A simple modal logic for belief revision

We propose a modal logic based on three operators, representing intial beliefs, information and revised beliefs. Three simple axioms are used to provide a sound and complete axiomatization of the qualitative part of Bayes’ rule. Some theorems of this logic are derived concerning the interaction between current beliefs and future beliefs. Information flows and iterated revision are also discussedmodel logic, beliefs

A simple modal logic for belief revision

We propose a logic based on three modal operators, representing intial beliefs, information and revised beliefs. Three simple and transparent axioms are used to provide a sound and complete axiomatization of the qualitative part of Bayes'' rule. Some theorems of this logic are derived concerning the interaction between current beliefs and future beliefs. Information flows and iterated revision are also discussed.Bayes rule, belief revision, intertemporal beliefs

Monotonicity and Persistence in Preferential Logics

An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be safely added to the premises without destroying any of the consequences: we say they respect monotonicity. Also, there may be formulae that, when they are a consequence, can not be invalidated when adding any formula to the premises: we call them conservative. We study these two classes of formulae for preferential logics, and show that they are closely linked to the formulae whose truth-value is preserved along the (preferential) ordering. We will consider some preferential logics for illustration, and prove syntactic characterization results for them. The results in this paper may improve the efficiency of theorem provers for preferential logics.Comment: See http://www.jair.org/ for any accompanying file

The Cost of Monitoring Alone

We compare the succinctness of two monitoring systems for properties of infinite traces, namely parallel and regular monitors. Although a parallel monitor can be turned into an equivalent regular monitor, the cost of this transformation is a double-exponential blowup in the syntactic size of the monitors, and a triple-exponential blowup when the goal is a deterministic monitor. We show that these bounds are tight and that they also hold for translations between corresponding fragments of Hennessy-Milner logic with recursion over infinite traces.Comment: 22 page

Approaches to abductive reasoning : an overview

Abduction is a form of non-monotonic reasoning that has gained increasing interest in the last few years. The key idea behind it can be represented by the following inference rule frac{varphirightarrowomega,}{varphi}omega, i.e., from an occurrence of omega and the rule "varphi implies omega';, infer an occurrence of varphi as a plausible hypothesis or explanation for omega. Thus, in contrast to deduction, abduction is as well as induction a form of "defeasible'; inference, i.e., the formulae sanctioned are plausible and submitted to verification. In this paper, a formal description of current approaches is given. The underlying reasoning process is treated independently and divided into two parts. This includes a description of methods for hypotheses generation and methods for finding the best explanations among a set of possible ones. Furthermore, the complexity of the abductive task is surveyed in connection with its relationship to default reasoning. We conclude with the presentation of applications of the discussed approaches focusing on plan recognition and plan generation