Online research in philosophy

A syntactic formalism for the modeling of belief revision in perfect information games is presented that allows to define the rationality of a player's choice of moves relative to the beliefs he holds as his respective decision nodes have been reached. In this setting, true common belief in the structure of the game and rationality held before the start of the game does not imply that backward induction will be played. To derive backward induction, a “forward belief” condition is formulated in terms of revised rather than initial beliefs. Alternative notions of rationality as well as the use of knowledge instead of belief are also studied within this framework. Footnotes1 I would like to thank Wlodek Rabinowicz and three anonymous referees for very helpful comments.

According to epistemological internalism, the rationality of a belief supervenes purely on "internal facts" about the thinker's mind. But what are "internal facts"? Why does the rationality of a belief supervene on them? The standard answers are unacceptable. This paper proposes new answers. "Internal facts" are facts about the thinker's nonfactive mental states. The rationality of a belief supervenes on such internal facts because we need rules of belief revision that we can follow directly, not by means of following any other rules, and the proximate explanation of any belief revision always consists of such internal facts.

This paper presents a theory of belief revision that allows people to come tobelieve in contradictions. The AGM theory of belief revision takes revision,in part, to be consistency maintenance. The present theory replacesconsistency with a weaker property called coherence. In addition to herbelief set, we take a set of statements that she rejects. These two sets arecoherent if they do not overlap. On this theory, belief revision maintains coherence.

Scientific inquiry is represented as a process of rational hypothesis revision in the face of data. For the concept of rationality, we rely on the theory of belief dynamics as developed in [5, 9]. Among other things, it is shown that if belief states are left unclosed under deductive logic then scientific theories can be expanded in a uniform, consistent fashion that allows inquiry to proceed by any method of hypothesis revision based on "kernel" contraction. In contrast, if belief states are closed under logic, then no such expansion is possible.

Belief revision theory aims to describe how one should change one’s beliefs when they are contradicted by newly input information. The guiding principle of belief revision theory is to change one’s prior beliefs as little as possible in order to maintain consistency with the new information. Learning theory focuses, instead, on learning power: the ability to arrive at true beliefs in a wide range of possible environments. The goal of this paper is to bridge the two approaches by providing a learning theoretic analysis of the learning power of belief revision methods proposed by Spohn, Boutilier, Darwiche and Pearl, and others. The results indicate that learning power depends sharply on details of the methods. Hence, learning power can provide a well-motivated constraint on the design and implementation of concrete belief revision methods.

This paper presents and discusses a novel approach to indeterministic belief revision. An indeterministic belief revision operator assumes that, when an agent is confronted with a new piece of information, it can revise its belief sets in more than one way. We define a rational agent not only in terms of what it believes but also of what it desires and wants to achieve. Hence, we propose that the agent’s goals play a role in the choice of (possibly) one of the several available revision options. Properties of the new belief revision mechanism are also investigated.

In this paper, it is argued that both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation, and an axiomatic characterization of this operation is given. Unlike most belief revision operations, the one developed here can handle both multiple belief revision and iterated belief revision.

This paper extends the AGM theory of belief revision to accommodate infinitary belief change. We generalize both axiomatization and modeling of the AGM theory. We show that most properties of the AGM belief change operations are preserved by the generalized operations whereas the infinitary belief change operations have their special properties. We prove that the extended axiomatic system for the generalized belief change operators with a Limit Postulate properly specifies infinite belief change. This framework provides a basis for first-order belief revision and the theory of revising a belief state by a belief state.

We contrast Bonanno’s ‘Belief Revision in a Temporal Framework’ [15] with preference change and belief revision from the perspective of dynamic epistemic logic (DEL). For that, we extend the logic of communication and change of [11] with relational substitutions [8] for preference change, and show that this does not alter its properties. Next we move to a more constrained context where belief and knowledge can be defined from preferences [29; 14; 5; 7], prove completeness of a very expressive logic of belief revision, and define a mechanism for updating belief revision models using a combination of action priority update [7] and preference substitution [8].

The theory of belief revision deals with (rational) changes in beliefs in response to new information. In the literature a distinction has been drawn between belief revision and belief update (see [6]). The former deals with situations where the objective facts describing the world do not change (so that only the beliefs of the agent change over time), while the letter allows for situations where both the facts and the doxastic state of the agent change over time. We focus on belief revision and propose a temporal framework that allows for iterated revision. We model the notion of “minimal” or “conservative” belief revision by considering logics of increasing strength. We move from one logic to the next by adding one or more axioms and show that the corresponding logic captures more stringent notions of minimal belief revision. The strongest logic that we propose provides a full axiomatization of the well-known AGM theory of belief revision.