## Logic-based Knowledge Representation (1996)

Venue: | Artificial Intelligence Today, Recent Trends and Developments, number 1600 in Lecture Notes in Computer Science |

Citations: | 27 - 0 self |

### BibTeX

@INPROCEEDINGS{Baader96logic-basedknowledge,

author = {Franz Baader},

title = {Logic-based Knowledge Representation},

booktitle = {Artificial Intelligence Today, Recent Trends and Developments, number 1600 in Lecture Notes in Computer Science},

year = {1996},

pages = {13--41},

publisher = {Springer Verlag}

}

### OpenURL

### Abstract

. After a short analysis of the requirements that a knowledge representation language must satisfy, we introduce Description Logics, Modal Logics, and Nonmonotonic Logics as formalisms for representing terminological knowledge, time-dependent or subjective knowledge, and incomplete knowledge respectively. At the end of each section, we briefly comment on the connection to Logic Programming. 1 Introduction This section is concerned with the question under which conditions one may rightfully claim to have represented knowledge about an application domain, and not just stored data occurring in this domain. 1 In the early days of Artificial Intelligence and Knowledge Representation, there was a heated discussion on whether logic can at all be used as a formalism for Knowledge Representation (see e.g. [135, 91, 92]). One aspect of the requirements on knowledge representation formalisms that can be derived from the considerations in this section is very well satisfied by logical for...

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Citation Context ...onal Logic Programming languages. To overcome this deficit, extensions of Logic Programming languages by disjunction and classical negation (in contrast to "negation as failure") have been i=-=ntroduced [76, 151, 119, 23, 35]. However,-=- these extensions treat only some aspects of these constructors: for example, the "classical negation" in these approaches only represents the aspect that a set and its complement are disjoi... |

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Citation Context ...owing, we give a very short introduction, which emphasizes the connection between Description Logics and Modal Logics. For more detailed introductions and overviews of the area we refer the reader to =-=[44, 102, 88, 68]-=-. The propositional multi-modal logic Kn extends propositional logic by n pairs of unary operators, which are called box and diamond operators. The K stands for the basic modal logic on which most mod... |

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Citation Context ...ther option) explicit (see below). Systems and applications. Description Logics are descended from so-called "structured inheritance networks" [31, 32], which were first realized in the syst=-=em kl-one [34]-=-. Their main idea is to start with atomic concepts (unary predicates) and roles (binary predicates), and use a (rather small) set of epistemologically adequate constructors to build complex concepts a... |

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Citation Context ...which none seems to be "the best" approach. A very positive development is the fact that recently several results clarifying the connection between different approaches have been obtained (s=-=ee, e.g., [105, 108, 109, 118, 111]-=-). In the following, we briefly introduce the four most important types of approaches. Consistency-based approaches , of which Reiter's Default Logic [157] is a typical example, consider nonmonotonic ... |

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Citation Context ...owing, we give a very short introduction, which emphasizes the connection between Description Logics and Modal Logics. For more detailed introductions and overviews of the area we refer the reader to =-=[44, 102, 88, 68]-=-. The propositional multi-modal logic Kn extends propositional logic by n pairs of unary operators, which are called box and diamond operators. The K stands for the basic modal logic on which most mod... |

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Citation Context ...roles. This idea has been further developed both from the theoretical and the practical point of view. In particular, there is a great variety of successor systems (e.g., Back [143, 149, 96], Classic =-=[29, 33]-=-, Crack [36], DLP [148], FaCT [98], Flex [152], K-Rep [127, 128], Kris [14], Loom [122, 121], Sb-one [106]), which have been used in different application domains such as natural language processing [... |

336 |
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Citation Context ...s to a nonmonotonic behaviour of Logic Programs. Thus, it is not surprising that there is a close connection between approaches for defining declarative semantics for (extended) logic programs (e.g., =-=[74, 75, 27, 173]-=-) and formalisms for nonmonotonic reasoning. In principle, these semantics depend on a preference relation between models. Their development was strongly influenced by the semantics for autoepistemic ... |

277 | Description logics
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Citation Context ...ges with number restrictions; [6] for transitive closure of roles and [159, 99, 101] for transitive roles; [12, 89, 87, 22] for constructs that allow to refer to concrete domains such as numbers; and =-=[10, 40, 8]-=- for the treatment of general axioms of the form C : = D, where C; D may both be complex concept terms). Undecidability and complexity results. Other important research contributions for DL are concer... |

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Citation Context ...and to various description languages extending ALC (see, e.g., [95, 94, 20, 21, 8] for languages with number restrictions; [6] for transitive closure of roles and [159, 99, 101] for transitive roles; =-=[12, 89, 87, 22]-=- for constructs that allow to refer to concrete domains such as numbers; and [10, 40, 8] for the treatment of general axioms of the form C : = D, where C; D may both be complex concept terms). Undecid... |

251 | Using an expressive description logic: FaCT or fiction
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Citation Context ...loped both from the theoretical and the practical point of view. In particular, there is a great variety of successor systems (e.g., Back [143, 149, 96], Classic [29, 33], Crack [36], DLP [148], FaCT =-=[98]-=-, Flex [152], K-Rep [127, 128], Kris [14], Loom [122, 121], Sb-one [106]), which have been used in different application domains such as natural language processing [154], configuration of technical s... |

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Citation Context ...ke KR languages." use a Logic Programming approach for KR. Overviews on the topic of extended Logic Programs with declarative semantics and their application to representing knowledge can be foun=-=d in [53, 134, 23, 4]-=-. 2 Description Logics The attempt to provide for a structured representation of information was one of the main motivations for introducing early KR formalisms such as Semantic Networks and Frames. D... |

228 | W.: The complexity of concept languages
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Citation Context ... both complete and polynomial. In the meantime, the worst-case complexity of the subsumption problem in a large class of DL languages, the so-called AL-family, has (almost completely) been determined =-=[59, 58, 57]-=-. With the exception of a few polynomially decidable languages, the complexity results range between NP or coNP and PSPACE. Whereas these results are given with respect to an empty TBox (i.e., they co... |

224 | M.: Logic Programming and Knowledge Representation
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Citation Context ...te that these deficiencies can be overcome with the help of other logic-based formalisms, namely Description Logics, Modal Logics, and Nonmonotonic Logics. More recently, it has been argued (see e.g. =-=[110, 23]-=-) that Logic Programming can serve as a convenient and universal formalism for Knowledge Representation. However, as indicated by their name, Logic Programming languages are programming languages, and... |

221 | Living with CLASSIC: When and how to use a KL-ONE-like language
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Citation Context ...roles. This idea has been further developed both from the theoretical and the practical point of view. In particular, there is a great variety of successor systems (e.g., Back [143, 149, 96], Classic =-=[29, 33]-=-, Crack [36], DLP [148], FaCT [98], Flex [152], K-Rep [127, 128], Kris [14], Loom [122, 121], Sb-one [106]), which have been used in different application domains such as natural language processing [... |

217 | First-Order Modal Logic
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Citation Context ...stead of using tableau-based algorithms, decidability of certain propositional modal logics (and thus of the corresponding DL), can also be shown by establishing the finite model property (see, e.g., =-=[68]-=-, Section 1.14) of the logic (i.e., showing that a formula/concept is satisfiable iff it is satisfiable in a finite interpretation) or by employing tree automata (see, e.g, [174]). It should be noted,... |

214 | Reasoning in description logics
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Citation Context ...her hand, it could mean that any frog has at least the colour green, but may have other colours too (it might be 4 Although there is no overview article that covers all aspects of this research area, =-=[177, 15, 62]-=- can serve as a starting point. - colour 6 6 6 Z Z Z Z - Animal Frog Kermit IS-A IS-A IS-A IS-A colour Brown Green Treefrog Grassfrog Fig. 1. A semantic network. green with red stripes). A partial rec... |

213 | Modal languages and bounded fragments of predicate logic
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Citation Context ...the quantified variable y is guarded by R(x; y). For this reason, the formulae obtained as translations of ALC-concept terms belong to the so-called guarded fragment GF of first-order predicate logic =-=[2]-=-, which has the following inductive definition: -- Every atomic formula belongs to GF. -- GF is closed under the Boolean connectives. -- If x; y are tuples of variables, R is a predicate symbol, and /... |

185 | A.: Decidable reasoning in terminological knowledge representation systems
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Citation Context ...ges with number restrictions; [6] for transitive closure of roles and [159, 99, 101] for transitive roles; [12, 89, 87, 22] for constructs that allow to refer to concrete domains such as numbers; and =-=[10, 40, 8]-=- for the treatment of general axioms of the form C : = D, where C; D may both be complex concept terms). Undecidability and complexity results. Other important research contributions for DL are concer... |

185 |
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Citation Context ...rties that a "reasonable" nonmonotonic inference relation j should satisfy were, on the one hand, introduced for the purpose of comparing and evaluating different approaches to nonmonotonic =-=reasoning [69, 124]-=-. On the other hand, these properties can also be interpreted as inference rules (like modus ponens), which can be used to generate new nonmonotonic consequences [114]. Figure 4 gives several examples... |

166 | LaSSIE: A knowledgebased software information system
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Citation Context ...], Sb-one [106]), which have been used in different application domains such as natural language processing [154], configuration of technical systems [178, 42, 158, 133], software information systems =-=[50]-=-, optimizing queries to databases [41, 25, 24], or planning [107]. Syntax and semantics. Figure 2 introduces syntax and semantics of some of the concept constructors employed in systems or investigate... |

161 | A semantics and complete algorithm for subsumption in the CLASSIC description logic system
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Citation Context ...6], a four-valued semantics characterizing the behaviour of a structural subsumption algorithm is introduced. The system Classic [29, 33] employs an "almost" complete structural subsumption =-=algorithm [30]-=-. Its only incompleteness stems from the treatment of individuals inside concept terms, which can, however, again be characterized with the help of a non-standard semantics. Since 1988, a new type of ... |

148 |
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Citation Context ...which none seems to be "the best" approach. A very positive development is the fact that recently several results clarifying the connection between different approaches have been obtained (s=-=ee, e.g., [105, 108, 109, 118, 111]-=-). In the following, we briefly introduce the four most important types of approaches. Consistency-based approaches , of which Reiter's Default Logic [157] is a typical example, consider nonmonotonic ... |

148 |
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(Show Context)
Citation Context ...rties that a "reasonable" nonmonotonic inference relation j should satisfy were, on the one hand, introduced for the purpose of comparing and evaluating different approaches to nonmonotonic =-=reasoning [69, 124]-=-. On the other hand, these properties can also be interpreted as inference rules (like modus ponens), which can be used to generate new nonmonotonic consequences [114]. Figure 4 gives several examples... |

145 | On the relative expressiveness of description logics and predicate logics
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Citation Context ...y; z)sA(z)) does not contain x, this variable can be re-used: renaming the bound variable z into x yields the equivalent formula 8y:(R(x; y) ! (9x:(R(y; x) A(x)))), which uses only two variables (see =-=[28]-=- for details). This connection between ALC and L 2 shows that any extension of ALC by constructors that can be expressed with the help of only two variables yields a decidable DL. Number restrictions ... |

142 |
Nonmonotonic Reasoning: Logical Foundations of Commonsense
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(Show Context)
Citation Context ...we cannot describe in detail here. The following is a brief introduction into the existing approaches and the problems treated by these approaches. Overviews of the area can, for example, be found in =-=[42, 23, 24]-=-. Knowledge representation languages based on classical logics (e.g., first-order predicate logic) are monotonic in the following sense: if a statement OE can be derived from a knowledge base, then OE... |

140 | An empirical analysis of optimization techniques for terminological representation systems or: Making KRIS get a move on
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(Show Context)
Citation Context ... these complexity results, one may ask whether incomplete, but polynomial algorithms should be preferred over the complete ones, which are necessarily of high worst-case complexity. First experiences =-=[11, 36, 98]-=- with implemented systems using complete algorithms show, however, that on realistic KBs the run time is comparable to that of Classic and Loom (i.e., mature systems using incomplete algorithms). Thes... |

123 | Augmenting concept languages by transitive closure of roles: An alternative to terminological cycles
- Baader
- 1991
(Show Context)
Citation Context ...signing subsumption algorithms was extended to the instance problem [93, 15] and to various description languages extending ALC (see, e.g., [95, 94, 20, 21, 8] for languages with number restrictions; =-=[6]-=- for transitive closure of roles and [159, 99, 101] for transitive roles; [12, 89, 87, 22] for constructs that allow to refer to concrete domains such as numbers; and [10, 40, 8] for the treatment of ... |

121 | On the restraining power of guards
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(Show Context)
Citation Context ...nevertheless has the finite model property, which implies that satisfiability of formulae in GF is decidable. More precisely, the satisfiability problem for GF is complete for double exponential time =-=[84]-=-. Decidability of GF can also be shown with the help of resolution methods [48]. Connection with Logic Programming Since Logic Programming languages are computationally complete and DL languages are u... |

118 |
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(Show Context)
Citation Context ...s. Whereas [11] concentrated mostly on reducing the number of subsumption tests during classification, more recent work in this direction is concerned with optimizing the subsumption algorithm itself =-=[83, 97, 98, 82, 100, 104]-=-. Connections with other logical formalisms. Before we turn to the connection between DL and Logic Programming, we should like to mention several interesting connections between DL and more traditiona... |

117 |
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(Show Context)
Citation Context ...ive, which led to undecidability of the subsumption problem [165, 147]. More recent undecidability results for extensions of ALC can be found in [13, 89, 20, 21, 87, 22]. The first complexity results =-=[115, 139]-=- showed that, even for very small languages, there cannot exist subsumption algorithms that are both complete and polynomial. In the meantime, the worst-case complexity of the subsumption problem in a... |

115 |
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(Show Context)
Citation Context ...to the existing approaches and the problems treated by these approaches. Overviews of this research area can, for example, be found in [71, 38]. In addition, there are several monographs on the topic =-=[37, 120, 126, 3]-=-. An annotated collection of influential papers in the area can be found in [80]. Motivation. Knowledge representation languages based on classical logics (e.g., first-order predicate logic) are monot... |

115 |
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Citation Context ...e 4 gives several examples of such reasonable properties. It has also turned out that there is a close connection between preferential semantics and inferences relations satisfying certain properties =-=[123, 111]-=-. OE j OE Reflexivity If OE j / and OE equivalent to OE 0 then OE 0 j / Left equivalence If OE j / and / implies / 0 then OE j / 0 Right weakening If OEsOE 0 j / and OE j OE 0 then OE j / Cut If OE j ... |

110 |
The LOOM knowledge representation language
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Citation Context ...int of view. In particular, there is a great variety of successor systems (e.g., Back [143, 149, 96], Classic [29, 33], Crack [36], DLP [148], FaCT [98], Flex [152], K-Rep [127, 128], Kris [14], Loom =-=[122, 121]-=-, Sb-one [106]), which have been used in different application domains such as natural language processing [154], configuration of technical systems [178, 42, 158, 133], software information systems [... |

100 |
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(Show Context)
Citation Context ...s to a nonmonotonic behaviour of Logic Programs. Thus, it is not surprising that there is a close connection between approaches for defining declarative semantics for (extended) logic programs (e.g., =-=[74, 75, 27, 173]-=-) and formalisms for nonmonotonic reasoning. In principle, these semantics depend on a preference relation between models. Their development was strongly influenced by the semantics for autoepistemic ... |

97 | CARIN: A Representation Language Combining Horn Rules and Description Logics
- Levy, Rousset
- 1996
(Show Context)
Citation Context ...n into account. The integration of Description Logics with a rule calculus that is able to express Horn rules has been investigated in [90]. Other work in this direction can, for example, be found in =-=[117, 116]-=-. 3 Modal Logics This is an area of logics that has been investigated for quite a while, and for which a great variety of methods and results are available. In the following, we give a very short intr... |

95 | A terminological knowledge representation system with complete inference algorithms
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- 1991
(Show Context)
Citation Context ...her hand, it could mean that any frog has at least the colour green, but may have other colours too (it might be 4 Although there is no overview article that covers all aspects of this research area, =-=[177, 15, 62]-=- can serve as a starting point. - colour 6 6 6 Z Z Z Z - Animal Frog Kermit IS-A IS-A IS-A IS-A colour Brown Green Treefrog Grassfrog Fig. 1. A semantic network. green with red stripes). A partial rec... |

84 | Boosting the correspondence between description logics and propositional dynamic logics
- Giacomo, Lenzerini
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(Show Context)
Citation Context ...ABox individuals) did not focus on decidability issues. The extension of results from propositional modal and dynamic logic to logics allowing for number restrictions and individuals was addressed in =-=[77, 46, 79]. Axiomatizations. I-=-f one wants to assign the modal operators with a specific meaning (like "knowledge of an intelligent agent" or "in the future"), then using the basic modal logic Kn is not sufficie... |

84 |
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Citation Context ...e constructors of Figure 2. Since then, this approach for designing subsumption algorithms was extended to the instance problem [93, 15] and to various description languages extending ALC (see, e.g., =-=[95, 94, 20, 21, 8]-=- for languages with number restrictions; [6] for transitive closure of roles and [159, 99, 101] for transitive roles; [12, 89, 87, 22] for constructs that allow to refer to concrete domains such as nu... |

83 | Subsumption algorithms for concept description languages
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Citation Context ...e constructors of Figure 2. Since then, this approach for designing subsumption algorithms was extended to the instance problem [93, 15] and to various description languages extending ALC (see, e.g., =-=[95, 94, 20, 21, 8]-=- for languages with number restrictions; [6] for transitive closure of roles and [159, 99, 101] for transitive roles; [12, 89, 87, 22] for constructs that allow to refer to concrete domains such as nu... |

82 | TBox and ABox reasoning in expressive description logics
- Giacomo, Lenzerini
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(Show Context)
Citation Context ...pretation) or by employing tree automata (see, e.g, [174]). It should be noted, however, that some of the very expressive DL languages considered in this context (e.g., the language CIQ introduced in =-=[79]-=-) no longer satisfy the finite model property. For these languages, reasoning with respect to finite models (which is, for example, of interest for database applications) differs from reasoning with r... |

81 |
The logic of frames
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Citation Context ...n. 1 In the early days of Artificial Intelligence and Knowledge Representation, there was a heated discussion on whether logic can at all be used as a formalism for Knowledge Representation (see e.g. =-=[135, 91, 92]-=-). One aspect of the requirements on knowledge representation formalisms that can be derived from the considerations in this section is very well satisfied by logical formalisms. We shall see, however... |

78 | A.: Deduction in concept languages: From subsumption to instance checking
- Donini, Lenzerini, et al.
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(Show Context)
Citation Context ...axioms (in ALC) even causes the subsumption problem to become ExpTime-complete [163]. It has also been shown that for certain languages the instance problem can be harder than the subsumption problem =-=[160, 61]-=-. Optimizations. Considering these complexity results, one may ask whether incomplete, but polynomial algorithms should be preferred over the complete ones, which are necessarily of high worst-case co... |

73 | Semantics of Logic Programs: Their Intuitions and Formal Properties. An Overview
- Dix
- 1995
(Show Context)
Citation Context ...ke KR languages." use a Logic Programming approach for KR. Overviews on the topic of extended Logic Programs with declarative semantics and their application to representing knowledge can be foun=-=d in [53, 134, 23, 4]-=-. 2 Description Logics The attempt to provide for a structured representation of information was one of the main motivations for introducing early KR formalisms such as Semantic Networks and Frames. D... |

73 |
Modal logic with names
- Gargov, Goranko
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(Show Context)
Citation Context ...reasoning, or for reasoning in DL languages with number restrictions. More recent work on modal logics with "graded modalities " [66, 64, 172] (which correspond to number restrictions) and &=-=quot;nominals" [72]-=- (which correspond to ABox individuals) did not focus on decidability issues. The extension of results from propositional modal and dynamic logic to logics allowing for number restrictions and individ... |

70 | Adding Epistemic Operators to Concept Languages
- Donini, Lenzerini, et al.
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(Show Context)
Citation Context ...55, 56] and "Logic Programming and Nonmonotonic Reasoning" [125, 54]. Connection with Description Logics The integration of default rules into Description Logics was investigated in [153, 16=-=, 17]. In [60], an epist-=-emic operator K is added to the DL ALC. This operator is similar to the modal operators employed in modal nonmonotonic logic, and it can, for example, be used to impose a "local" closed worl... |

64 |
The Foundations of Mathematics
- Beth
- 1959
(Show Context)
Citation Context ...d as deduction problems in logics. In principle, these algorithms are methods for generating finite models. They can be seen as specializations of the tableau calculus for first-order predicate logic =-=[26, 170]-=-. The non-standard syntax of DL and the restricted expressiveness of these logics allows to design terminating procedures, i.e., for many description languages one obtains decision procedures for the ... |