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A model of information retrieval based on a terminological logic
, 1993
"... According to the logical model of Information Retrieval (IR), the task of IR can be described as the extraction, from a given document base, of those documents d that, given a query q, make the formula d → q valid, where d and q are formulae of the chosen logic and “→ ” denotes the brand of logical ..."
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Cited by 101 (20 self)
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According to the logical model of Information Retrieval (IR), the task of IR can be described as the extraction, from a given document base, of those documents d that, given a query q, make the formula d → q valid, where d and q are formulae of the chosen logic and “→ ” denotes the brand of logical implication formalized by the logic in question. In this paper, although essentially subscribing to this view, we propose that the logic to be chosen for this endeavour be a Terminological Logic (TL): accordingly, the IR task becomes that of singling out those documents d such that d � q, where d and q are terms of the chosen TL and “�” denotes subsumption between terms. We call this the terminological model of IR. TLs are particularly suitable for modelling IR; in fact, they can be employed: 1) in representing documents under a variety of aspects (e.g. structural, layout, semantic content); 2) in representing queries; 3) in representing lexical, “thesaural ” knowledge. The fact that a single logical language can be used for all these representational endeavours ensures that all these sources of knowledge will participate in the retrieval process in a uniform and principled way. In this paper we introduce Mirtl, a TL for modelling IR according to the above guidelines; its syntax, formal semantics and inferential algorithm are described. 1
A Sequent Calculus for Reasoning in Fourvalued Description Logics
 IN PROC. OF THE INT. CONF. ON ANALYTIC TABLEAUX AND RELATED METHODS (TABLEAUX97), NUMBER 1227 IN LECTURE NOTES IN ARTIFICIAL INTELLIGENCE
, 1997
"... Description Logics (DLs, for short) provide a logical reconstruction of the socalled framebased knowledge representation languages. Originally, fourvalued DLs have been proposed in order to develop expressively powerful DLs with tractable subsumption algorithms. Recently, fourvalued DLs have bee ..."
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Cited by 28 (5 self)
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Description Logics (DLs, for short) provide a logical reconstruction of the socalled framebased knowledge representation languages. Originally, fourvalued DLs have been proposed in order to develop expressively powerful DLs with tractable subsumption algorithms. Recently, fourvalued DLs have been proposed as a model for (multimedia) document retrieval. In this context, the main reasoning task is instance checking. Unfortunately, the known subsumption algorithms for fourvalued DLs, based on "structural" subsumption, do not work with respect to the semantics proposed in the DLbased approach to document retrieval. Moreover, they are unsuitable for solving the instance checking problem, as this latter problem is more general than the subsumption problem. We present an alternative decision procedure for fourvalued DLs with the aim to solve these problems. The decision procedure is a sequent calculus for instance checking. Since in general the fourvalued subsumption problem can be ...
Logical and computational properties of the description logic MIRTL
 Proceedings of DL95, 4th International Workshop on Description Logics
, 1995
"... In recent years a number of positive (i.e. tractability and decidability) results have been found concerning the computational complexity of Description Logics (DLs) [Buchheit et al.,1993; Donini et al.,1991; ..."
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Cited by 6 (2 self)
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In recent years a number of positive (i.e. tractability and decidability) results have been found concerning the computational complexity of Description Logics (DLs) [Buchheit et al.,1993; Donini et al.,1991;
Document retrieval by relevance terminological logics
 Proceedings of MIRO95, Workshop on Multimedia Information Retrieval
, 1996
"... Information Retrieval (IR) is presented as the task of retrieving the documents that are relevant to a given query. In the context of a Terminological Logic (TL) based approach to IR, this amounts to embodying a notion of relevance in the logical implication relation of the chosen TL. Among the many ..."
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Information Retrieval (IR) is presented as the task of retrieving the documents that are relevant to a given query. In the context of a Terminological Logic (TL) based approach to IR, this amounts to embodying a notion of relevance in the logical implication relation of the chosen TL. Among the many possible readings of the term “relevance”, the one captured by relevance logic, and in particular by firstorder tautological entailment, can be viewed as a promising source of inspiration, to the end of incorporating a logicbased form of relevance in the inference mechanism of TLs. The aim of this paper is to present a Relevant Terminological Logic, while maintaining the desired “relevance” flavour of relevance logics, which could be considered as a base towards a suitable document description logic for IR purposes. 1
Complexity Sources in Fuzzy Description Logic
"... Abstract. In recent years many Fuzzy Description Logics (FDLs) based on infinite tnorms have been proved to be undecidable. On the other hand, several FDLs based on finite tnorms, not only have been proved to be decidable, but they have been proved to belong to the same complexity classes as the c ..."
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Abstract. In recent years many Fuzzy Description Logics (FDLs) based on infinite tnorms have been proved to be undecidable. On the other hand, several FDLs based on finite tnorms, not only have been proved to be decidable, but they have been proved to belong to the same complexity classes as the corresponding crisp DLs. In light of such results, a question that naturally arises is whether the finitevalued fuzzy framework is no more complex than the crispvalued formalism. The aim of this work is to analyze some of the complexity sources that are not present in the crisp framework. To this end, we will consider FDL languages with low expressivity that allow us to observe how the need for more complex deciding strategies, not required in the crisp framework, arises in manyvalued FDLs. 1
Document Retrieval by Relevance Terminological Logics
, 1995
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Terminological Logics (TLs, also known as Frame Representation Languages
"... Terminological Logics are knowledge representation formalisms of enormous applicative interest, as they are specifically oriented to the vast class of application domains that are describable by means of taxonomic organizations of complex objects. A number of results relative to the computational co ..."
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Terminological Logics are knowledge representation formalisms of enormous applicative interest, as they are specifically oriented to the vast class of application domains that are describable by means of taxonomic organizations of complex objects. A number of results relative to the computational complexity of terminological logics have recently appeared in the literature. Unfortunately, most of these results are “negative ” in nature, as they show that, in the logics they refer to, deciding subsumption (i.e. the metalinguistic relation which corresponds to validity in standard logics) is computationally intractable. In this paper, after briefly introducing the fundamental concepts underlying terminological logics, we show that computing subsumption is O(n log n)intheALN logic, an extension of Brachman and Levesque’s FL − logic. ALN is obtained by endowing FL − with the two operators atleast and atmost, which allow the specification of number restrictions, and the operator anot, which introduces a limited form of negation. The result we present is of theoretical significance, in that ALN is one of the few terminological logics that have been shown tractable. ALN is also a pragmatically significant extension of FL − , as it results from the addition of operators of considerable applicative interest.