Partial Deduction for Linear Logic—The Symbolic Negotiation Perspective

Symbolic negotiation is regarded in the field of computer science as a process, where parties try to reach an agreement on the high-level means for achieving their goals by applying symbolic reasoning techniques. It has been proposed [1] that symbolic negotiation could be formalised as Partial Deduction (PD) in Linear Logic (LL). However, the paper [1] did not provided a formalisation of the PD process in LL.

In this paper we fill the gap by providing a formalisation of PD for !-Horn fragment of LL. The framework can be easily extended for other fragments of LL as well such that more comprehensive aspects of negotiation can be described. In this paper we consider also soundness and completeness of the formalism. It turns out that, given a certain PD procedure, PD for LL in !-Horn fragment is sound and complete.

We adopt the hypothesis that an essential component of symbolic negotiation is Cooperative Problem Solving (CPS). Thus a formal system for symbolic negotiation would consist of CPS rules plus negotiation-specific rules. In this paper only CPS rules are under investigation while negotiation-specific rules shall be published in another paper.