Logical Theories for Agent Introspection

Thomas Bolander: Logical Theories for Introspective Agents Artificial intelligence systems (agents) generally have models of the environments they inhabit which they use for representing facts, for reasoning about these facts and for planning actions. Much intelligent behaviour seems to involve an ability to model not only one’s external environment but also oneself and one’s own reasoning. We would therefore wish to be able to construct artificial intelligence systems having such abilities. We call these abilities introspective. In the attempt to construct agents with introspective abilities, a number of theoretical problems is encountered. In particular, problems related to self-reference make it difficult to avoid the possibility of such agents performing self-contradictory reasoning. It is the aim of this thesis to demonstrate how we can construct agents with introspective abilities, while at the same time circumventing the problems imposed by self-reference. In the standard approach taken in artificial intelligence, the model that an agent has of its environment is represented as a set of beliefs. These beliefs are expressed as logical formulas within a formal, logical theory. When the logical theory is expressive enough to allow introspective reasoning, the presence of self-reference causes the theory to be prone to inconsistency. The challenge therefore becomes to construct logical theories supporting introspective reasoning while at the same time ensuring that consistency is retained. In the thesis, we meet this challenge by devising several such logical theories which we prove to be consistent. These theories are all based on first-order predicate logic. To prove our consistency results, we develop a general mathematical framework, suitable for proving a large number of consistency results concerning logical theories involving various kinds of reflection. The principal idea of the framework is to relate self-reference and other problems involved in introspection to properties of certain kinds of graphs. These are graphs representing the semantical dependencies among the logical sentences. The framework is mainly inspired by developments within semantics for logic programming within computational logic and formal theories of truth within philosophical logic. The thesis provides a number of examples showing how the developed theories can be used as reasoning frameworks for agents with introspective abilities.