2010: Abductive Belief Revision in Science

Handbook of Knowledge Representation, 2008

Journal of Philosophical Logic, 1994

and an anonymous referee for the Journal of Philosophical Logic for their insightful comments on earlier versions of this paper. I also thank Prasanta Bandyopadhyay, Jim Cain, Francis Je ry Pelletier and Ted Sider for their sugges tions and encouragement, and acknowledge the help of my friend Ramkrishnan Nambimadom in the construction of a crucial proof. We take Cn to be a mapping from sets of propositions to sets of propositions with the following properties: for all sets A and B of propositions, A Cn(A) (inclusion) Cn(A) = Cn(Cn(A)) (iteration; or idempotence) Cn(A) Cn(B) whenever A B (monotonicity): Furthermore we assume Cn to include tautological implication, to satisfy the rule of introduction of disjunction in the premises, i.e. if x 2 Cn(A fyg) and x 2 Cn(A fzg) then x 2 Cn(A fy _ zg) 3 and to be compact, i.e. if x 2 Cn(?) for a set of propositions ?; then there is a nite subset ? of ? such that x is in Cn(? ): Throughout this paper K denotes the belief-set (also called \knowledge corpus" or \theory") of our doxastic agent. K is always taken to be closed under Cn; i.e. Cn(K) K; and usually consistent. We also assume that there is a contextually xed set of basic beliefs that generates K: We take this set of basic beliefs to be nite, and is denoted by B: Hence De nition 1.1 K = Cn(B). In other words, when we talk of a belief-set K; we really talk of the pair hK; Bi where B is the contextually determined base of K: When required, we use superscripts or subscripts on K or B to denote other belief-sets or belief bases.

1999

In this paper we present a the structuralist framework of belief revision.This is considered to be an extension of AGM framework of belief revision with some semantic properties which constitute the structure. The properties are causal properties, causal mechanism, causal process, intervention. In the theories of belief revision based on classical AGM [1], beliefs are being represented as a set of sentences that are closed under logical implication. Operations for belief change such as expansion, contraction and revision, are defined only with respect to belief sets. As a result , structural information given by an epistemic entrenchment ordering disappears after operations of belief change. Although the AGM model is mathematically elegant, simple, it only merely serve as an idealized model for belief change. Also, some postulates such as success(in case of revision), recovery (in case of contraction) are found to be unsatisfactory in case of rational belief revision. Success Postulate states that new information needs to be reflected in the revised belief state of an agent, no matter whether it is relevant or not. An agent has no choice of rejecting the undesirable irrelevant information. Some other postulates are also found to be controversial, counter-intuitive. Belief revision models based on AGM are geared up for one step revisions of simple plain beliefs and fails to handle cases where the new information comes in iterations and in the form of conditional beliefs. Keeping these issues in mind the problem seems to be as follows: how does an agent after discovering causal relations from the environment revises her beliefs such that beliefs closer to the core are not lost? The problem lies in finding a mechanism with the help of which one can give up conditional beliefs in the process of Belief revision while preserving the core conditional beliefs such as laws or causal statements. We present a theory of belief revision which preserves the structural information after iterated revisions. Following the constructive approach to belief revision, we propose a new entrenchment ordering called " causal epistemic en-trenchment ordering " , which is constrained by the structural and semantic properties such as structure, intervention, causal properties, causal mechanisms. We show how the ordering of beliefs are influenced by these semantic factors. The resulting entrenchment ordering of beliefs (CEE) would help us in ordering conditional beliefs (1) 2. preserve the structure in iterated revisions 3. It can be applied to the scientific theory change.

Journal of Logic, Language and Information, 1998

Alchourrón, CE, Gärdenfors, P., and Makinson, D., 1985, “On the logic of theory change: Partial meet contraction and revision functions,” Journal of Symbolic Logic 50, 510–530. Booth, R. and Paris, JB, 1998, “A note on the rational closure of knowledge bases with both positive and ...

Journal of Logic, Language and Information, 2010

The present paper aims at a synthesis of belief revision theory with the Sneed formalism known as the structuralist theory of science. This synthesis is brought about by a dynamisation of classical structuralism, with an abductive inference rule and base generated revisions in the style of Rott (2001). The formalism of prioritised default logic (PDL) serves as the medium of the synthesis. Why seek to integrate the Sneed formalism into belief revision theory? With the hybrid system of the present investigation, a substantial simplification of the ranking information that is necessary to define revisions and contractions uniquely is achieved. This system is, furthermore, expressive enough to capture complex and nontrivial scientific examples. It is thus closely related to a novel research area within belief revision theory which addresses the dynamics of scientific knowledge.

Logic Journal of the IGPL, 2017

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo, is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations.

In this project, a new model for belief revision based on abduction will be elaborated within the framework of AGM belief revision. We construe "abduction" as the process of reasoning in which explanatory (causal) hypothesis are formed and evaluated. Our basic hypothesis is that agent seeks explanation, before she accepts and integate the new evidential information with the old. As a result, it generates heirarchies of explanation and out of which causal ex- planations are considered to be most plaussible explanations. Here, not all explanations are acceptable for abduction, but only the best or atleast good ones (41). The dynamics of belief based on plaussibility of explanations would give us a reasonable mechanism whether or not to give priority to the incomming information. In this proposed research, we will (1) extend AGM framework with abductive revision operators (2) we characterize such revision with an ordering called causal epistemic entrenchment ordering. We prov...

Erkenntnis, 2011

Belief revision (BR) and truthlikeness (TL) emerged independently as two research programmes in formal methodology in the 1970s. A natural way of connecting BR and TL is to ask under what conditions the revision of a belief system by new input information leads the system towards the truth. It turns out that, for the AGM model of belief revision, the only safe case is the expansion of true beliefs by true input, but this is not very interesting or realistic as a model of theory change in science. The new accounts of non-prioritized belief revision do not seem more promising in this respect, and the alternative BR account of updating by imaging leads to other problems. Still, positive results about increasing truthlikeness by belief revision may be sought by restricting attention to special kinds of theories. Another approach is to link truthlikeness to epistemic matters by an estimation function which calculates expected degrees of truthlikeness relative to evidence. Then we can study how the expected truthlikeness of a theory changes when probabilities are revised by conditionalization or imaging. Again, we can ask under what conditions such changes lead our best theories towards the truth.

2011

Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal techniques like, for example, independence friendly logic, dialogical logics, multimodal logics, game theoretic semantics and linear logics, have the potential to cast new light on basic issues in the discussion of the unity of science. This series provides a venue where philosophers and logicians can apply specific technical insights to fundamental philosophical problems. While the series is open to a wide variety of perspectives, including the study and analysis of argumentation and the critical discussion of the relationship between logic and the philosophy of science, the aim is to provide an integrated picture of the scientific enterprise in all its diversity.