Power constructs and propositional systems

Bibliography : p. 161-176.Propositional systems are deductively closed sets of sentences phrased in the language of some propositional logic. The set of systems of a given logic is turned into an algebra by endowing it with a number of operations, and into a relational structure by endowing it with a number of relations. Certain operations and relations on systems arise from some corresponding base operation or relation, either on sentences in the logic or on propositional valuations. These operations and relations on systems are called power constructs. The aim of this thesis is to investigate the use of power constructs in propositional systems. Some operations and relations on systems that arise as power constructs include the Tarskian addition and product operations, the contraction and revision operations of theory change, certain multiple- conclusion consequence relations, and certain relations of verisimilitude and simulation. The logical framework for this investigation is provided by the definition and comparison of a number of multiple-conclusion logics, including a paraconsistent three-valued logic of partial knowledge

Informative Armstrong RDF datasets for n-Ary relations

The W3C standardized Semantic Web languages enable users to capture data without a schema in a manner which is intuitive to them. The challenge is that, for the data to be useful, it should be possible to query the data and to query it efficiently, which necessitates a schema. Understanding the structure of data is thus important to both users and storage implementers: The structure of the data gives insight to users in how to query the data while storage implementers can use the structure to optimize queries. In this paper we propose that data mining routines be used to infer candidate n-ary relations with related uniqueness- and null-free constraints, which can be used to construct an informative Armstrong RDF dataset. The benefit of an informative Armstrong RDF dataset is that it provides example data based on the original data which is a fraction of the size of the original data, while capturing the constraints of the original data faithfully. A case study on a DBPedia person dataset showed that the associated informative Armstrong RDF dataset contained 0.00003% of the statements of the original DBPedia dataset.https://www.iospress.nl/bookserie/frontiers-in-artificial-intelligence-and-applicationsam2019Informatic

Principles of KLM-style Defeasible Description Logics

The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferen- tial and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our seman- tics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC

Rational Defeasible Reasoning for Description Logics

In this paper, we extend description logics (DLs) with non-monotonic reasoning fea- tures. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus and colleagues in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investi- gate syntactic properties (à la Gentzen) for both preferential and rational subsumptions and prove representation results for the description logic ALC. Such representation results pave the way for more effective decision procedures for defeasible reasoning in DLs. We analyse the problem of non-monotonic reasoning in DL at the level of entailment for both TBox and ABox reasoning, and present an adaptation of rational closure for the DL en- vironment. Importantly, we also show that computing it can be reduced to classical ALC entailment. One of the stumbling blocks to evaluating performance scalability of rational closure is the absence of naturally occurring DL-based ontologies with defeasible features. We overcome this barrier by devising an approach to introduce defeasible subsumption into classical real-world ontologies. Such semi-natural defeasible ontologies, together with a purely artificial set, are used to test our rational closure algorithms. We found that performance is scalable on the whole with no major bottlenecks

Relations and programs

Thesis (M. Sc.) -- University of Stellenbosch, 1988.Full text to be digitised and attached to bibliographic record

Preferential Modalities Revisited

International audienc

Preferential Tableaux for Contextual Defeasible ALC

International audienc

Towards a Logic of Dilation

International audienc