In this paper we explore a class of belief update operators, in which the definition of the operator is compositional with respect to the sentence to be added. The goal is to provide an update operator that is intuitive, in that its definition is based on a recursive decomposition of the update sentence’s structure, and that may be reasonably implemented. In addressing update, we first provide a definition phrased in terms of the models of a knowledge base. While this operator (...) satisfies a core group of the benchmark Katsuno Mendelzon update postulates, not all of the postulates are satisfied. Other Katsuno Mendelzon postulates can be obtained by suitably restricting the syntactic form of the sentence for update, as we show. In restricting the syntactic form of the sentence for update, we also obtain a hierarchy of update operators with Winslett’s standard semantics as the most basic interesting approach captured. We subsequently give an algorithm which captures this approach; in the general case the algorithm is exponential, but with some not unreasonable assumptions we obtain an algorithm that is linear in the size of the knowledge base. Hence the resulting approach has much better complexity characteristics than other operators in some situations. We also explore other compositional belief change operators: erasure is developed as a dual operator to update; we show that a forget operator is definable in terms of update; and we give a definition of the compositional revision operator. We obtain that compositional revision, under the most natural definition, yields the Satoh revision operator. (shrink)

We pursue an account of merging through the use of geodesic semantics, the semantics based on the length of the shortest path on a graph. This approach has been fruitful in other areas of belief change such as revision and update. To this end, we introduce three binary merging operators of propositions defined on the graph of their valuations and we characterize them with a finite set of postulates.

The 1985 paper by Carlos Alchourrón, Peter Gärdenfors, and David Makinson, “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. (shrink)

The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources (...) of classical logic. Among the contributions included in the volume, one chapter focuses on the “inferential preferential method”, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson’s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the role of logic in philosophy. (shrink)

Communication between natural or artificial agents relies on the use of a common vocabulary. Since sharing terms does not necessarily imply that the terms have exactly the same meanings for all agents, integrating statements into a formal ontology requires mechanisms for resolving conflicts that are caused by the ambiguity of terms specified in different but similar ontologies.We define and analyze a family of ontology-revision operators that resolve conflicts by disambiguating concept symbols occurring in both the ontology and the trigger statements. (...) The operators yield bridging axioms relating the different readings of the terms and, by including representations for both readings, preserve the initial ontology as well as the trigger statements. The operators differ regarding which reading of the ambiguous term is assigned to further uses of the common term and regarding the semantic relation assumed between the two readings. The ontology-revision operators are analyzed regarding their adaptability to consistent sequences of trigger statements. One group of operators preserves all conflicts with the trigger sequence. Operators from the other group can resolve the conflicts, which is demonstrated by showing under which conditions weak type-2 operators yield stabilizing sequences of ontologies. Stronger type-2 operators can result in closer approximations of the terminology underlying the sequence of trigger statements but can also yield non-stabilizing sequences of ontologies. (shrink)