James G. Schmolze and David J. Israel. KL-ONE: Semantics and classification. In Research in Knowledge Representation and Natural Language Understanding, BBN Technical Report, No. 5421, pages 27-- 39. Bolt, Beranek, and Newman Inc., Cambridge, MA, 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....time and world indices potentially on each constant in WML, we must first state the role those indices play in the NIKL por tion of the hybrid. Figure 1: Two Typical Facts Stated in NIKL In a first order extensional logic, the normal semantics of SUPERC and of roles in NIKL are well defined [26]. For instance, the diagram in figure 1 would mean ( x) B x) A x) x) S x) y (C y) R x.v) Due to a suggestion by David Stallard, we have chosen to interpret SUPERC and the role link similarly, but interpreted under modal necessity, i.e. as propositions true at all times in all worlds. ....

....be handled with NIKE (The additional problematic vocabulary were upgrade, project, report, change, and expect. 3. Example Representational Decisions Here we mention some of the issues we focussed on in developing Janus. The specification of WML appears in [15] specifications for NIKL appear in [22, 26]. Few constants. One decision was to use as few constants as possible, deriving as many entities as possible using operators in the intensionai logic. In this section we illustrate this point by showing how definitely referenced sets, information about kinds, indefinitely identified sets, and ....

Schmolze, J. G., and Israel, D.J. KL-ONE: Semantics and Classification. In Research in Knowledge Representation for Natural Language Understanding - Annual Report, I September 1982 - 31 August 1983, Sidner, C.L., et al., Eds., BBN Laboratories Report No. 5421, 1983, pp. 27-39.

....and prepositions. IRules are used by the semantic interpreter in enforcing selectional restrictions and producing a logical form as the meaning representation of the input sentence. IRACQ makes extensive use of information present in a model of the domain, which is represented using NIKL [18, 21], the terminological reasoning component of KL TWO [26] Information from the domain model is used in guiding the IRACQJuser interaction, assuring that acquisition and editing yield IRules consistent with the model. Further support exists for the IRule developer through a flexible editing and ....

....binary predicates. Objects are represented by unary predicates and are related through binary relations. Using such a representation limits the kind and numbers of questions that have to be asked of the user by the semantic acquisition component. The representation dovetails well with using NIKL [18, 21], a taxonomic knowledge representation system with a formal semantics, for stating axioms about the domain. 3.3 Model of the domain One may choose to have an explicit, separate representation for concepts of the domain, along with axioms relating them. Both IRUS and TEAM have explicit models. ....

Schmolze, J. G., and Israel. D.J. KL-ONE: Semantics and Classification. In Research in Knowledge Representation for Natural Language Understanding. Annual Report, I September 1982 - 31 August 1983, Sidner, C.L., et al., Eds., BBN Laboratories Report No. 5421, 1983, pp. 27-39.

....for every interpretation I, D I # E I = #. 3 Relating descriptions to predicate calculus There is an obvious similarity between concepts (respectively roles) in DLs, and monadic (resp. dyadic) predicates in predicate calculus. Such a similarity was already exploited by Schmolze and Israel [20] to give a semantics for the original kl one language using the # calculus. Our aim is to compare the expressive power of various sublanguages of descriptions and predicate calculus. To do so we need to set up a common framework for the two formalisms. 3.1 Predicate Calculus We start, as usual, ....

....language L 2 is as expressive as language L 1 , if there is a total function transl from L 1 to L 2 such that for every sentence L in L 1 , transl(L) expresses the meaning of L. Two languages are equally expressive if each is as expressive as the other. For example, Schmolze and Israel [20] show that FOPC is as expressive as DL trans by essentially defining a translation function # #.#, which maps concepts to formulas with free variable x, and roles to formula with free variables x and y. For example, # #all[p,C]# is #x.#w.p(x, w) # C(w) while the translation of ....

J.G. Schmolze and D. Israel, "KL-ONE: semantics and classification", in Research in Knowledge Represetnation for NL Understanding, Tech Report 5421, BBN Laboratories, 1983.

.... , krypton [Brachman et al. 1985] meson [Edelmann and Owsnicki, 1986] back [von Luck et al. 1987; Nebel and von Luck, 1988] loom [MacGregor, 1988] classic [Brachman et al. 1989; Borgida et al. 1989] and sb one [Kobsa, 1989] and the formal properties of these systems were investigated [Schmolze and Israel, 1983; Brachman and Levesque, 1984; Patel Schneider, 1986; Levesque and Brachman, 1987; Nebel, 1988; Schild, 1988; Patel Schneider, 1989a; PatelSchneider, 1989b; Schmidt Schau , 1989; Schmidt Schau and Smolka, 1990; Nebel and Smolka, 1990; Nebel, 1990; Donini et al. 1990; Hollunder et al. 1990] ....

....in terms of the meaning of its parts and the way these are composed [Schmolze and Brachman, 1982, p. 11] In trying to understand the meaning of Human, we inevitably end up trying to figure out what the meaning of Human could be. Additionally, the subsumption algorithms usually employed (see e.g. [Schmolze and Israel, 1983]) would end up in an infinite loop on such definitions. For these reasons terminological cycles have been excluded in theoretical investigations and practical terminological knowledge representation systems. Terminological Cycles 3 This exclusion would be justified if terminological cycles were ....

James G. Schmolze and David J. Israel. KLONE: Semantics and classification. In Research in Knowledge Representation and Natural Language Understanding, BBN Technical Report, No. 5421, pages 27--39. Bolt, Beranek, and Newman Inc., Cambridge, Mass., 1983.

.... terminological logics were introduced originally with an informal semantics only, it quickly became obvious that a formal semantics is necessary to describe the intended meaning and the obvious candidate, first order predicate calculus and its associated model theory, was used for this purpose [Schmolze and Israel, 1983; Brachman and Levesque, 1984] A similar process took place in the area of unification grammars [Kasper and Rounds, 1986; Johnson, 1987; Smolka, 1988] This logical reconstruction revealed in both cases that the formalisms correspond to subsets of ordinary first order predicate logic. Although ....

James G. Schmolze and David J. Israel. KL-ONE: Semantics and classification. In Research in Knowledge Representation and Natural Language Understanding, BBN Technical Report, No. 5421, pages 27-- 39. Bolt, Beranek, and Newman Inc., Cambridge, MA, 1983.

....on description logics or frame like representations. By and large, these representations capture only a subset of the expressive power of standard FOL, and in terms of their inference capabilities are aimed primarily at subsumption checking [Brachman and Levesque, 1984; Nebel and Smolka, 1991; Schmolze and Israel, 1983; Hayes, 1979] 8 8 In lexically oriented work such as [Dorr, 1993] Jackendoff s Lexical Conceptual Structures are gaining Our KR formalisms, especially the el and crt representations for language, were seen to be considerably more expressive than FOL. One might ask whether in retrospect the ....

Schmolze, J. G. and Israel, D. J. (1983). KL-ONE: Semantics and classification. In Research in Knowledge Representation and Natural Language Understanding, pages 27--39. Bolt, Beranek, and Newman Inc. BBN Technical Report No. 5421.

....a set UserRel as follows: UserRel = fR : dom(R) User range(R) Userg For a formal description of the connection of DL and FIL, we give a translation mapping from DL to FIL which is sort of sensitive to UserRel defined above. The mapping, of course, resembles Borgida s [3] and the one by [16] and is identical except of the names of roles: R) ae x; y: fR(x; y)g;R(x; y) R 2 UserRel x; y:R(x; y) otherwise 2 In fact, 1] explains that an interpretation function for Phi can assign 1 to Phi ( Phi is acceptable, written: Phi) or 0 ( Phi is inacceptable: Gamma Phi) ....

....of First Order Predicate Logic and the translation from FIL to FOPL only uses the FOPL sublanguage of FIL. i.e. if a formula has some model in DL, then it has one in FIL, too. On the other hand, if a FIL expression is satisfiable, then it is in DL, too, if no ionic formula is contained (see [16]) A ionic formula (R(ff; fi) R(ff; fi) is the translation of some role R 2 UserRel whose justification context R(ff; fi) can have one of the following states of acceptance ffl R(ff; fi) or GammaR(ff; fi) i.e. for any model M it is impossible that Mj6j= R(ff; fi) M j= R(ff; fi) This ....

Schmolze, J.G. and Israel, D.: KL-ONE: Semantics and Classification, in Research in Knowledge Representation for NL Understanding, Tech Report 5421, BBN Laboratories 1983

.... terminological logics [Bobrow and Webber, 1980; Alshawi, 1987; Herzog and Rollinger, 1991; Kuhlen, 1983] or typed feature structure (TFS) logics [Copestake et al. 1993; Copestake and Briscoe, 1992] Representationally, terminological logics are subsets of FOL [Nebel and Smolka, 1991; Schmolze and Israel, 1983; Brachman and Levesque, 1984; Schubert, 1990; Hayes, 1979] as are TFS logics [Nebel and Smolka, 1991; Kasper and Rounds, 1986; Johnson, 1987; Smolka, 1991] 3 Thus, we suggest that lexical semanticists interested in supporting lexically based inferences need to look for ways to enrich their ....

J. G. Schmolze and D. J. Israel, "KL-ONE: Semantics and classification," In Research in Knowledge Representation and Natural Language Understanding, pages 27--39. Bolt, Beranek, and Newman Inc., 1983, BBN Technical Report No. 5421.

....of computing subsumption for various DLs 3 . 3 Relating descriptions to predicate calculus There is an obvious similarity between concepts (respectively roles) in DLs, and unary (resp. binary) predicates in predicate calculus. Such a similarity was already exploited by Schmolze Israel [38] to give a semantics for the original kl one language using calculus. We wish to pursue this similarity, but in order to compare the two formalisms we need a common framework. Since almost all the work on DLs has been carried out in the framework of binary (as opposed to n ary) ....

Schmolze, J.G., D. Israel, "KL-ONE: semantics and classification", in Research in Knowledge Represetnation for Natural Language Understanding --- ANnual Report, Tech Report 5421, BBN Laboratories, 1983.

....description logics. Theoretical Investigations Though Brachman mentioned the importance of a formal semantics in his papers, it took some years before Description Logics were thoroughly investigated from a theoretical point of view. Schmolze and Israel presented a formal semantics for KL ONE in [Schmolze, Israel 83] One year later, Brachman and Levesque raised the question of tractability of KR formalisms [Brachman, Levesque 84] In the late 1980 s several results were obtained concerning the tractability of different DLs. In order to understand these results we now have to take a closer look on the ....

....each instance of the concept c 1 is also an instance of the concept c 2 . A formal syntax and semantics for DL is given in Chapter C. Note that DL are subsets of First Order Logic (with Equality) which can be shown easily by specifying translation functions from DL formulae into FOL formulae [Schmolze, Israel 83, Royer, Quantz 92] To summarize these theoretical issues, we can say that DLs are characterized by a particular stance towards the essentials of KR formalisms in order to call something a KR formalism 1. it has to be a formal language in the sense that there is a formal specification of its ....

[Article contains additional citation context not shown here]

J. Schmolze, D. Israel, "KL-ONE: Semantics and Classification ", in BBN Annual Report, Rep.No. 5421, 27--39, 1983

....3. Therefore, we need a theoretical basis for the combination of DL and FIL. For a formal description of the connection of DL and FIL, we give a translation mapping from DL to FIL which is sort of sensitive to UserRel defined above. The mapping, of course, resembles Borgida s [3] and the one by [16] and actually is identical except of the names of roles: R) 8 : x; y: fR(x; y)g;R(x; y) R 2 UserRel x; y:R(x; y) otherwise This says that all role names of a given TBox marked as partial are translated as ionic formulae, e.g. want dep) x; y: fwant dep(x; y)g; ....

....of First Order Predicate Logic and the translation from FIL to FOPL only uses the FOPL sublanguage of FIL. i.e. if a formula has some model in DL, then it has one in FIL, too. On the other hand, if a FIL expression is satisfiable, then it is in DL, too, if no ionic formula is contained (see [16]) A ionic formula (R(ff; fi) R(ff; fi) is the translation of some role R 2 UserRel whose justification context R(ff; fi) can have one of the following states of acceptance 2 : ffl R(ff; fi) or GammaR(ff; fi) i.e. for any model M it is impossible that Mj 6j= R(ff; fi) M j= R(ff; fi) ....

Schmolze, J.G. and Israel, D.: KL-ONE: semantics and classification, in Research in Knowledge Representation for NL Understanding, Tech Report 5421, BBN Laboratories 1983

....iff for every interpretation I, D I E I = 3 Relating descriptions to predicate calculus There is an obvious similarity between concepts (respectively roles) in DLs, and monadic (resp. dyadic) predicates in predicate calculus. Such a similarity was already exploited by Schmolze and Israel [20] to give a semantics for the original kl one language using the calculus. Our aim is to compare the expressive power of various sublanguages of descriptions and predicate calculus. To do so we need to set up a common framework for the two formalisms. 3.1 Predicate Calculus We start, as usual, ....

....that some language L 2 is as expressive as language L 1 , if there is a total function transl from L 1 to L 2 such that for every sentence L in L 1 , transl(L) expresses the meaning of L. Two languages are equally expressive if each is as expressive as the other. For example, Schmolze and Israel [20] show that FOPC is as expressive as DL Gammaf trans g by essentially defining a translation function h.i, which maps concepts to formulas with free variable x, and roles to formula with free variables x and y. For example, hall[p,C]i is x:8w:p(x; w) C(w) while the translation of ....

J.G. Schmolze and D. Israel, "KL-ONE: semantics and classification", in Research in Knowledge Represetnation for NL Understanding, Tech Report 5421, BBN Laboratories, 1983.

.... noted [15] The intuitive idea behind subsumption, however, was very clear, namely that concept 1 subsumes concept 2 m all objects which are a concept 2 are also a concept 1 When this idea was first formalized by specifying a formal semantics for (a subset of) KL ONE by Schmolze and Israel [19], it was discovered that the subsumption procedure implemented in KL ONE was sound, i.e. every detected subsumption relationship was correct with respect to the semantics, but incomplete some relationships were not detected by the procedure. This fact could have been taken as a starting point ....

Schmolze, J. G. and Israel, D. J., KL-ONE: Semantics and Classification, in: Sidner, C. L., Research in Knowledge Representation and Natural Language Understanding, BBN Technical Report 5421, Bolt, Beranek and Newman, Inc., Cambridge, Mass., 1983, 27--39.

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James G. Schmolze and David J. Israel. KL-ONE: Semantics and classification. In Research in Knowledge Representation and Natural Language Understanding, BBN Technical Report, No. 5421, pages 27-- 39. Bolt, Beranek, and Newman Inc., Cambridge, MA, 1983.

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