Possible worlds semantics for partial meet multiple contraction

In the logic of theory change, the standard model is AGM, proposed by Alchourrón et al. (J Symb Log 50:510–530, 1985). This paper focuses on the extension of AGM that accounts for contractions of a theory by a set of sentences instead of only by a single sentence. Hansson (Theoria 55:114–132, 1989), Fuhrmann and Hansson (J Logic Lang Inf 3:39–74, 1994) generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of sentences. In this paper we present the possible worlds semantics for partial meet multiple contractions.info:eu-repo/semantics/publishedVersio

On theory multiple contraction

The one which is considered the standard model of theory change was presented in [AGM85] and is known as the AGM model. In particular, that paper introduced the class of partial meet contractions. In subsequent works several alternative constructive models for that same class of functions were presented, e.g.: safe/kernel contractions ([AM85, Han94]), system of spheres-based contractions ([Gro88]) and epistemic entrenchment-based contractions ([G ar88, GM88]). Besides, several generalizations of such model were investigated. In that regard we emphasise the presentation of models which accounted for contractions by sets of sentences rather than only by a single sentence, i.e. multiple contractions. However, until now, only two of the above mentioned models have been generalized in the sense of addressing the case of contractions by sets of sentences: The partial meet multiple contractions were presented in [Han89, FH94], while the kernel multiple contractions were introduced in [FSS03]. In this thesis we propose two new constructive models of multiple contraction functions, namely the system of spheres-based and the epistemic entrenchment-based multiple contractions which generalize the models of system of spheres-based and of epistemic entrenchment-based contractions, respectively, to the case of contractions (of theories) by sets of sentences. Furthermore, analogously to what is the case in what concerns the corresponding classes of contraction functions by one single sentence, those two classes are identical and constitute a subclass of the class of partial meet multiple contractions. Additionally, and as the rst step of the procedure that is here followed to obtain an adequate de nition for the system of spheres-based multiple contractions, we present a possible worlds semantics for the partial meet multiple contractions analogous to the one proposed in [Gro88] for the partial meet contractions (by one single sentence). Finally, we present yet an axiomatic characterization for the new class(es) of multiple contraction functions that are here introduced.Eduardo Ferm

System of spheres-based multiple contractions

We propose a new class of multiple contraction operations — the system of spheres-based multiple contractions — which are a generalization of Grove’s system of spheres-based (singleton) contractions to the case of contractions by (possibly non-singleton) sets of sentences. Furthermore, we show that this new class of functions is a subclass of the class of the partial meet multiple contractions.info:eu-repo/semantics/publishedVersio

AGM 25 years: twenty-five years of research in belief change

The 1985 paper by Carlos Alchourrón (1931–1996), Peter Gärdenfors, and David Makinson (AGM), “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions” was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twenty five years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original framework, iterated change, applications of the model, its connections with other formal frameworks, computatibility of AGM operations, and criticism of the model.info:eu-repo/semantics/publishedVersio

An Investigation of Darwiche and Pearl's Postulates for Iterated Belief Update

Belief revision and update, two significant types of belief change, both focus on how an agent modify her beliefs in presence of new information. The most striking difference between them is that the former studies the change of beliefs in a static world while the latter concentrates on a dynamically-changing world. The famous AGM and KM postulates were proposed to capture rational belief revision and update, respectively. However, both of them are too permissive to exclude some unreasonable changes in the iteration. In response to this weakness, the DP postulates and its extensions for iterated belief revision were presented. Furthermore, Rodrigues integrated these postulates in belief update. Unfortunately, his approach does not meet the basic requirement of iterated belief update. This paper is intended to solve this problem of Rodrigues's approach. Firstly, we present a modification of the original KM postulates based on belief states. Subsequently, we migrate several well-known postulates for iterated belief revision to iterated belief update. Moreover, we provide the exact semantic characterizations based on partial preorders for each of the proposed postulates. Finally, we analyze the compatibility between the above iterated postulates and the KM postulates for belief update

Belief Change in Reasoning Agents: Axiomatizations, Semantics and Computations

The capability of changing beliefs upon new information in a rational and efficient way is crucial for an intelligent agent. Belief change therefore is one of the central research fields in Artificial Intelligence (AI) for over two decades. In the AI literature, two different kinds of belief change operations have been intensively investigated: belief update, which deal with situations where the new information describes changes of the world; and belief revision, which assumes the world is static. As another important research area in AI, reasoning about actions mainly studies the problem of representing and reasoning about effects of actions. These two research fields are closely related and apply a common underlying principle, that is, an agent should change its beliefs (knowledge) as little as possible whenever an adjustment is necessary. This lays down the possibility of reusing the ideas and results of one field in the other, and vice verse. This thesis aims to develop a general framework and devise computational models that are applicable in reasoning about actions. Firstly, I shall propose a new framework for iterated belief revision by introducing a new postulate to the existing AGM/DP postulates, which provides general criteria for the design of iterated revision operators. Secondly, based on the new framework, a concrete iterated revision operator is devised. The semantic model of the operator gives nice intuitions and helps to show its satisfiability of desirable postulates. I also show that the computational model of the operator is almost optimal in time and space-complexity. In order to deal with the belief change problem in multi-agent systems, I introduce a concept of mutual belief revision which is concerned with information exchange among agents. A concrete mutual revision operator is devised by generalizing the iterated revision operator. Likewise, a semantic model is used to show the intuition and many nice properties of the mutual revision operator, and the complexity of its computational model is formally analyzed. Finally, I present a belief update operator, which takes into account two important problems of reasoning about action, i.e., disjunctive updates and domain constraints. Again, the updated operator is presented with both a semantic model and a computational model

A Generalized Notion of Time for Modeling Temporal Networks

Most approaches for modeling and analyzing temporal networks do not explicitly discuss the underlying notion of time. In this paper, we therefore introduce a generalized notion of time for temporal networks. Our approach also allows for considering non-deterministic time and incomplete data, two issues that are often found when analyzing data-sets extracted from online social networks, for example. In order to demonstrate the consequences of our generalized notion of time, we also discuss the implications for the computation of (shortest) temporal paths in temporal networks

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