Like any other logical theory, domain descriptions in reasoning about actions may evolve, and thus need revision methods to adequately accommodate new information about the behavior of actions. The present work is about changing action domain descriptions in propositional dynamic logic. Its contribution is threefold: first we revisit the semantics of action theory contraction that has been done in previous work, giving more robust operators that express minimal change based on a notion of distance between Kripke-models. Second we give algorithms for syntactical action theory contraction and establish their correctness w.r.t. our semantics. Finally we state postulates for action theory contraction and assess the behavior of our operators w.r.t. them. Moreover, we also address the revision counterpart of action theory change, showing that it benefits from our semantics for contraction.
The work by Eiter al @cite_5 @cite_52 is similar to ours in that they also propose a framework that is oriented to updating action laws. They mainly investigate the case where a new effect law is added to the description (and then has to be true in all models of the modified theory). This problem is the dual of contraction and is then closer to our definition of revision ( ).
@cite_5 @cite_52
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The Katsuno and Mendelzon theory of belief update has been proposed as a reasonable model for revising beliefs about a changing world. However, the semantics of update relies on information which is not readily available. We describe an alternative semantical view of update in which observations are incorporated into a belief set by: a) explaining the observation in terms of a set of plausible events that might have caused that observation; and b) predicting further consequences of those explanations. We also allow the possibility of conditional explanations. We show that this picture naturally induces an update operator under certain assumptions. However, we argue that these assumptions are not always reasonable, and they restrict our ability to integrate update with other forms of revision when reasoning about action. This paper presents a general, consistency-based framework for expressing belief change. The framework has good formal properties while being well-suited for implementation. For belief revision, informally, in revising a knowledge base K by a sentence α, we begin with α and include as much of K as consistently possible. This is done by expressing K and α in disjoint languages, asserting that the languages agree on the truth values of corresponding atoms wherever consistently possible, and then re-expressing the result in the original language of K. There may be more than one way in which the languages of K and α can be so correlated: in choice revision, one such "extension" represents the revised state; alternately (skeptical) revision consists of the intersection of all such extensions. Contraction is similarly defined although, interestingly, it is not interdefinable with revision.The framework is general and flexible. For example, one could go on and express other belief change operations such as update and erasure, and the merging of knowledge bases. Further, the framework allows the incorporation of static and dynamic integrity constraints. The approach is well-suited for implementation: belief change can be equivalently expressed in terms of a finite knowledge base; and the scope of a belief change operation can be restricted to just those propositions common to the knowledge base and sentence for change. We give a high-level algorithm implementing the procedure, and an expression of the approach in Default Logic. Lastly, we briefly discuss two implementations of the approach. In this paper, we present a semantical approach to multi-agent belief revision and belief update. For this, we introduce relational structures called conditional doxastic models (CDM's, for short). We show this setting to be equivalent to an epistemic version of the classical AGM Belief Revision theory. We present a logic of conditional beliefs that is complete w.r.t. CDM's. Moving then to belief updates (sometimes called ''dynamic'' belief revision) induced by epistemic actions, we consider two particular cases: public announcements and private announcements to subgroups of agents. We show how the standard semantics for these types of updates can be appropriately modified in order to apply it to CDM's, thus incorporating belief revision into our notion of update. We provide a complete axiomatization of the corresponding dynamic doxastic logics. As an application, we solve a ''cheating version'' of the Muddy Children Puzzle. The process of integrating knowledge coming from different sources has been widely investigated in the literature. Three distinct conceptual approaches to this problem have been most succesful: belief revision, merging and update. In this paper we present a framework that integrates these three approaches. In the proposed framework all three operations can be performed. We provide an example that can only be solved by applying more than one single style of knowledge integration and, therefore, cannot be addressed by anyone of the approaches alone. The framework has been implemented, and the examples shown in this paper (as well as other examples from the belief revision literature) have been successfully tested. Ontology evolution is an important problem in the Semantic Web research. Recently, Alchourron, Gardenfors and Markinson's (AGM) theory on belief change has been applied to deal with this problem. However, most of current work only focuses on the feasibility of the application of AGM postulates on contraction to description logics (DLs), a family of ontology languages. So the explicit construction of a revision operator is ignored. In this paper, we first generalize the AGM postulates on revision to DLs. We then define two revision operators in DLs. One is the weakening-based revision operator which is defined by weakening of statements in a DL knowledge base and the other is its refinement. We show that both operators capture some notions of minimal change and satisfy the generalized AGM postulates for revision. We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, we show how various abstract postulates for belief revision can be analyzed by standard modal frame correspondences for model-changing operations. This paper proposes a method of nonmonotonic theory change. We first introduce a new form of abduction that can account for observations in nonmonotonic situation. Then we provide a framework of autoepistemic update, which describes nonmonotonic theory change through the extended abductive framework. The proposed update semantics is fairly general and provides a unified framework for various update semantics such as first-order update, view update of databases, and contradiction removal of nonmonotonic theories. In this paper, we investigate the revision of argumentation systems a la Dung. We focus on revision as minimal change of the arguments status. Contrarily to most of the previous works on the topic, the addition of new arguments is not allowed in the revision process, so that the revised system has to be obtained by modifying the attack relation only. We introduce a language of revision formulae which is expressive enough for enabling the representation of complex conditions on the acceptability of arguments in the revised system. We show how AGM belief revision postulates can be translated to the case of argumentation systems. We provide a corresponding representation theorem in terms of minimal change of the arguments statuses. Several distance-based revision operators satisfying the postulates are also pointed out, along with some methods to build revised argumentation systems. We also discuss some computational aspects of those methods. Recently, the problem of inconsistency handling in description logics has attracted a lot of attention. Many approaches have been proposed to deal with this problem based on existing techniques for inconsistency management. In this paper, we first define two revision operators in description logics; one is called a weakening-based revision operator and the other is its refinement. Based on the revision operators, we then propose an algorithm to handle inconsistency in a stratified description logic knowledge base. We show that when the weakening-based revision operator is chosen, the resulting knowledge base of our algorithm is semantically equivalent to the knowledge base obtained by applying refined conjunctive maxi-adjustment (RCMA) which refines disjunctive maxi-adjusment (DMA), known to be a good strategy for inconsistency handling in classical logic. How can an intelligent agent update her knowledge base about an action domain, relative to some conditions (possibly obtained from earlier observations)? We study this question in a formal framework for reasoning about actions and change, in which the meaning of an action domain description can be represented by a directed graph whose nodes correspond to states and whose edges correspond to action occurrences. We define the update of an action domain description in this framework, and show among other results that a solution to this problem can be obtained by a divide-and-conquer approach in some cases. We also introduce methods to compute a solution and an approximate solution to this problem, and analyze the computational complexity of these problems. Finally, we discuss techniques to improve the quality of solutions. When a planning task cannot be solved then it can often be made solvable by modifying it a bit: one may change either the set of actions, or the initial state, or the goal description. We show that modification of actions can be reduced to initial state modification. We then apply Katsuno and Mendelzon's distinction between update and revision and show that the modification of the initial state is an update and the modification of the goal description is a revision. We consider variants of Forbus's update and Dalal's revision operation and argue that existing belief change operations do not apply as they stand because their inputs are boolean formulas, while plan task modification involves counterfactual statements. We show that they can be captured in Dynamic Logic of Propositional Assignments DL-PA. We generalize AGM belief revision theory to the multi-agent case. To do so, we first generalize the semantics of the single-agent case, based on the notion of interpretation, to the multi-agent case. Then we show that, thanks to the shape of our new semantics, all the results of the AGM framework transfer. Afterwards we investigate some postulates that are specific to our multi-agent setting. Abstract Belief revision and belief update are two different forms of belief change, and they serve different purposes. In this paper we focus on belief update, the formalization of change in beliefs due to changes in the world. The complexity of the basic update (introduced by Winslett, 1990) has been determined by Eiter and Gottlob (1992). Since then, many other formalizations have been proposed to overcome the limitations and drawbacks of Winslett's update. In this paper we analyze the complexity of the proposals presented in the literature: the standard semantics by Winslett (1986), the minimal change with exception and the minimal change with maximal disjunctive information by Zhang and Foo (1996), the update with disjunctive function by Herzig (1996), the abduction-based update and the generalized update by Boutilier (1996). We relate some of these approaches to belief update to previous work on closed world reasoning. In real-world applications, knowledge bases consisting of all the available information for a specific domain, along with the current state of affairs, will typically contain contradictory data, coming from different sources, as well as data with varying degrees of uncertainty attached. An important aspect of the effort associated with maintaining such knowledge bases is deciding what information is no longer useful; pieces of information may be outdated; may come from sources that have recently been discovered to be of low quality; or abundant evidence may be available that contradicts them. In this paper, we propose a probabilistic structured argumentation framework that arises from the extension of Presumptive Defeasible Logic Programming (PreDeLP) with probabilistic models, and argue that this formalism is capable of addressing these basic issues. The formalism is capable of handling contradictory and uncertain data, and we study non-prioritized belief revision over probabilistic PreDeLP programs that can help with knowledge-base maintenance. For belief revision, we propose a set of rationality postulates -- based on well-known ones developed for classical knowledge bases -- that characterize how these belief revision operations should behave, and study classes of operators along with theoretical relationships with the proposed postulates, including representation theorems stating the equivalence between classes of operators and their associated postulates. We then demonstrate how our framework can be used to address the attribution problem in cyber security cyber warfare. Among others, (1998) presented an approach for updating logic programs with sets of rules based on dynamic logic programs. We syntactically redefine dynamic logic programs and investigate their semantical properties, looking at them from perspectives such as a belief revision and abstract consequence relation view. Since the approach does not respect minimality of change, we refine its stable model semantics and present minimal stable models and strict stable models. We also compare the update approach to related work, and find that is equivalent to a class of inheritance programs independently defined by (1999). In this paper, a new syntax-based approach to belief revision is presented. It is developed within a nonmonotonic framework that allows a two-steps handling of inconsistency to be adopted. First, a disciplined use of non-monotonic ingredients is made available to the knowledge engineer to prevent many inconsistencies that would occur if a standard logical interpretation and representation of beliefs were conducted. Remaining inconsistencies are considered unexpected and revised by weakening the formulas occurring in any minimally inconsistent subbase, as if they were representing exceptional cases that do not actually occur. While the computation of revised knowledge bases remains intractable in the worst case, our approach benefits from an efficient local search-based heuristic technique that empirically proves often viable, even in the context of very large prepositional applications. We consider a modified version of the situation calculus built using a two-variable fragment of the first-order logic extended with counting quantifiers. We mention several additional groups of axioms that can be introduced to capture taxonomic reasoning. We show that the regression operator in this framework can be defined similarly to regression in the Reiter's version of the situation calculus. Using this new regression operator, we show that the projection and executability problems are decidable in the modified version even if an initial knowledge base is incomplete and open. For an incomplete knowledge base and for context-dependent actions, we consider a type of progression that is sound with respect to the classical progression. We show that the new knowledge base resulting after our progression is definable in our modified situation calculus if one allows actions with local effects only. We mention possible applications to formalization of Semantic Web services. We suggest here a methodology for updating databases with integrity constraints and rules for deriving inexphcit information. First we consider the problem of updating arbitrary theories by inserting into them or deleting from them arbitrary sentences. The solution involves two key ideas when replacing an old theory by a new one we wish to minimize the change in the theory, and when there are several theories that involve minimal changes, we look for a new theory that reflects that ambiguity. The methodology is also adapted to updating databases, where different facts can carry different priorities, and to updating user views. This paper describes a change theory based on abductive reasoning. We take the AGM postulates for revisions, expansions and contractions, and Katsuno and Mendelzon postulates for updates and incorporate abduction into them. A key feature of the theory is that presents a unified view of standard change operators and abductive change operators rather than a new and independent change theory for abductive changes. Abductive operators reduce to standard change operators in the limiting cases. Many real-world knowledge-based systems must deal with information coming from different sources that invariably leads to incompleteness, overspecification, or inherently uncertain content. The presence of these varying levels of uncertainty doesn't mean that the information is worthless --- rather, these are hurdles that the knowledge engineer must learn to work with. In this paper, we continue work on an argumentation-based framework that extends the well-known Defeasible Logic Programming (DeLP) language with probabilistic uncertainty, giving rise to the Defeasible Logic Programming with Presumptions and Probabilistic Environments (DeLP3E) model. Our prior work focused on the problem of belief revision in DeLP3E, where we proposed a non-prioritized class of revision operators called AFO (Annotation Function-based Operators) to solve this problem. In this paper, we further study this class and argue that in some cases it may be desirable to define revision operators that take quantitative aspects into account, such as how the probabilities of certain literals or formulas of interest change after the revision takes place. To the best of our knowledge, this problem has not been addressed in the argumentation literature to date. We propose the QAFO (Quantitative Annotation Function-based Operators) class of operators, a subclass of AFO, and then go on to study the complexity of several problems related to their specification and application in revising knowledge bases. Finally, we present an algorithm for computing the probability that a literal is warranted in a DeLP3E knowledge base, and discuss how it could be applied towards implementing QAFO-style operators that compute approximations rather than exact operations.