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Recent years have seen the advent of large and complex ontologies, most notably in the medical domain. As a consequence, structuring mechanisms for ontolo-gies are nowadays viewed as an indispensible tool. A basic such mechanism is the automatic decomposition of the vocabulary of an ontology into independent parts. In this paper, we study decompositions… (More)

The integration of the various specialized components of cognitive systems poses a challenge, in particular for those architectures that combine planning , inference, and human-computer interaction (HCI). An approach is presented that exploits a single source of common knowledge contained in an ontology. Based upon the knowledge contained in it, specialized… (More)

An inductive probabilistic approach to formal concept analysis (FCA) is proposed in which probability on formal contexts is considered; probabilistic formal concepts that have predictive force are defined: nonclassified objects can be assigned to earlier found probabilistic formal concepts; random attributes are eliminated from probabilistic formal… (More)

We generalize the main notions of Formal Concept Analysis with the ideas of the semantic probabilistic inference. We demonstrate that under standard restrictions, our definitions completely correspond to the original notions of Formal Concept Analysis. From the point of view of applications, we propose a method of recovering concepts in formal contexts in… (More)

The research on applied logic in the mid 2000s has brought important method-ological and algorithmic results on modularization of finitely axiomatizable logical theories. In particular, the research has been focused on the question whether logical theories have an inherent modular structure which could allow one to identify, in some sense, independent "… (More)

- Denis Ponomaryov
- 2008

We prove that each elementary theory has a unique decomposition into indecomposable components and formulate a decomposability criterion. Definition 1 A theory T of signature Σ is called decomposable, if T is the deductive closure in the predicate calculus of signature Σ of all sentences of some theories S 1 and S 2 with the disjoint signatures Σ 1 and Σ 2… (More)

- Denis Ponomaryov
- 2009

In the paper, a natural class of logical calculi is fixed for which we formulate the notion of a ∆–decomposable set of formulas. We demonstrate that the property of uniqueness of signature decom-positions holds in those calculi of this class that have the Craig interpolation property. In conclusion, we give a sufficient condition for the ∆–decomposability… (More)

We present an approach for integrating ontological reasoning and planning within cognitive systems. Patterns and mechanisms that suitably link planning domains and interrelated knowledge in an ontology are devised. In particular , this enables the use of (standard) ontology reasoning for extending a (hierarchical) planning domain. Furthermore, explanations… (More)

AND-decomposition of a boolean formula means finding two (or several) formulas such that their conjunction is equivalent to the given one. Decomposition is called disjoint if the component formulas do not have variables in common. In the paper, we show that deciding AND-decomposability is intractable for boolean formulas given in CNF or DNF and prove… (More)