Modelling Multilateral Negotiation in Linear Logic

We show how to embed a framework for multilateral negotiation, in which a group of agents implement a sequence of deals concerning the exchange of a number of resources, into linear logic. In this model, multisets of goods, allocations of resources, preferences of agents, and deals are all modelled as formulas of linear logic. Whether or not a proposed deal is rational, given the preferences of the agents concerned, reduces to a question of provability, as does the question of whether there exists a sequence of deals leading to an allocation with certain desirable properties, such as maximising social welfare. Thus, linear logic provides a formal basis for modelling convergence properties in distributed resource allocation

Non-normal modalities in variants of Linear Logic

This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of Linear Logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic Linear Logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource models extended with a neighbourhood function: modal Kripke resource models. We propose a Hilbert-style axiomatization and a Gentzen-style sequent calculus. We show that the proof theories are sound and complete with respect to the class of modal Kripke resource models. We show that the sequent calculus admits cut elimination and that proof-search is in PSPACE. We then show how to extend the results when non-commutative connectives are added to the language. Finally, we put the logical framework to use by instantiating it as logics of agency. In particular, we propose a logic to reason about the resource-sensitive use of artefacts and illustrate it with a variety of examples

Modelling Combinatorial Auctions in Linear Logic

We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winner determination problem, i.e., the problem of computing an allocation of goods to bidders producing a certain amount of revenue for the auctioneer, can be modelled as the problem of finding a proof for a particular linear logic sequent

Logic-Based Specification Languages for Intelligent Software Agents

The research field of Agent-Oriented Software Engineering (AOSE) aims to find abstractions, languages, methodologies and toolkits for modeling, verifying, validating and prototyping complex applications conceptualized as Multiagent Systems (MASs). A very lively research sub-field studies how formal methods can be used for AOSE. This paper presents a detailed survey of six logic-based executable agent specification languages that have been chosen for their potential to be integrated in our ARPEGGIO project, an open framework for specifying and prototyping a MAS. The six languages are ConGoLog, Agent-0, the IMPACT agent programming language, DyLog, Concurrent METATEM and Ehhf. For each executable language, the logic foundations are described and an example of use is shown. A comparison of the six languages and a survey of similar approaches complete the paper, together with considerations of the advantages of using logic-based languages in MAS modeling and prototyping.Comment: 67 pages, 1 table, 1 figure. Accepted for publication by the Journal "Theory and Practice of Logic Programming", volume 4, Maurice Bruynooghe Editor-in-Chie