Belief Revision For Rational Fully Introspective Agents

In recent several decades, many logicians have become interested in actions played by agents and processes of cognitive reasoning. Dynamic structure is now one of the central themes of contemporary logic. There are lots of subjects such as dynamic epistemic logic, update logic, belief revision, branching time and etc. which represent the dynamic trend. As we know, traditional belief revision theory studies the belief change of rational agents; it is one of the most important affairs in this"Dynamic epistemic turn". And it has close relations to other non-monotonic logics, conditional logics, and etc. In classical belief revision literature, belief state of an agent is represented as a belief set which is closed under classical logical consequence Cn. If smarter agents are concerned, we need to consider"introspections". So stable sets, which are closed under positive introspection, negative introspection and Cn should be taken as representations for belief states of rational fully-introspective agents. In order to reflect belief revision of fully-introspective agents, the main task of this dissertation is to explore the revision on stable sets with any new information from the language containing belief formulae. We study the problem in several different perspectives. Main works have been done in this dissertation are concluded as in the following:(1) After considering difficulties and critical points in the problem, we employ"maxi-choice contraction"and revision on canonical models of stable sets to revise stable sets.(2) We apply S5 non-implying subsets of a stable theory to construct"partial meet contraction"similar as in AGM theory; revision from a stable theory to an intermediate theory is presented, and a representation theorem between"partial meet contraction from stable theories to intermediate theories and postulates of contraction has been proved; it is also showed there that the revision operator from stable sets to intermediate theories satisfies some postulates we want; we put forward some notions of"positive introspective expansion"and variant version of"Levi Identity"to guarantee the revised intermediate theory to have at least one stable expansion; then we borrow an idea from Konolige's hierachic autoepistemic logic to select a desired stable set from stable expansions of an intermediate theory.(3) We construct a"sphere system"and"epistemic entrenchment ordering"for revision from stable sets to intermediate theories similar as in classical belief revision theory; some representation theorems between them and contraction operators have been proved respectively; and it is also showed that the respective revision operators defined from those two semantical representations via variant version of"Levi Identity"satisfy all rational postulates we want; then a general selection method is provided to select a desired stable theory within stable expansions.(4) According to the properties of dynamic doxastic logic (DDL) and stable sets, we built a DDL system for revision on stable sets; model completeness has been proved there.(5) Similarly as"model update", we provide an approach called"model revision"; it is used to revise stable sets through revising their respective universal models; then a selection method for selecting a desired universal model is presented.(6) We employ"update semantics"to discuss"Moore Paradox"as done in Gillies (2001); similarly as"unsuccessful update", we put forward a notion"unsuccessful revision", using the"model revision"method to explain the problem of how the"positive introspection inconsistent"new information revise stable sets.