Stit, Iit, and Deontic Logic for Action Types
Martin Mose Bentzen

Abstract:
This thesis presents new tools and improvements of existing tools for
reasoning about actions and norms. The theoretical setting of the work
is the multi agent logic stit theory, a formal theory in the tradition
of modal logic.  In this thesis, stit theory is limited to cover only
strategic situations. This basic framework is then extended in several
ways throughout the thesis, but the two most important extensions are
intentions and action types.  Intentions are an important component
of informal reasoning in ethics and law but they have not been part of
stit theory so far. In this thesis intentions are represented via
subsets of outcomes of individual actions. An intention operator, the
iit operator, is added to the language.  Many natural language
modalities operate on expressions denoting action types. Until now,
there has been no way to talk about action types in stit theory. A
proposal of how to do that is developed in this thesis.

  In Chapter 1, some philosophical presuppositions and intuitions that
have guided the theorizing in later chapters are laid out. It is
discussed, e.g. how one can think about agents, situations and
values. In Chapter 2, the basic formal definition of a situation is
presented. The specific contribution of the chapter is a
generalization of Horty's ought to do operator by means of the game
theoretical device of simultaneously removing all dominated actions of
all agents in an iterative process. In Chapter 3, intentions are added
and definitions of various concepts of individual responsibility
relative to outcomes of specific situations are presented. The
knowledge of agents in situations is also considered. Chapters 4, 5,
and 6 treat special topics related to preceding chapters. Chapter 4
takes a closer look at ability modalities and the metaphysics of
agency. A cube of opposition for ability modalities is presented and
different kinds of agents are defined relative to this cube. It is
shown that if an omnipotent agent (called God) exists it is unique and
solely responsible for everything. In Chapter 5, concepts of group
responsibility and responsibility of individual members of groups are
suggested. In Chapter 6, the theory is applied to a discussion of
Frankfurt examples. Overdetermination of events and the differences
between causal responsibility and agentive responsibility are
discussed. Chapter 7 breaks with the framework provided by stit theory
and used in the rest of the thesis. In this chapter, the starting
point is a foundational discussion of deontic logic considering
e.g. Ross' paradox and free choice inferences and the role action
types play in informal reasoning. A new deontic logic for action types
is then presented where deontic must and may operators are applied to
action type terms. In Chapter 8, it turns out that the break with the
stit framework can be mended by introducing action types into stit
theory. It is shown how to reason with action types using stit models
and how to reason about double effects of actions.


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