AGM's belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been largely used to specify the agent's belief state - whether representing the agent's `explicit beliefs' or as a computational model for her belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in a dynamic epistemic logic. This work investigates how priority graphs, a syntactic representation of preference relations deeply connected to prioritised bases, can be used to characterise belief change operators, focusing on well-known postulates of Iterated Belief Change. We provide syntactic representations of belief change operators in a dynamic context, as well as new negative results regarding the possibility of representing an iterated belief revision operation using transformations on priority graphs.
La Trobe University（乐卓博大学）；Cardiff University（卡迪夫大学）
Recent work has considered the problem of extending to the case of iterated belief change the so-called `Harper Identity' (HI), which defines single-shot contraction in terms of single-shot revision. The present paper considers the prospects of providing a similar extension of the Levi Identity (LI), in which the direction of definition runs the other way. We restrict our attention here to the three classic iterated revision operators--natural, restrained and lexicographic, for which we provide here the first collective characterisation in the literature, under the appellation of `elementary' …
Institute of Mathematics and Statistics, Federal University of Bahia - UFBA（巴伊亚联邦大学数学与统计学院）
AGM's belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been primarily used to specify the agent's belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in dynamic epistemic logic. Particularly, it has been shown that some postulates can be characterised through transfo…
On Definite Iterated Belief Revision with Belief Algebras
School of Mathematics, Southwest Jiaotong University, China（数学学院，西南交通大学）；School of Computing and Artificial Intelligence, Southwest Jiaotong University, China（计算与人工智能学院，西南交通大学）；LIRMM UMR 5506, University of Montpellier & CNRS, France（蒙彼利埃大学及CNRS LIRMM研究中心）
Universidad Simón Bolívar（西蒙玻利瓦尔大学）；Universidad de Los Andes（德洛斯安第斯大学）
In most classical models of belief change, epistemic states are represented by theories (AGM) or formulas (Katsuno-Mendelzon) and the new pieces of information by formulas. The Representation Theorem for revision operators says that operators are represented by total preorders. This important representation is exploited by Darwiche and Pearl to shift the notion of epistemic state to a more abstract one, where the paradigm of epistemic state is indeed that of a total preorder over interpretations. In this work, we introduce a 3-valued logic where the formulas can be identified with a generalisa…
FernUniversität in Hagen（哈根开放大学）；Technical University Dortmund（多特蒙德工业大学）
According to Boutillier, Darwiche, Pearl and others, principles for iterated revision can be characterised in terms of changing beliefs about conditionals. For iterated contraction a similar formulation is not known. This is especially because for iterated belief change the connection between revision and contraction via the Levi and Harper identity is not straightforward, and therefore, characterisation results do not transfer easily between iterated revision and contraction. In this article, we develop an axiomatisation of iterated contraction in terms of changing conditional beliefs. We pro…
Iterated Belief Change is the research area that investigates principles for the dynamics of beliefs over (possibly unlimited) many subsequent belief changes. In this paper, we demonstrate how iterated belief change is connected to computation. In particular, we show that iterative belief revision is Turing complete, even under the condition that broadly accepted principles like the Darwiche-Pearl postulates for iterated revision hold.
Darwiche and Pearl's seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most of the suggestions made have resulted in a form of `reductionism' that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka `Independence', characteristic of `admissible' revision operators, remain commendably more modest. In this paper, we s…
Several forms of iterable belief change exist, differing in the kind of change and its strength: some operators introduce formulae, others remove them; some add formulae unconditionally, others only as additions to the previous beliefs; some only relative to the current situation, others in all possible cases. A sequence of changes may involve several of them: for example, the first step is a revision, the second a contraction and the third a refinement of the previous beliefs. The ten operators considered in this article are shown to be all reducible to three: lexicographic revision, refineme…
While research on iterated revision is predominant in the field of iterated belief change, the class of iterated contraction operators received more attention in recent years. In this article, we examine a non-prioritized generalisation of iterated contraction. In particular, the class of weak decrement operators is introduced, which are operators that by multiple steps achieve the same as a contraction. Inspired by Darwiche and Pearl's work on iterated revision the subclass of decrement operators is defined. For both, decrement and weak decrement operators, postulates are presented and for ea…
In recent years, multi-agent epistemic planning has received attention from both dynamic logic and planning communities. Existing implementations of multi-agent epistemic planning are based on compilation into classical planning and suffer from various limitations, such as generating only linear plans, restriction to public actions, and incapability to handle disjunctive beliefs. In this paper, we propose a general representation language for multi-agent epistemic planning where the initial KB and the goal, the preconditions and effects of actions can be arbitrary multi-agent epistemic formula…
We propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots. The proposed memory architecture---called the {\em universal memory architecture} (UMA)---maintains an epistemic state in the form of a system of default rules similar to those studied by Pearl and by Goldszmidt and Pearl (systems $Z$ and $Z^+$). A duality between the category of UMA representations and the category of the corresponding model spaces, extending the Sageev-Roller duality between discrete poc sets and discrete median algebras provides a tw…
Federal University of Bahia（巴伊亚联邦大学）；Pontifical Catholic University of Rio Grande do Sul（南里奥格兰德天主教大学）；Federal University of Rio Grande do Sul（南里奥格兰德联邦大学）
AGM's belief revision is one of the main paradigms in the study of belief change operations. Recently, several logics for belief and information change have been proposed in the literature and used to encode belief change operations in rich and expressive semantic frameworks. While the connections of AGM-like operations and their encoding in dynamic doxastic logics have been studied before by the work of Segerberg, most works on the area of Dynamic Epistemic Logics (DEL) have not, to our knowledge, attempted to use those logics as tools to investigate mathematical properties of belief change o…
La Trobe University（拉筹伯大学）；Cardiff University（卡迪夫大学）
The belief revision literature has largely focussed on the issue of how to revise one's beliefs in the light of information regarding matters of fact. Here we turn to an important but comparatively neglected issue: How might one extend a revision operator to handle conditionals as input? Our approach to this question of 'conditional revision' is distinctive insofar as it abstracts from the controversial details of how to revise by factual sentences. We introduce a 'plug and play' method for uniquely extending any iterated belief revision operator to the conditional case. The flexibility of our…
In the field of knowledge representation, the considered epistemic states are often based on propositional interpretations, also called worlds. E.g., epistemic states of agents can be modelled by ranking functions or total preorders on worlds. However, there are usually different ways of how to describe a real world situation in a propositional language; this can be seen as different points of view on the same situation. In this paper we introduce the concept of model transformations to convert an epistemic state from one point of view to another point of view, yielding a novel notion of equiv…
A General Framework of Epistemic Forgetting and its Instantiation by Ranking Functions
Faculty of Mathematics（数学系）；Computer Science, University of Hagen, 58084 Hagen, Germany（计算机科学，海因斯大学，德国）；Department of Computer Science, Technology Dortmund University, 44221 Dortmund, Germany（计算机科学系，多特蒙德技术大学，德国）
Paraconsistent Belief Revision: A Replacement-Enriched LFI for Epistemic Entrenchment
Centre for Logic, Epistemology and the History of Science (CLE), State University of Campinas (Unicamp)（圣保罗州立大学逻辑、认识论与科学史中心）；Institute of Philosophy and the Humanities (IFCH), Unicamp（圣保罗州立大学哲学与人文学院）；Departamento de Matemática. Universidad Nacional del Sur（南国立大学数学系）
Institute of Philosophy and the Humanities (IFCH) and Centre for Logic, Epistemology and The History of Science (CLE), University of Campinas (UNICAMP)（坎皮纳斯大学哲学与人文学院（IFCH）及逻辑、认识论与科学史中心（CLE））
Recently there have been numerous proposed solutions to the problem of logical omniscience in doxastic and epistemic logic. Though these solutions display an impressive breadth of subtlety and motivation, the crux of these approaches seems to have a common theme-minor revisions around the ubiquitous Kripke semantics-rooted approach. In addition, the psychological mechanisms at work in and around both belief and knowledge have been left largely untouched. In this paper, we cut straight to the core of the problem of logical omniscience, taking a psychologically-rooted approach, taking as bedrock…
