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A Logic for Policy Based Resource Exchanges in Multiagent Systems

Lorenzo Ceragioli, Pierpaolo Degano, Letterio Galletta, Luca Viganò

TL;DR

This work proposes exchange environments as a formal setting where agents specify and obey exchange policies, which are declarative statements about what resources they offer and what they require in return.

Abstract

In multiagent systems autonomous agents interact with each other to achieve individual and collective goals. Typical interactions concern negotiation and agreement on resource exchanges. Modeling and formalizing these agreements pose significant challenges, particularly in capturing the dynamic behaviour of agents, while ensuring that resources are correctly handled. Here, we propose exchange environments as a formal setting where agents specify and obey exchange policies, which are declarative statements about what resources they offer and what they require in return. Furthermore, we introduce a decidable extension of the computational fragment of linear logic as a fundamental tool for representing exchange environments and studying their dynamics in terms of provability.

A Logic for Policy Based Resource Exchanges in Multiagent Systems

TL;DR

This work proposes exchange environments as a formal setting where agents specify and obey exchange policies, which are declarative statements about what resources they offer and what they require in return.

Abstract

In multiagent systems autonomous agents interact with each other to achieve individual and collective goals. Typical interactions concern negotiation and agreement on resource exchanges. Modeling and formalizing these agreements pose significant challenges, particularly in capturing the dynamic behaviour of agents, while ensuring that resources are correctly handled. Here, we propose exchange environments as a formal setting where agents specify and obey exchange policies, which are declarative statements about what resources they offer and what they require in return. Furthermore, we introduce a decidable extension of the computational fragment of linear logic as a fundamental tool for representing exchange environments and studying their dynamics in terms of provability.
Paper Structure (19 sections, 44 theorems, 42 equations, 5 figures)

This paper contains 19 sections, 44 theorems, 42 equations, 5 figures.

Table of Contents

  1. Working examples and exchange policies
  2. Policy Based Exchange Environments
  3. Exchange Environments
  4. Exchange Policies
  5. Policies and Valuation Functions
  6. A Logic for Characterizing Agreements
  7. Contractual Exchange Logic
  8. Deriving Transitions of Exchange Environments
  9. Extending CEL with debts
  10. Related Work
  11. Conclusions and future work
  12. Value Functions
  13. Normalization
  14. Decidability
  15. Solving the Normal Form 1
  16. ...and 4 more sections

Key Result

Theorem 1

Let $\mathit{C}$ be a coalition and let $\mathit{exc}$ be an exchange accepted by $\mathit{pol}_{\mathit{C}}$. If every $\mathit{exc}" \triangleleft \mathit{exc}' \in \mathit{pol}_{\mathit{C}}$ is such that $\,\forall \mathit{a} \in \mathit{C}.\,W(a, \mathit{exc}" \uplus \mathit{exc}') \geq 0$, then

Figures (5)

  • Figure 1: Examples of agreements among players.
  • Figure 2: CEL rules.
  • Figure 3: CEL proof in the normal form 2, the proof $\Pi"$ is omitted for simplicity, and uses (Ax), ($\otimes$-left), ($\otimes$-right) and ($\multimap$-left).
  • Figure 4: Cut rule for CEL.
  • Figure 5: Specific forms for ($\otimes$-left)

Theorems & Definitions (101)

  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Definition 1: Resource Allocation
  • Definition 2: Transfer, Exchange and Exchange Environment
  • Definition 3: Exchange Rules and Policies
  • Example 5
  • Example 6
  • Definition 4: Accepted Exchanges
  • ...and 91 more