Programming and reasoning with partial observability

Abstract

Computer programs are increasingly being deployed in partially-observable environments. A partially observable environment is an environment whose state is not completely visible to the program, but from which the program receives partial observations. Developers typically deal with partial observability by writing a state estimator that, given observations, attempts to deduce the hidden state of the environment. In safety-critical domains, to formally verify safety properties developers may write an environment model. The model captures the relationship between observations and hidden states and is used to prove the software correct.In this paper, we present a new methodology for writing and verifying programs in partially observable environments. We present belief programming, a programming methodology where developers write an environment model that the program runtime automatically uses to perform state estimation. A belief program dynamically updates and queries a belief state that captures the possible states the environment could be in.To enable verification, we present Epistemic Hoare Logic that reasons about the possible belief states of a belief program the same way that classical Hoare logic reasons about the possible states of a program. We develop these concepts by defining a semantics and a program logic for a simple core language called BLIMP. In a case study, we show how belief programming could be used to write and verify a controller for the Mars Polar Lander in BLIMP. We present an implementation of BLIMP called CBLIMP and evaluate it to determine the feasibility of belief programming. CCS Concepts: • Software and its engineering → General programming languages; Semantics; • Theory of computation → Operational semantics; Pre-and post-conditions; Invariants; Modal and temporal logics; Hoare logic; Program reasoning; • Computing methodologies → Reasoning about belief and knowledge.

Sound and Relatively Complete Belief Hoare Logic for Statistical Hypothesis Testing Programs

“…This program logic is then extended and adapted so that it can handle various types of programs and assertions, including heap-manipulating programs [5], hybrid systems [6], and probabilistic programs [7]. Atkinson and Carbin propose an extension of Hoare logic with epistemic assertions [8]. In their work, an epistemic assertion is used to reason about the belief of a program about a partially observable environment, whereas their logic does not deal with a statistical belief arising from statistical tests conducted in a program.…”

Formalizing Statistical Beliefs in Hypothesis Testing Using Program Logic

“…This program logic is then extended and adapted so that it can handle various types of programs and assertions, including heap-manipulating programs (Reynolds 2002), hybrid systems (Suenaga and Hasuo 2011), and probabilistic programs (den Hartog and de Vink 2002). Atkinson and Carbin propose an extension of Hoare logic with epistemic assertions (Atkinson and Carbin 2020). In their work, an epistemic assertion is used to reason about the belief of a program about a partially observable environment, whereas their logic does not deal with a statistical belief arising from statistical tests conducted in a program.…”