## Mirlog: A logic for multimedia information retrieval (1998)

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Venue: | LOGIC AND UNCERTAINTY IN INFORMATION RETRIEVAL: ADVANCED MODELS FOR THE |

Citations: | 8 - 2 self |

### BibTeX

@INPROCEEDINGS{Meghini98mirlog:a,

author = {Carlo Meghini and Fabrizio Sebastiani and Umberto Straccia},

title = {Mirlog: A logic for multimedia information retrieval},

booktitle = {LOGIC AND UNCERTAINTY IN INFORMATION RETRIEVAL: ADVANCED MODELS FOR THE},

year = {1998},

pages = {151--185},

publisher = {Kluwer Academic Publishing}

}

### OpenURL

### Abstract

This chapter presents a logic for the retrieval of multimedia information, whose ultimate goal is to model retrieval as an uncertain logical inference, in accordance to the logic-based view of retrieval. The logic being presented is the product of a number of extensions to a Description Logic, which constitutes the kernel of our model. Each extension is meant to capture an important aspect of the retrieval endeavour that is not adequately dealt with by the kernel logic. The extensions are: a 4-valued semantics, aiming at capturing relevance in retrieval; closure assertions, aiming at allowing closed-world reading of selectively specified parts of a document base; fuzzy assertions, aiming at handling the uncertainty intrinsic in retrieval. The resulting logic is to be understood as a modelling retrieval tool, which can be used for the specification and the rapid prototyping of applications.

### Citations

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Citation Context ... to a query can 23 thus be established only up to a limited degree of certainty. To this end, we extend Mirlog with fuzzy assertions. Fuzzy assertions take inspiration from Zadeh's work on fuzzy sets =-=[58]-=-. A fuzzy set A with respect to a set X is characterized by a membership function A : X # [0, 1], assigning an A-membership degree, A (x), to each element x in X. This membership degree gives us an es... |

1651 |
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Citation Context ...the language). 22 It is worth noting that there is a big methodological di#erence between our approach and NCWA, or, for that matter, all other approaches with the same goal, as for example in Datalog=-=[1]-=-: in Mirlog, CWA is not something happening behind the scene, but is explicitly called upon, via closures, by the document indexer, who has therefore full control of the situation, and is free to appl... |

785 |
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Citation Context ... A # B) # (# A # # B). # has 2 di#erent letters, which means that it has 4 possible two-valued interpretations. As a consequence, a semantic based decision procedure like the Davis-Longemann-Loveland =-=[12]-=-, can test its satisfiability after enumerating at most 4 interpretations. On the other hand, an analytic tableaux calculus [20] using the two rules: #-rule A, B A # B #-rule A B A # B (13) generates ... |

441 |
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Citation Context ..., a semantic based decision procedure like the Davis-Longemann-Loveland [12], can test its satisfiability after enumerating at most 4 interpretations. On the other hand, an analytic tableaux calculus =-=[20]-=- using the two rules: #-rule A, B A # B #-rule A B A # B (13) generates a proof tree with O(2 3 ) leafs, as shown in Figure 3. Essentially, each path from a leaf to the root of the tree is an attempt ... |

299 | A logic of implicit and explicit belief
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Citation Context ...tional properties: while decision in the general case is co-NP-complete, whenever # and # are formulae in Conjunctive Normal Form there exists an O(|#|s|#|) algorithm that tests the validity of # # # =-=[32]-=-. Relevance description logics based on a 4-valued semantics have already been proposed by PatelSchneider for use in knowledge representation, and have been proven to possess a generally better comput... |

282 | An analysis of first-order logics of probability
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Citation Context ...xist well-known techniques for reasoning in fuzzy logics (see e.g. [10, 29, 31]). This is not the case for alternative logics, such as, for instance, probabilistic logics [26, 30, 49]. In particular, =-=[25]-=- shows that probabilistic reasoning is computationally more di#cult than non-probabilistic reasoning, and in most cases a complete axiomatization is missing. Fuzzy logic is not appropriate to deal wit... |

239 | H.: Possibilistic logic
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Citation Context ...lable information we may only be able to estimate to what degree a certain object in an image is e.g. a polygon. The logics dealing with this kind of uncertainty have been called Possibilistic Logics =-=[17]-=-. Possibilistic DLs are discussed in [28]. The combination of possibilistic and fuzzy logic would lead to the treatment of uncertain fuzzy assertions, i.e. fuzzy assertions for which the available ref... |

236 | The Complexity of Concept Languages
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Citation Context ...tially an analytic tableaux-based decision procedure, for deciding KB satisfiability. This proof 28 method has also allowed the derivation of many complexity results concerning 2-valued DLs (see e.g. =-=[8, 13]-=-) 11 . If we switch to a 4-valued setting, we need an alternative proof procedure as relation (12) no longer holds. There exists a well known subsumption testing procedure, which is a DL adaption of L... |

194 | Decidable reasoning in terminological knowledge representation systems
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Citation Context ...tially an analytic tableaux-based decision procedure, for deciding KB satisfiability. This proof 28 method has also allowed the derivation of many complexity results concerning 2-valued DLs (see e.g. =-=[8, 13]-=-) 11 . If we switch to a 4-valued setting, we need an alternative proof procedure as relation (12) no longer holds. There exists a well known subsumption testing procedure, which is a DL adaption of L... |

189 |
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Citation Context ...d Mirtl, embodied a different choice of operators than ALC. The reason why we have now opted for a slight extension of ALC is twofold: • in a recent study [9] we have found that Mirtl has, unlike ALC =-=[47]-=-, bad computational properties; • ALC is universally considered the “standard” description logic (as much as K is considered the “standard” modal logic) and is therefore regarded as the most convenien... |

188 | Description Logics in Data Management
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Citation Context ...g [36], the kernel of our model is based on a logic from the class of Description Logics 1 (DLs), the descendants of the frame-based knowledge representation languages of the late seventies (see e.g. =-=[5]-=-). The basic entities of the language of a DL are: individuals (denoted by the letter a, with optional subscript), representing objects of the application domain; concepts (letter C, with optional sub... |

183 | A non-classical logic for Information Retrieval - Rijsbergen - 1986 |

170 |
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Citation Context ...that is, is decided by the user from session to session and from time to time, and is then heavily dependent on judgments where highly subjective and scarcely reproducible factors are brought to bear =-=[3, 46]-=-. The very possibility of a logical theory of IR is then dependent on the possibility of giving a formal definition of relevance capable of approximating the operational definition of relevance given ... |

167 | A semantics and complete algorithm for subsumption in the classic description logic
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(Show Context)
Citation Context ...s that reflects the intuition behind these assertions. And this is precisely our approach. Furthermore, it is not at all clear how the closure of a role for a certain individual, a feature of classic =-=[6]-=- that is o#ered by our model under the name of pointwise role closure, would be simulated in the epistemic approach. 4.3 Knowledge bases with closures Let a be an individual, P a primitive role and T ... |

149 |
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(Show Context)
Citation Context ...ed Mirtl, embodied a di#erent choice of operators than ALC. The reason why we have now opted for a slight extension of ALC is twofold: . in a recent study [9] we have found that Mirtl has, unlike ALC =-=[47], bad computational -=-properties; . ALC is universally considered the "standard" description logic (as much as K is considered the "standard" modal logic) and is therefore regarded as the most convenien... |

115 |
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(Show Context)
Citation Context ...ction of meaning between # and #" (or, more generally, the idea of # being relevant to #) has been shown to be amenable to formal treatment by the logicians who defined relevance (or relevant) lo=-=gics [2, 19]-=-. Relevance logics attempt to formalise a conditional notion in which relevance is a primary concern. By doing this, they challenge classical logic and its extensions in a number of ways, i.e. by intr... |

99 |
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(Show Context)
Citation Context ...have a Boolean representation, and in which the relevance of one to the other is the parameter of interest. In addition, E fde has a 4-valued denotational semantics, independently developed by Belnap =-=[4]-=- and Dunn [18]. Compliance with the denotational approach makes this logic amenable to the various extensions (e.g. to reasoning about uncertainty) needed for modelling IR. The logic E fde has also be... |

98 | Building decision procedures for modal logics from propositional decision procedures - the case study of modal K(m
- Giunchiglia, Sebastiani
- 2000
(Show Context)
Citation Context ...x methods for two-valued DLs are quite ine#cient, as the length of the proof of a formula may be exponential in the length of the formula rather than in the number of di#erent letters occurring in it =-=[23, 22]-=-. In fact, consider the formula: # = (A # B) # (# A # B) # (# A # # B). # has 2 di#erent letters, which means that it has 4 possible two-valued interpretations. As a consequence, a semantic based deci... |

97 |
Fuzzy Sets and Systems
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Citation Context ...(x)}, and A (x) = 1 - A (x), where A is the complement of A in X. Other membership functions have been proposed, but it is not our aim to investigate them here (the interested reader can consult e.g. =-=[16]-=-). When we switch to logic, and to DLs in particular, we have terms rather than sets and speak about degrees of truth instead of membership degrees. For instance, the assertion that individual a is an... |

94 | Philosophy of Logics - Haack - 1978 |

94 | C.: A model of information retrieval based on a terminological logic
- Meghini, Sebastiani, et al.
- 1993
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Citation Context ...ctured objects, allowing to view the problem of retrieval as one of deciding whether an object (a document) is an instance of a class (a query). As we show in Section 2, and as we more fully argue in =-=[36], thi-=-s allows a more natural account of retrieval, and also allows both documents 4 and queries to be given rich, structured representations that describe them under multiple viewpoints. The same "obj... |

73 | Adding epistemic operators to concept languages
- Donini, Lenzerini, et al.
- 1992
(Show Context)
Citation Context ...only on KBs that are universal theories without equality. Notoriously, a Mirlog KB is not in general a universal theory 10 . Versions of the CWA specifically formulated for DLs have recently appeared =-=[14, 15] which are-=- based on the use (within the query language) of an explicit epistemic operator K, whose natural language reading is the adjective "known". The basic idea behind these proposals is to enforc... |

73 | Towards an Information Logic
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- 1989
(Show Context)
Citation Context ...s (see e.g. [24, Chapter 10]), much beyond the case of omonimy. Therefore, it seems just natural to think that, if we view retrieval as essentially consisting of a disguised form of logical inference =-=[55]-=-, relevance logic and IR might constitute the theoretical side and the applied side of the same coin. This eventually calls for the adoption of a relevance logic as the non-probabilistic kernel of a f... |

71 |
Probabilistic description logics
- HEINSOHN
- 1994
(Show Context)
Citation Context ...preted as the degree of relevance of the document identified by a to the query Q. The choice of fuzzy set theory as a way of endowing a DL with the capability to deal with uncertainty is not uncommon =-=[26, 28, 30, 49]-=- and can be motivated both from the syntactical and the semantical point of view. From a semantical point of view, fuzzy logics capture the notion of vague concept, that is a concept that is intrinsic... |

70 |
Intuitive Semantics for First-Degree Entailments and "Coupled Trees
- Dunn
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(Show Context)
Citation Context ...#erent notion of relevance. The relevance logic that we think best complies with the requirements of the IR world is the logic E fde , also called the logic of first degree (tautological) entailments =-=[18]. This con-=-sists of the fragment of the famous relevance logics E and R that deals with first degree entailments only, i.e. pairs of propositional (classical) formulae separated by one "#" symbol. This... |

66 |
Logic and the Complexity of Reasoning
- Levesque
- 1992
(Show Context)
Citation Context ...ick inferences that do not overtax its resources. Those inferences that 2-valued semantics licenses and 4-valued semantics does not are those for drawing which the agent must reason, as Levesque says =-=[33]-=-, in puzzle mode, i.e. in the style that humans adopt once we try to solve a challenging mathematical problem or a logical puzzle. This interpretation brings further evidence to the fact that Mirlog i... |

59 | A probabilistic terminological logic for modelling information retrieval
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(Show Context)
Citation Context ...thor Italian)) encoded in the "Lisp-like" syntax of [36]. Also, we use the now standard name "Description logics" instead of the name "Terminological logics" used in [36]=-=. 3 The DL we had employed in [36, 48]-=-, called Mirtl, embodied a di#erent choice of operators than ALC. The reason why we have now opted for a slight extension of ALC is twofold: . in a recent study [9] we have found that Mirtl has, unlik... |

57 | A SAT-based decision procedure for ALC
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(Show Context)
Citation Context ...x methods for two-valued DLs are quite ine#cient, as the length of the proof of a formula may be exponential in the length of the formula rather than in the number of di#erent letters occurring in it =-=[23, 22]-=-. In fact, consider the formula: # = (A # B) # (# A # B) # (# A # # B). # has 2 di#erent letters, which means that it has 4 possible two-valued interpretations. As a consequence, a semantic based deci... |

57 |
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Citation Context ...d for finite sets of first-order sentences without equality and whose prenex normal forms contain no existential quantifiers. If T is one such sets, then the naive closure of T , NCWA(T), is given by =-=[34]-=-: NCWA(T) = T # {A : T #|= A and A # HB(T )}, where HB(T ) is the Herbrand Base of T . Now, the first-order translation of a set of Mirlog assertions yields a set of sentences which may contain existe... |

57 |
A four-valued semantics for terminological logics
- Patel-Schneider
- 1989
(Show Context)
Citation Context ...ued semantics have already been proposed by PatelSchneider for use in knowledge representation, and have been proven to possess a generally better computational behaviour than their 2-valued analogues=-=[40, 41, 42, 43]-=-. The semantics we adopt departs from Patel-Schneider's, whose loss of inferential capabilities is too drastic for the needs of IR: in fact, that semantics sanctions the loss of modus ponens and, in g... |

56 |
Fuzzy Logic and the Resolution Principle
- Lee
- 1972
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Citation Context ...sy to see that fuzzy assertions play a key role in content descriptions of documents. From a proof theoretical point of view, there exist well-known techniques for reasoning in fuzzy logics (see e.g. =-=[10, 29, 31]-=-). This is not the case for alternative logics, such as, for instance, probabilistic logics [26, 30, 49]. In particular, [25] shows that probabilistic reasoning is computationally more di#cult than no... |

56 | A new Theoretical Framework for Information Retrieval - Rijsbergen - 1986 |

55 | The taming of the cut. Classical refutations with analytic cut
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Citation Context ...g the satisfiability of a formula, an analytic tableaux method performs syntactic branching, that is, a branching guided by the syntactic structure of the formula under consideration. As discussed in =-=[11]-=-, any application of the # - rule may generate two subtrees which are not mutually inconsistent, that is two subtrees which may share models. This is the case of the subtrees generated from the node m... |

49 | Entailment: the logic of relevance and necessity, volume 1 - Anderson, Belnap - 1975 |

35 |
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(Show Context)
Citation Context ...preted as the degree of relevance of the document identified by a to the query Q. The choice of fuzzy set theory as a way of endowing a DL with the capability to deal with uncertainty is not uncommon =-=[26, 28, 30, 49]-=- and can be motivated both from the syntactical and the semantical point of view. From a semantical point of view, fuzzy logics capture the notion of vague concept, that is a concept that is intrinsic... |

35 | A relevance terminological logic for information retrieval
- Meghini, Straccia
- 1996
(Show Context)
Citation Context ...t types of knowledge whose representation contributes to deciding retrieval, and that, while some of them are naturally interpreted in a closed way, some others require open-world reasoning (see also =-=[38]-=- for a fuller discussion of this point). In order to account for this phenomenon, we extend the logic with capabilities for selective closed-world reasoning ; this means the possibility of reasoning i... |

33 |
On closed-world data bases
- Reiter
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(Show Context)
Citation Context ...lock inferences that were previously valid. For instance, the following should hold: # # {CL(doc3)} # {Book[doc3]} #|= c Book[doc3]. 4.2 Relation to other approaches Since the seminal paper by Reiter =-=[44]-=-, many forms of closed-world assumption (CWA) have been investigated (see [34, Chapter 7] for a thorough review). The proposal most similar in spirit to ours is the so-called careful CWA [21], by mean... |

28 |
N.: Prolog-ELF: incorporating fuzzy logic
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(Show Context)
Citation Context ...sy to see that fuzzy assertions play a key role in content descriptions of documents. From a proof theoretical point of view, there exist well-known techniques for reasoning in fuzzy logics (see e.g. =-=[10, 29, 31]-=-). This is not the case for alternative logics, such as, for instance, probabilistic logics [26, 30, 49]. In particular, [25] shows that probabilistic reasoning is computationally more di#cult than no... |

25 |
Ex contradictione nihil sequitur, in
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(Show Context)
Citation Context ...dence. We will see that one of the e#ects of 4-valued semantics is the possibility of entertaining inconsistent beliefs about some proposition without this inconsistency "spreading" througho=-=ut the KB [56]-=-. This property , that we might dub the locality of inconsistency, is shared by other relevance logics, and is considered one of the advantages of relevance logics, especially when modelling the epist... |

24 |
A hybrid, decidable, logic-based knowledge representation system
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(Show Context)
Citation Context ...ued semantics have already been proposed by PatelSchneider for use in knowledge representation, and have been proven to possess a generally better computational behaviour than their 2-valued analogues=-=[40, 41, 42, 43]-=-. The semantics we adopt departs from Patel-Schneider's, whose loss of inferential capabilities is too drastic for the needs of IR: in fact, that semantics sanctions the loss of modus ponens and, in g... |

23 |
Negation as Failure: Careful Closure Procedure
- Gelfond, Przymusinska
- 1986
(Show Context)
Citation Context ...y Reiter [44], many forms of closed-world assumption (CWA) have been investigated (see [34, Chapter 7] for a thorough review). The proposal most similar in spirit to ours is the so-called careful CWA =-=[21]-=-, by means of which one can confine the closed-world reading to a pre-specified subset of predicate symbols only. Without going into the details of this and the other CWA proposals, we observe that ne... |

22 | A four-valued semantics for frame-based description languages
- Patel-Schneider
- 1986
(Show Context)
Citation Context ...ued semantics have already been proposed by PatelSchneider for use in knowledge representation, and have been proven to possess a generally better computational behaviour than their 2-valued analogues=-=[40, 41, 42, 43]-=-. The semantics we adopt departs from Patel-Schneider's, whose loss of inferential capabilities is too drastic for the needs of IR: in fact, that semantics sanctions the loss of modus ponens and, in g... |

22 |
On asking what a database knows
- Reiter
- 1990
(Show Context)
Citation Context ...to be Scottish. As made clear by these examples, the use of an epistemic operator in queries would allow one to ask questions not only about the world, but also about the state of knowledge of the KB =-=[45]-=-. It is by now evident that this use permits to capture, among other things, some form of CWA. However, clear connections between epistemic queries posed to DL KBs and the various CWA formulations hav... |

20 | A sequent calculus for reasoning in four-valued description logics
- Straccia
- 1997
(Show Context)
Citation Context ...o the di#erent DLs described in the literature. For space reason, we do not present this proof procedure here, the interested reader may refer to [37]. On the basis of this method, it has been proven =-=[51]-=- that deciding entailment (|= 4 ) for a language with closures but without definitions is a PSPACE-complete problem, while the same problem becomes EXPTIME-hard when definitions are considered. Recent... |

13 |
A sound and complete fuzzy logic system using Zadeh’s implication operator
- Chen, Kundu
- 1996
(Show Context)
Citation Context ...sy to see that fuzzy assertions play a key role in content descriptions of documents. From a proof theoretical point of view, there exist well-known techniques for reasoning in fuzzy logics (see e.g. =-=[10, 29, 31]-=-). This is not the case for alternative logics, such as, for instance, probabilistic logics [26, 30, 49]. In particular, [25] shows that probabilistic reasoning is computationally more di#cult than no... |

12 |
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(Show Context)
Citation Context ...t. And even granted that a program could come up with the semantic structure of any piece of text, the resulting logical theory would raise computational problems of unattackable complexity (see e.g. =-=[27]-=-). Things go from bad to worse once one moves from the case of textual documents, to that of documents pertaining to other media. The scenario in which IR systems are supposed to operate has undergone... |

12 | A non-classical logic for information retrieval. The Computer Journal 29,6 - Rijsbergen - 1986 |

10 | The Terminological Image Retrieval Model - Meghini, Sebastiani, et al. - 1997 |

8 |
Probabilistic reasoning in terminological logics
- Jäger
- 1994
(Show Context)
Citation Context ...preted as the degree of relevance of the document identified by a to the query Q. The choice of fuzzy set theory as a way of endowing a DL with the capability to deal with uncertainty is not uncommon =-=[26, 28, 30, 49]-=- and can be motivated both from the syntactical and the semantical point of view. From a semantical point of view, fuzzy logics capture the notion of vague concept, that is a concept that is intrinsic... |

6 | Logical and computational properties of the description logic MIRTL
- BUONGARZONI, MEGHINI, et al.
- 1995
(Show Context)
Citation Context ...]. 3 The DL we had employed in [36, 48], called Mirtl, embodied a di#erent choice of operators than ALC. The reason why we have now opted for a slight extension of ALC is twofold: . in a recent study =-=[9] we have found that -=-Mirtl has, unlike ALC [47], bad computational properties; . ALC is universally considered the "standard" description logic (as much as K is considered the "standard" modal logic) a... |