Verifying time, memory and communication bounds in systems of reasoning agents

Abstract

We present a framework for verifying systems composed of heterogeneous reasoning agents, in which each agent may have differing knowledge and inferential capabilities, and where the resources each agent is prepared to commit to a goal (time, memory and communication bandwidth) are bounded. The framework allows us to investigate, for example, whether a goal can be achieved if a particular agent, perhaps possessing key information or inferential capabilities, is unable (or unwilling) to contribute more than a given portion of its available computational resources or bandwidth to the problem. We present a novel temporal epistemic logic, BMCL, which allows us to describe a set of reasoning agents with bounds on time, memory and the number of messages they can exchange. The bounds on memory and communication are expressed as axioms in the logic. As an example, we show how to axiomatize a system of agents which reason using resolution and prove that the resulting logic is sound and complete. We then show how to encode a simple system of reasoning agents specified in BMCL in the description language of a model checker, and verify that the agents can achieve a goal only if they are prepared to commit certain time, memory and communication resources.

Formal Approaches to Modelling and Verifying Resource-bounded Agents-state of the Art and Future Prospects

“…However, memory bounds have not been imposed in their framework, and the encoding of the system in the model checker's specification language had to be handcrafted, rules had to be propositionalised using all possible substitutions for variables, and scalability of the verification approach was not explored. In recent work Alechina et al [9,10], proposed frameworks for the representation, specification and verification of resourcebounded agents that allow developers to model computational and communication resources explicitly, and to reason about and verify tradeoffs between time, memory and communication in systems of distributed reasoning agents.…”

Reasoning about Other Agents’ Beliefs under Bounded Resources

“…The logic BMCL presented in [20] formalises reasoning about the beliefs of a system of reasoners who reason using propositional resolution and can exchange information to solve a problem together. The set up is similar to, for example, [22].…”

“…by model-checking, as in for example [20]. However, adding reasoning about beliefs poses a significant challenge, both in the complexity of the system and in the way this reasoning is modelled.…”

“…In a somewhat different direction, [16] proposed a logic where agents reason about each others beliefs, but have no explicit time or memory limit; however there is a restriction on the depth of belief nestings (context switching by the agents). Epistemic logics for bounded-memory agents were investigated in, for example, [17][18][19][20], and the interplay between bounded recall and bounded memory (ability to store strategies of only bounded size) was studied in [21].…”

“…An epistemic logic BMCL for communicating agents with communication limits on the number of exchanged messages (and connections to space complexity of proofs and communication complexity) was investigated in [20]. In this paper we expand BMCL by adding rules for reasoning about other agents' beliefs, demonstrate that epistemic reasoning done in resource-bounded fashion has an inherent problem of incorrect belief ascription, and propose the use of reasoning strategies as a solution to this problem.…”