All Scenarios

Although chain-of-thought (CoT) prompting combined with language models has achieved encouraging results on complex reasoning tasks, the naive greedy decoding used in CoT prompting usually causes the repetitiveness and local optimality. To address this shortcoming, ensemble-optimization tries to obtain multiple reasoning paths to get the final answer assembly. However, current ensemble-optimization methods either simply employ rule-based post-processing such as \textit{self-consistency}, or train an additional model based on several task-related human annotations to select the best one among multiple reasoning paths, yet fail to generalize to realistic settings where the type of input questions is unknown or the answer format of reasoning paths is unknown. To avoid their limitations, we propose \textbf{self-agreement}, a generalizable ensemble-optimization method applying in almost all scenarios where the type of input questions and the answer format of reasoning paths may be known or unknown. Self-agreement firstly samples from language model's decoder to generate a \textit{diverse} set of reasoning paths, and subsequently prompts the language model \textit{one more time} to determine the optimal answer by selecting the most \textit{agreed} answer among the sampled reasoning paths. Self-agreement simultaneously achieves remarkable performance on six public reasoning benchmarks and superior generalization capabilities.Comment: Work in progres