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\chapter{Agreements}

In philosophy and economimcs, promises are often mixed together with
the notions like contractsand agreements, and all considered to be
related. In our theory of $\mu$-promises, however, promises are a
fundamental unit from which we can derive these other concepts.

\section{Promise proposals and signing}\label{propose}

Promises can exist and be discussed without them ever having been
made or intended to be kept by an agent. We have used the notation
$\psi(\pi)$ for a description of the promise $\pi$. This description
must be adopted by an agent before it can be said to have made the promise.
It is therefore useful to maintain the idea of promise proposals.
\begin{definition}[Promise proposals]
The statement of a promise that is posited for consideration by one or
more parties, prior to keeping or discarding the promise.
\end{definition}

Promise proposals are often discussed as part of treaty negotiations
and commercial relationships. The terminology of these proposals is
somewhat confused, so we define our own terminology below.

\begin{definition}[Signing a proposal]
The concept of signing a proposal is to attach an agent's identity to
is as a promise to use the proposal.
\end{definition}

\section{The notion of an agreement}\label{contracts}

Not all agreements involve promises. An agreement is simply the
arrival at a common conclusion by two individuals. For example, two
parties can agree that $2+2=4$.
\begin{definition}[Agreement]
A state of acceptance about a proposal that is shared between two or more parties.
\end{definition}
Two agents may or may not know about their common state of agreement.

Agreement about some body of information can be turned into a promise
however if we phrase the acceptance as a promise, usually by
signing. If all parties promise that a set of proposals will be
honoured, then an agreement may be expressed as a promise to keep some
specification or promise proposals. This may be called the {\em body}
of the agreement. The term contract is also used here.

\begin{definition}[Contract]
A bilateral bundle of promise proposals between two agents, that is
intended to serve as the body of an agreement.
\end{definition}

Agreements are often assumed to be about policies or actions
(agreements to act) and are often formalized using contracts in which
case both parties agree to the terms of a common contract.

\bigskip
\begin{definition}[Promise agreement]
A promise agreement is a pair of use-promises between two parties to
acknowledge and adopt the body of a proposal.
\end{definition}
\bigskip

\section{Legal agreements, terms and conditions}

Many legal agreements may be considered sets of promises that define
hypothetical boundary conditions for an interaction between parties or
agents. The law is one such example. One expects the promises
described in the terms and conditions of the contract will rarely need
to be enforced, because one hopes that it will never reach such a
point, however the terms define a standard response to such
infractions. Legal contracts define what happens mainly at the edge
states of the behaviour one hopes to ensue.

Note that a collection of promises is not necessarily consistent or
sustainable. An agreement has to be worked out so that it is of mutual
economic benefit to both parties, from each of their perspectives.
This, however, has to do with the economic sustainability of the
promises.  An agent can clearly make a promise that it is in fact
incapable of keeping.

\subsection{Example: Service Level Agreements}

Promises to keep within certain behavioural limits are clearly
analogous to items that would be mentioned in Service Level
Agreements, and hence we expect to be able to use them, within a
suitable framework, to discuss Service Level Agreements.  A promise,
however, is not an agreement by itself. We must first explore the
relationship between promises and agreements.

A service contract, for example, would be a contract from an agent
that takes on the role of provider to another agent that has the role
of client.  The body of the agreement consists of the promised
behaviours surrounding the delivery and consumption of a
service,. From this we may define a Service Level Agreement as

\bigskip
\begin{definition}[Service Level Agreement]
An agreement between two agents whose body describes a contract
for service delivery and consumption.
\end{definition}
\bigskip

We can supplment this with defintions of the roles\cite{siri1}.

\section{Cooperative agreement or treaty negotiation}

If two agents agree to agree to behave according to the same standard
as one another, then their common agreement is the intersection.
\begin{definition}[Agreement]
\beq
\frac{a \promise{C(\pi_1)} b, b \promise{C(\pi_2)} a}
{a \stackrel{\pi_1\cap\pi_2}{\leftrightarrow} b}
\eeq
We still have to decide what this actually means.
\end{definition}
This clarifies the process and limitations of an agreement..  Each
party might promise asymmetrically to keep certain behaviours, but the
overlap is the only part on which they agree.  Note that neither party
can be subordinate to the other in such an agreement.

\section{Conract economics}

There is more to be said about contracts and agreements in connection
with the economics of promises. See section \ref{pam}.