格值一阶逻辑系统LF(X)中的广义量词

给出格值一阶逻辑系统LF(X)中广义量词的定义,讨论了带广义量词的不确定性推理的性质,为语言值逻辑推理提供科学的逻辑平台。     

二值逻辑中命题的条件真度理论

基于条件概率的思想,在二值经典命题逻辑中引入条件真度的概念。在二值逻辑系统中初步给出了在信息Σ下的近似推理理论。     

Temporal logic guided safe model-based reinforcement learning: A hybrid systems approach

This paper studies the problem of synthesizing control policies for uncertain continuous-time nonlinear systems from linear temporal logic (LTL) specifications using model-based reinforcement learning (MBRL). Rather than taking an abstraction-based approach, we view the interaction between the LTL formula’s corresponding Büchi automaton and the nonlinear system as a hybrid automaton whose discrete dynamics match exactly those of the Büchi automaton. To find satisfying control policies, we pose a sequence of optimal control problems associated with states in the accepting run of the automaton and leverage control barrier functions (CBFs) to prevent specification violation. Since solving many optimal control problems for a nonlinear system is computationally intractable, we take a learning-based approach in which the value function of each problem is learned online in real-time. Specifically, we propose a novel off-policy MBRL algorithm that allows one to simultaneously learn the uncertain dynamics of the system and the value function of each optimal control problem online while adhering to CBF-based safety constraints. Unlike related approaches, the MBRL method presented herein decouples convergence, stability, and safety, allowing each aspect to be studied independently, leading to stronger safety guarantees than those developed in related works. Numerical results are presented to validate the efficacy of the proposed method.