Some Computational Problems Related to Pseudo-intents

We investigate the computational complexity of several decision, enumeration and counting problems related to pseudo-intents. We show that given a formal context and a set of its pseudo-intents, checking whether this context has an additional pseudo-intent is in conp and it is at least as hard as checking whether a given simple hypergraph is saturated. We also show that recognizing the set of pseudo-intents is also in conp and it is at least as hard as checking whether a given hypergraph is the transversal hypergraph of another given hypergraph. Moreover, we show that if any of these two problems turns out to be conp-hard, then unless p = np, pseudo-intents cannot be enumerated in output polynomial time. We also investigate the complexity of finding subsets of a given Duquenne-Guigues Base from which a given implication follows. We show that checking the existence of such a subset within a specified cardinality bound is np-complete, and counting all such minimal subsets is #p-complete

On the Complexity of Axiom Pinpointing in Description Logics

We investigate the computational complexity of axiom pinpointing in Description Logics, which is the task of finding minimal subsets of a knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic EL. We show complexity results for several other related decision and enumeration problems for these fragments that extend to more expressive logics. In particular we show that hardness of these problems depends not only on expressivity of the fragment but also on the shape of the axioms used

On the complexity of enumerating pseudo-intents

AbstractWe investigate whether the pseudo-intents of a given formal context can efficiently be enumerated. We show that they cannot be enumerated in a specified lexicographic order with polynomial delay unless P=NP. Furthermore we show that if the restriction on the order of enumeration is removed, then the problem becomes at least as hard as enumerating minimal transversals of a given hypergraph. We introduce the notion of minimal pseudo-intents and show that recognizing minimal pseudo-intents is polynomial. Despite their less complicated nature, surprisingly it turns out that minimal pseudo-intents cannot be enumerated in output-polynomial time unless P=NP

Completing Description Logic Knowledge Bases using Formal Concept Analysis

We propose an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the assertional part and by a domain expert. The use of techniques from Formal Concept Analysis ensures that, on the one hand, the interaction with the expert is kept to a minimum, and, on the other hand, we can show that the extended knowledge base is complete in a certain sense

Kavram örgüleri hakkında temel teoremin Isabelle/HOL'da ispatı

Formel Concept Analysis is an emerging field of applied mathematics based on a lattice-theoretic formalization of the notions of concept and conceptual hierarchy. It thereby facilitates mathematical thinking for conceptual data analysis and knowledge processing. Isabelle, on the other hand, is a generic interactive theory development environment for implementing logical formalisms. It has been instantiated to support reasoning in several object-logics. Specialization of Isabelle for Higher Order Logic is called Isabelle/HOL. Our long term is to formalize the theory of Formal Concept Analysis in Isabelle/HOL. This will provide a mechanized theory for researchers who want to prove their own theorems with utmost precision, and for developers who want to design knowledge processing algorithms. The speccific accomplishment of this thesis is a machinechecked version of the proof of the Basic Theorem of Concept Lattices, which appears in the book "Formal Concept Analysisé by Ganter and Wille. As a by product, the underlying lattice theory by F. Kammueller has been extended.M.S. - Master of Scienc

Some Computational Problems Related to Pseudo-intents

We investigate the computational complexity of several decision, enumeration and counting problems related to pseudo-intents. We show that given a formal context and a set of its pseudo-intents, checking whether this context has an additional pseudo-intent is in conp and it is at least as hard as checking whether a given simple hypergraph is saturated. We also show that recognizing the set of pseudo-intents is also in conp and it is at least as hard as checking whether a given hypergraph is the transversal hypergraph of another given hypergraph. Moreover, we show that if any of these two problems turns out to be conp-hard, then unless p = np, pseudo-intents cannot be enumerated in output polynomial time. We also investigate the complexity of finding subsets of a given Duquenne-Guigues Base from which a given implication follows. We show that checking the existence of such a subset within a specified cardinality bound is np-complete, and counting all such minimal subsets is #p-complete

Some Computational Problems Related to Pseudo-intents

We investigate the computational complexity of several decision, enumeration and counting problems related to pseudo-intents. We show that given a formal context and a set of its pseudo-intents, checking whether this context has an additional pseudo-intent is in conp and it is at least as hard as checking whether a given simple hypergraph is saturated. We also show that recognizing the set of pseudo-intents is also in conp and it is at least as hard as checking whether a given hypergraph is the transversal hypergraph of another given hypergraph. Moreover, we show that if any of these two problems turns out to be conp-hard, then unless p = np, pseudo-intents cannot be enumerated in output polynomial time. We also investigate the complexity of finding subsets of a given Duquenne-Guigues Base from which a given implication follows. We show that checking the existence of such a subset within a specified cardinality bound is np-complete, and counting all such minimal subsets is #p-complete

On the Complexity of Axiom Pinpointing in Description Logics

We investigate the computational complexity of axiom pinpointing in Description Logics, which is the task of finding minimal subsets of a knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic EL. We show complexity results for several other related decision and enumeration problems for these fragments that extend to more expressive logics. In particular we show that hardness of these problems depends not only on expressivity of the fragment but also on the shape of the axioms used

On the Complexity of Axiom Pinpointing in Description Logics

We investigate the computational complexity of axiom pinpointing in Description Logics, which is the task of finding minimal subsets of a knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic EL. We show complexity results for several other related decision and enumeration problems for these fragments that extend to more expressive logics. In particular we show that hardness of these problems depends not only on expressivity of the fragment but also on the shape of the axioms used