Conditional Ranking Revision - Iterated Revision with Sets of Conditionals

In the context of a general framework for belief dynamics which interprets revision as doxastic constraint satisfaction, we discuss a proposal for revising quasi-probabilistic belief measures with finite sets of graded conditionals. The belief states are ranking measures with divisible values (generalizing Spohn's epistemology), and the conditionals are interpreted as ranking constraints. The approach is inspired by the minimal information paradigm and based on the principle-guided canonical construction of a ranking model of the input conditionals. This is achieved by extending techniques known from conditional default reasoning. We give an overview of how it handles different principles for conditional and parallel revision and compare it with similar accounts

Interpreting an action from what we perceive and what we expect

International audienceIn update logic as studied by Baltag, Moss, Solecki and van Benthem, little attention is paid to the interpretation of an action by an agent, which is just assumed to depend on the situation. This is actually a complex issue that nevertheless complies to some logical dynamics. In this paper, we tackle this topic. We also deal with actions that change propositional facts of the situation. In parallel, we propose a formalism to accurately represent an agent's epistemic state based on hyperreal numbers. In that respect, we use infinitesimals to express what would surprise the agents (and by how much) by contradicting their beliefs. We also use a subjective probability to model the notion of belief. It turns out that our probabilistic update mechanism satisfies the AGM postulates of belief revision

A Model of Minimal Probabilistic Belief Revision

A probabilistic belief revision function assigns to every initial probabilistic belief and every observable event some revised probabilistic belief that only attaches positive probability to states in this event. We propose three axioms for belief revision functions: (1) linearity, meaning that if the decision maker observes that the true state is in {a,b}, and hence state c is impossible, then the proportions of c''s initial probability that are shifted to a and b, respectively, should be independent of c''s initial probability; (2) transitivity, stating that if the decision maker deems belief β equally similar to states a and b, and deems β equally similar to states b and c, then he should deem β equally similar to states a and c; (3) information-order independence, stating that the way in which information is received should not matter for the eventual revised belief. We show that a belief revision function satisfies the three axioms above if and only if there is some linear one-to-one function ϕ, transforming the belief simplex into a polytope that is closed under orthogonal projections, such that the belief revision function satisfies minimal belief revision with respect to ϕ. By the latter, we mean that the decision maker, when having initial belief β₁ and observing the event E, always chooses the revised belief β₂ that attaches positive probability only to states in E and for which ϕ(β₂) has minimal Euclidean distance to ϕ(β₁).microeconomics ;

Epistemic Foundations for Backward Induction: An Overview

In this survey we analyze, and compare, various sufficient epistemic conditions for backward induction that have been proposed in the literature. To this purpose we present a simple epistemic base model for games with perfect information, and translate the different models into the language of this base model. As such, we formulate the various sufficient conditions for backward induction in a uniform language, which enables us to explictly analyze their differences and similarities.mathematical economics;

Is Everything Revisable?

Over the decades, the claim that everything is revisable (defended by Quine and others) has played an important role in Epistemology and Philosophy of Science. Some time ago, Katz (1988) argued that this claim is paradoxical. This paper does not discuss this objection but rather argues that the claim of universal revisability allows for two different readings but in each case leads to a contradiction and is false

Dynamic reasoning in a knowledge-based system

Any space based system, whether it is a robot arm assembling parts in space or an onboard system monitoring the space station, has to react to changes which cannot be foreseen. As a result, apart from having domain-specific knowledge as in current expert systems, a space based AI system should also have general principles of change. This paper presents a modal logic which can not only represent change but also reason with it. Three primitive operations, expansion, contraction and revision are introduced and axioms which specify how the knowledge base should change when the external world changes are also specified. Accordingly the notion of dynamic reasoning is introduced, which unlike the existing forms of reasoning, provide general principles of change. Dynamic reasoning is based on two main principles, namely minimize change and maximize coherence. A possible-world semantics which incorporates the above two principles is also discussed. The paper concludes by discussing how the dynamic reasoning system can be used to specify actions and hence form an integral part of an autonomous reasoning and planning system

Datalog± Ontology Consolidation

Knowledge bases in the form of ontologies are receiving increasing attention as they allow to clearly represent both the available knowledge, which includes the knowledge in itself and the constraints imposed to it by the domain or the users. In particular, Datalog ± ontologies are attractive because of their property of decidability and the possibility of dealing with the massive amounts of data in real world environments; however, as it is the case with many other ontological languages, their application in collaborative environments often lead to inconsistency related issues. In this paper we introduce the notion of incoherence regarding Datalog± ontologies, in terms of satisfiability of sets of constraints, and show how under specific conditions incoherence leads to inconsistent Datalog ± ontologies. The main contribution of this work is a novel approach to restore both consistency and coherence in Datalog± ontologies. The proposed approach is based on kernel contraction and restoration is performed by the application of incision functions that select formulas to delete. Nevertheless, instead of working over minimal incoherent/inconsistent sets encountered in the ontologies, our operators produce incisions over non-minimal structures called clusters. We present a construction for consolidation operators, along with the properties expected to be satisfied by them. Finally, we establish the relation between the construction and the properties by means of a representation theorem. Although this proposal is presented for Datalog± ontologies consolidation, these operators can be applied to other types of ontological languages, such as Description Logics, making them apt to be used in collaborative environments like the Semantic Web.Fil: Deagustini, Cristhian Ariel David. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Martinez, Maria Vanina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Falappa, Marcelo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Simari, Guillermo Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; Argentin