Authors:
Lorenzo Ceragioli、Pierpaolo Degano、Letterio Galletta、Luca Viganò
Paper:
https://arxiv.org/abs/2408.09516
Introduction
In the realm of multiagent systems, autonomous agents interact to achieve both individual and collective goals. A central aspect of these interactions is the negotiation and agreement on resource exchanges. Modeling and formalizing these agreements pose significant challenges, particularly in capturing the dynamic behavior of agents and ensuring that resources are correctly handled. This study introduces exchange environments as a formal setting where agents specify and obey exchange policies. These policies are declarative statements about what resources they offer and what they require in return. The study also proposes a decidable extension of the computational fragment of linear logic, termed Computational Exchange Logic (CEL), to represent exchange environments and study their dynamics in terms of provability.
Related Work
Dynamic Resource Management
Dynamic resource management in multiagent systems has been addressed from various perspectives, including negotiation and optimization strategies, game-theoretical analysis, and logics. The logical approach emphasizes the development of frameworks to represent and study resource allocation and negotiation, leveraging logic as a fundamental tool.
Logical Modelling of Resource Exchange
Previous works have utilized linear logic to model resource-aware games and problems in artificial intelligence. These models describe agents’ goals and derive reasonable offers and strategies. However, this study introduces a novel approach by directly modeling what agents offer via exchange policies, combining descriptive and prescriptive approaches.
Contractual Logics
The study draws inspiration from the pioneering PCL (Process Contract Logic) proposed by Bartoletti and Zunino, which models contractual reasoning. CEL extends this by combining linear and contractual aspects, providing a unique framework for handling circular agreements and temporary debts.
Research Methodology
Exchange Environments
An exchange environment is a transition system where states record the ownership of resources, and transitions represent resource exchanges between agents. These exchanges are constrained by exchange policies, which agents specify in isolation to prescribe what resources they offer and what they require in return. The exchanges must guarantee that each participant gives the promised resources and gets the required ones, forming an agreement.
Computational Exchange Logic (CEL)
CEL extends the computational fragment of linear logic to handle circular agreements through a specific operator called linear contractual implication. This logic allows encoding exchanges as CEL formulas, reducing the verification of agreements to proving the corresponding formulas. The validity of CEL formulas is decidable, making it an effective tool for studying resource exchanges.
Experimental Design
Working Examples and Exchange Policies
The study presents several examples to illustrate the concept of exchange policies and agreements. For instance, consider three agents Alice, Bob, and Carl, who exchange resources like kiwis, lemons, and mandarins. Their policies dictate the conditions under which they accept exchanges, forming direct or circular agreements.
Policy Based Exchange Environments
The formal model of exchange environments is introduced, where states are resource allocations, and transitions are resource exchanges between agents of a coalition. Exchange policies are defined by coalitions to express what they offer and what they want in return. The transitions must obey the policies of the involved agents, forming agreements.
Valuation Functions and Deals
Valuation functions are introduced to capture the utility that a given resource allocation has for each agent. A deal is characterized as an exchange that increases the utility for the agents of a coalition. A policy is rational if it leads to deals, ensuring that the utility value of the obtained resources is greater than that of those given away.
Results and Analysis
Characterizing Agreements
Agreements are exchanges that satisfy the policies of all involved agents. The study shows that verifying an exchange as an agreement can be reduced to proving the corresponding CEL formula. This is effective because CEL is decidable, allowing for the verification of complex circular agreements.
Handling Debts
The study extends CEL to handle temporary debts, where an agent can offer resources they do not currently have but will acquire in a subsequent exchange. This is achieved by adding the cut rule to CEL, maintaining its decidability.
Decidability and Normal Proofs
The study proves that CEL is decidable and that proofs can be normalized. This ensures that the verification process is efficient and reliable. The normal forms of proofs are general, meaning a proof exists for an initial sequent only if a proof in normal form exists.
Overall Conclusion
The study introduces exchange environments and CEL as a formal model for resource exchanges in multiagent systems. This model effectively handles circular agreements and temporary debts, ensuring that resource exchanges are beneficial to all involved agents. The decidability of CEL makes it a powerful tool for verifying agreements, providing a robust framework for studying resource exchanges in multiagent systems.
Future work includes extending CEL with universal quantifiers, disjunction, and negation to express richer policies. Additionally, the model can be applied to real scenarios, such as exchanges of crypto-assets in blockchain systems.
