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In this talk I want to draw attentions on three fundamental questions
for the theory of intentions:

1. Intention, intentionality and intentional agency: what is the
connection?
2. What kind of constraints should rational intentions satisfy? Where do
these constraints come from?
3. What is the role of individual and collective intentions in shared
agency?

I will briefly present answers to these questions from the philosophical
literature, and argue that a logical theory of intentions can, and even
should try to answer them.

While there is an extensive literature developing logical
models to reason about informational attitudes (e.g. belief,
knowledge, certainty) in a dynamic environment, other mental states
have received relatively less attention. (A notable exception here is
work on logics of preferences and preference change.) However, this is
changing with recent articles developing a theory of intention
revision (see, for example, two recent articles: Towards a Theory of
Intention Revision by van der Hoek, Jamroga and Wooldridge and A Logic
of Intention and Attempt by Lorini and Herzig). These papers take as a
starting point logical frameworks derived from Cohen and Levesque’s
seminal paper aimed at formalizing Bratman’s planning theory of
intention.   In this talk, I will discuss a number of recent dynamic
logics of intention and beliefs.    In the process we will reexamine a
number of foundational issues surrounding so-called BDI-logics.

I will also discuss a recent paper on “joint revision of belief and
intention” (with Yoav Shoham and Thomas Icard) where we present a
formal semantical model to capture action,  belief and intention,
based on the “database perspective” of (Logical Theories of Intention
and the Database Perspective, Journal of Philosophical Logic,  2009,
by Yoav Shoham). We   provide postulates for belief and intention
revision, and state a representation theorem relating our postulates
to the formal model. Our belief postulates are in the spirit of the
AGM theory; the intention postulates stand in rough correspondence
with the belief postulates.

The talk presents ongoing work about the roles intentions play in
interaction, in particular as they relate to understanding information
flow. I discuss two such roles: information about an agent’s
intentions allows an observer to draw useful conclusions from the
former’s actions; and intentions can be viewed as “programs”, guiding
the actions of the participants towards an outcome state. I present a
Dynamic Epistemic Logic approach which formalizes the notions of
“intending to take an action” and “taking an action based on a
prior intention” to account for these phenomena, and discuss further
directions this research could take.