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...of T 1 into T 2 . 2 It is not hard to see that the unification problem for F-molecules is polynomial time isomorphic to the so-called first-order subsumption problem, which is known to be NP-complete =-=[44]-=-. 34 It is therefore not surprising that the worst-case complexity of the algorithm in Figure 10 is exponential, and so is the worst-case size of the set of unifiers. This complexity is due to the fol...

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...per. Last, but not least, thanks goes to the anonymous referees for their constructive critique. A Appendix: A Perfect-Model Semantics for F-logic To adapt the various semantics for negation (such as =-=[89, 46, 105, 104, 90, 5, 62]-=-) to F-logic, the general principle is to use method names in contexts where predicates are used in the classical setting. For the perfect-model semantics [89], this means that stratification has to b...

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...e triggers non-deterministically. In some cases, however, the user may want to have more control over trigger-firing. This approach is common in many programming languages, such as Eiffel [78] or C++ =-=[97]-=-, where the programmer has to resolve inheritance conflicts explicitly. User-defined inheritance can be expressed in F-logic as follows. To resolve a conflict, say, in a binary method, mthd, we can fi...

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...of the active triggers non-deterministically. In some cases, however, the user may want to have more control over trigger-firing. This approach is common in many programming languages, such as Eiffel =-=[78]-=- or C++ [97], where the programmer has to resolve inheritance conflicts explicitly. User-defined inheritance can be expressed in F-logic as follows. To resolve a conflict, say, in a binary method, mth...

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...paradigm as classical predicate calculus stands to relational programming. Apart from object-oriented databases, another important application of F-logic is in the area of frame-based languages in AI =-=[42, 80], since th-=-ese languages are also built around the concepts of complex objects, inheritance, and deduction. It is from this connection that the name "Frame Logic" was derived. However, most of our term...

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... (a 1 ); : : : ; (a k )) is undefined, where (o)2 U (c) and (c 1 )2 U (a 1 ), : : : , (c k )2 U (a k ), we have a null value of the kind "value missing," a situation well-known in the databa=-=se theory [103]-=-. When c [m@c 1 ; : : : ; c k ) ( )] is false, the welltyping conditions of Section 13 mandate that I ! ((m))((o); (a 1 ); : : : ; (a k )) must be undefined. This is analogous to a null value of the k...

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...eorem. In F-logic, Herbrand's theorem plays the same fundamental role. We establish this theorem by considering maximal finitely satisfiable sets, similarly to the proof of the compactness theorem in =-=[40]-=-. A set S of ground clauses is finitely satisfiable, if every finite subset of S is satisfiable. A finitely satisfiable set S is maximal, if no other set of ground clauses containing S is finitely sat...

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...finition of F-structures is now complete. In the rest of this subsection, we discuss the properties of I ) and I )) and show that they coincide with the standard properties of functional types (e.g., =-=[29]-=-), 8 Signatures constitute a fairly advanced level of F-logic; its basic features---is-a hierarchy and data expressions---do not depend on the specifics of the above type system. For this reason, on t...

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...xplicit mention of the object identity is redundant, as it can be determined from the context or from the object's structure. 16.4 Path Expressions Many calculus-like object-oriented languages (e.g., =-=[112, 15]) use syntactic cons-=-tructs known as path expressions. For instance, to select employees working in "CS" departments, one could use a path expression X:affiliation:dname : = "CS" instead of X [affiliat...

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...osely defined term, a number of concepts, such as complex objects, object identity, methods, encapsulation, typing, and inheritance, have been identified as the most salient features of that approach =-=[13, 96, 113, 107, 10]-=-. One of the important driving forces behind the interest in object-oriented languages in databases is the promise they show in overcoming the, so called, impedance mismatch [74, 113] between programm...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...that H satisfies every clause of T. Since S 0 ` T, H is an H-model of S. By Proposition 9.2, S is satisfiable. 2 Herbrand's Theorem is a basis for the resolution-based proof theory in classical logic =-=[31]-=-. In the next section we use Herbrand's Theorem for F-logic to develop a similar result, which extends the results in [60]. Just as classical proof theory was fundamental to the theory of logic progra...

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... \Gamma\Psi \Phi \Phi \Phi�� @ @ @I H H H H H Hj \Omega \Omega \Omega \Omega AE @ @ @R @ @ @R Q Q Q Qs Q Q Q Qk P P P Pq Exodus [30] O 2 [71] F-logic O-logic [60] C-logic [35] IQL [3] FQL [27] Dap=-=lex [95]-=- Orion [61] Pascal-R [94] Glue [87] Relational algebra Prolog [36] LDL [85] NAIL! [83] Deductive Functional Procedural oriented Object Relational Programming paradigm paradigm Data representation Figu...

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...s no agreement as to which models deserve to be called canonic. Nevertheless, for a vast class of programs, called locally stratified programs, such an agreement has been reached, and it was shown in =-=[89]-=- that every such program has a unique canonic H-model. 15 For a locally stratified program, its unique canonic model goes under the name perfect model. Appendix A develops a perfect-model semantics fo...

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...on procedure for F-logic queries. The answer to this question is believed to be positive: several major evaluation strategies developed for deductive databases (e.g., OLDT [98, 38, 106] or Magic Sets =-=[19, 91]-=-) are applicable here as well. Another important point is that one does not need to use some of the inference rules at run time. For instance, in proof-theoretic terms, the purpose of static type chec...

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...ogramming. He described a type inference procedure that is sound with respect to the denotational semantics of his system. Sound type inference systems for functional languages were also discussed in =-=[82, 37]-=- and in several other papers. LOGIN and LIFE [7, 8] incorporate structural inheritance into logic programming via a unification algorithm for /-terms, which are complex structures related to signature...

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... side effects. An important aspect of F-logic is its extensibility---it can be combined with a broad range of other specialized logics. In Section 17, we outline two such combinations: one with HiLog =-=[34]-=- and one with Transaction Logic [21, 22, 23]. Another possible candidate is Annotated Predicate Logic [20, 56, 57], which is a logic for reasoning with inconsistent and uncertain information. This ext...

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...can be an efficient evaluation procedure for F-logic queries. The answer to this question is believed to be positive: several major evaluation strategies developed for deductive databases (e.g., OLDT =-=[98, 38, 106]-=- or Magic Sets [19, 91]) are applicable here as well. Another important point is that one does not need to use some of the inference rules at run time. For instance, in proof-theoretic terms, the purp...

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...set is also commonly known as Herbrand Universe. Conceptually, ground id-terms play the role of logical object id's---a logical abstraction of the implementational concept of physical object identity =-=[53, 3]. Since this paper i-=-s about a logic, the term "object id" (abbr., oid) will be used for logical id's only. Objects represented by "compound" id-terms, such as addr(13; mainstreet; anywhere), usually a...

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... of other specialized logics. In Section 17, we outline two such combinations: one with HiLog [34] and one with Transaction Logic [21, 22, 23]. Another possible candidate is Annotated Predicate Logic =-=[20, 56, 57]-=-, which is a logic for reasoning with inconsistent and uncertain information. This extensibility places F-logic in the center of a powerful unifying formalism for reasoning about data and knowledge. T...

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...irit of objectoriented programming. In contrast, F-logic represents higher-order and object-oriented concepts directly, both syntactically and semantically. This work builds upon our previous papers, =-=[58, 55, 60]-=-, which in turn borrowed several important ideas from Maier's O-logic [73] (that, in its turn, was inspired by Ait-Kaci's work on /-terms [7, 6]). In [58, 60], we described a logic that adequately cov...

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... only in the class where they are declared. Other methods may be exported to some specific classes, but not to all classes. While the idea of encapsulation is simple, its logical rendition is not. In =-=[79]-=-, Miller suggested a way to represent modules in logic programming via the intuitionistic embedded implication. Chen [32] defines modules as second-order objects, where data encapsulation inside modul...

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...cally. This work builds upon our previous papers, [58, 55, 60], which in turn borrowed several important ideas from Maier's O-logic [73] (that, in its turn, was inspired by Ait-Kaci's work on /-terms =-=[7, 6]-=-). In [58, 60], we described a logic that adequately covered the structural aspect of complex objects but was short of capturing methods, types, and inheritance. The earlier version of F-logic reporte...

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...a AE @ @ @R @ @ @R Q Q Q Qs Q Q Q Qk P P P Pq Exodus [30] O 2 [71] F-logic O-logic [60] C-logic [35] IQL [3] FQL [27] Daplex [95] Orion [61] Pascal-R [94] Glue [87] Relational algebra Prolog [36] LDL =-=[85]-=- NAIL! [83] Deductive Functional Procedural oriented Object Relational Programming paradigm paradigm Data representation Figure 1: A Classification of Database Programming Languages is not necessarily...

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...at is sound with respect to the denotational semantics of his system. Sound type inference systems for functional languages were also discussed in [82, 37] and in several other papers. LOGIN and LIFE =-=[7, 8]-=- incorporate structural inheritance into logic programming via a unification algorithm for /-terms, which are complex structures related to signatures in F-logic but that are fundamentally different f...

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...re nixon : quaker is known to hold, nixon [policy ! hawk] is no longer a certainty but, rather, just one of two possibilities. Nonmonotonic inheritance has been a subject of intensive research (e.g., =-=[41, 100, 101, 50, 25, 99, 65, 45, 64, 88]-=-) for many years. The main difference between our approach and the above works is that we are developing an inheritance theory for a general-purpose object-oriented logical language. In contrast, most...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...on procedure for F-logic queries. The answer to this question is believed to be positive: several major evaluation strategies developed for deductive databases (e.g., OLDT [98, 38, 106] or Magic Sets =-=[19, 91]-=-) are applicable here as well. Another important point is that one does not need to use some of the inference rules at run time. For instance, in proof-theoretic terms, the purpose of static type chec...

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...osely defined term, a number of concepts, such as complex objects, object identity, methods, encapsulation, typing, and inheritance, have been identified as the most salient features of that approach =-=[13, 96, 113, 107, 10]-=-. One of the important driving forces behind the interest in object-oriented languages in databases is the promise they show in overcoming the, so called, impedance mismatch [74, 113] between programm...

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...he aforementioned "impurity" 3 F-LOGIC BY EXAMPLE 4 \Gamma \Gamma \Gamma \Gamma\Psi \Phi \Phi \Phi�� @ @ @I H H H H H Hj \Omega \Omega \Omega \Omega AE @ @ @R @ @ @R Q Q Q Qs Q Q Q Qk P =-=P P Pq Exodus [30]-=- O 2 [71] F-logic O-logic [60] C-logic [35] IQL [3] FQL [27] Daplex [95] Orion [61] Pascal-R [94] Glue [87] Relational algebra Prolog [36] LDL [85] NAIL! [83] Deductive Functional Procedural oriented ...

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...paradigm as classical predicate calculus stands to relational programming. Apart from object-oriented databases, another important application of F-logic is in the area of frame-based languages in AI =-=[42, 80], since th-=-ese languages are also built around the concepts of complex objects, inheritance, and deduction. It is from this connection that the name "Frame Logic" was derived. However, most of our term...

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...re nixon : quaker is known to hold, nixon [policy ! hawk] is no longer a certainty but, rather, just one of two possibilities. Nonmonotonic inheritance has been a subject of intensive research (e.g., =-=[41, 100, 101, 50, 25, 99, 65, 45, 64, 88]-=-) for many years. The main difference between our approach and the above works is that we are developing an inheritance theory for a general-purpose object-oriented logical language. In contrast, most...

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...spects of object-oriented systems, which are the focus of this paper. There has been extensive work on formalizing updates within logic. The reader is referred to the recent work on Transaction Logic =-=[21, 22, 23]-=- for a comprehensive discussion of the problem, for an overview of the related work in the field, and for solutions to many of the previously outstanding problems. In Section 17.4, we briefly touch up...

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... of other specialized logics. In Section 17, we outline two such combinations: one with HiLog [34] and one with Transaction Logic [21, 22, 23]. Another possible candidate is Annotated Predicate Logic =-=[20, 56, 57]-=-, which is a logic for reasoning with inconsistent and uncertain information. This extensibility places F-logic in the center of a powerful unifying formalism for reasoning about data and knowledge. T...

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...and the utility of " " in this context is not clear. However, below, we introduce another don't-care symbol, "", which can occur inside sets. The need for don't-care oid's was also=-= emphasized in ILOG [51], where a -=-special ""-notation was introduced for this purpose. An invention atom, p(; t 1 ; : : : ; t n ), of ILOG is semantically close to an F-molecule of the form p-tuple(t 1 ; : : : ; t n ) : p [a...

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...al object-oriented languages [58, 35, 55, 3] allow grouping of data around properties (i.e., relationally) as well as around objects. IQL [3] relies on a small number of procedural features. Pascal-R =-=[94] offers de-=-clarative access to data, although the overall structure of the language is procedural. We believe that the future belongs to multi-paradigm languages, so the aforementioned "impurity" 3 F-L...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...erve desired computational properties. In the past, a number of researchers suggested that many useful higher-order concepts of knowledge representation languages can be encoded in predicate calculus =-=[48, 77]-=-. From the programmer's point of view, however, encoding is not satisfactory, as it gives no direct semantics to the important higher-order constructs and it does not retain the spirit of objectorient...

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...query ? \Gamma browser [find @ "CS"!!X ] would return the set fcs 1 ; cs 2 ; bob; mary g. 12.4.3 Representation of Analogies Reasoning by analogy is an active field of research (e.g., see a =-=survey in [47]-=-). Apart from the semantic and heuristic issues, finding suitable languages in which to specify analogies is also a challenge. This subsection shows how certain kinds of analogies can be specified in ...

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... of other specialized logics. In Section 17, we outline two such combinations: one with HiLog [34] and one with Transaction Logic [21, 22, 23]. Another possible candidate is Annotated Predicate Logic =-=[20, 56, 57]-=-, which is a logic for reasoning with inconsistent and uncertain information. This extensibility places F-logic in the center of a powerful unifying formalism for reasoning about data and knowledge. T...

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...re nixon : quaker is known to hold, nixon [policy ! hawk] is no longer a certainty but, rather, just one of two possibilities. Nonmonotonic inheritance has been a subject of intensive research (e.g., =-=[41, 100, 101, 50, 25, 99, 65, 45, 64, 88]-=-) for many years. The main difference between our approach and the above works is that we are developing an inheritance theory for a general-purpose object-oriented logical language. In contrast, most...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...ogramming. He described a type inference procedure that is sound with respect to the denotational semantics of his system. Sound type inference systems for functional languages were also discussed in =-=[82, 37]-=- and in several other papers. LOGIN and LIFE [7, 8] incorporate structural inheritance into logic programming via a unification algorithm for /-terms, which are complex structures related to signature...

Citation Context

...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...erve desired computational properties. In the past, a number of researchers suggested that many useful higher-order concepts of knowledge representation languages can be encoded in predicate calculus =-=[48, 77]-=-. From the programmer's point of view, however, encoding is not satisfactory, as it gives no direct semantics to the important higher-order constructs and it does not retain the spirit of objectorient...

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...upply complete type specification with each program. However, in logic programming, complete type specification is often seen as a burdensome requirement. Adapting the ideas from ML to Prolog, Mishra =-=[81]-=- proposed to use type inference for determining the implied type for each predicate in a program and then use the inferred types for troubleshooting. For a program, P, its inferred type can be taken t...

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...per. Last, but not least, thanks goes to the anonymous referees for their constructive critique. A Appendix: A Perfect-Model Semantics for F-logic To adapt the various semantics for negation (such as =-=[89, 46, 105, 104, 90, 5, 62]-=-) to F-logic, the general principle is to use method names in contexts where predicates are used in the classical setting. For the perfect-model semantics [89], this means that stratification has to b...

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...r quite some time. For instance, some prologs provide syntactic sugar that, roughly, amounts to the incorporation of what we earlier called "complex values." A similar transformation was als=-=o used in [76]-=- to extend Prolog with object-style syntax. The reader whose faith was shaken by the fact that F-logic is, in a sense, equivalent to predicate calculus, may find comfort in the following arguments. Fi...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...osely defined term, a number of concepts, such as complex objects, object identity, methods, encapsulation, typing, and inheritance, have been identified as the most salient features of that approach =-=[13, 96, 113, 107, 10]-=-. One of the important driving forces behind the interest in object-oriented languages in databases is the promise they show in overcoming the, so called, impedance mismatch [74, 113] between programm...

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...e first reading it is possible to skip signature-related aspects of F-logic, including the remaining part of this subsection. 9 Actually, these functions are monotone with respect to Smyth's ordering =-=[28]-=-. For upward-closed sets, S ` smyth S 0 if and only if S ' S 0 . 5 SEMANTICS 18 albeit expressed in a different, model-theoretic notation. As with I ! , we use I (k) ) (m) to refer to the k-th compone...

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...per. Last, but not least, thanks goes to the anonymous referees for their constructive critique. A Appendix: A Perfect-Model Semantics for F-logic To adapt the various semantics for negation (such as =-=[89, 46, 105, 104, 90, 5, 62]-=-) to F-logic, the general principle is to use method names in contexts where predicates are used in the classical setting. For the perfect-model semantics [89], this means that stratification has to b...

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...cally. This work builds upon our previous papers, [58, 55, 60], which in turn borrowed several important ideas from Maier's O-logic [73] (that, in its turn, was inspired by Ait-Kaci's work on /-terms =-=[7, 6]-=-). In [58, 60], we described a logic that adequately covered the structural aspect of complex objects but was short of capturing methods, types, and inheritance. The earlier version of F-logic reporte...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...entioned "impurity" 3 F-LOGIC BY EXAMPLE 4 \Gamma \Gamma \Gamma \Gamma\Psi \Phi \Phi \Phi�� @ @ @I H H H H H Hj \Omega \Omega \Omega \Omega AE @ @ @R @ @ @R Q Q Q Qs Q Q Q Qk P P P Pq Ex=-=odus [30] O 2 [71]-=- F-logic O-logic [60] C-logic [35] IQL [3] FQL [27] Daplex [95] Orion [61] Pascal-R [94] Glue [87] Relational algebra Prolog [36] LDL [85] NAIL! [83] Deductive Functional Procedural oriented Object Re...

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... H H H H H Hj \Omega \Omega \Omega \Omega AE @ @ @R @ @ @R Q Q Q Qs Q Q Q Qk P P P Pq Exodus [30] O 2 [71] F-logic O-logic [60] C-logic [35] IQL [3] FQL [27] Daplex [95] Orion [61] Pascal-R [94] Glue =-=[87]-=- Relational algebra Prolog [36] LDL [85] NAIL! [83] Deductive Functional Procedural oriented Object Relational Programming paradigm paradigm Data representation Figure 1: A Classification of Database ...

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...ject identity---an implementational notion that also has a conceptual counterpart, which we call logical object identity. Logical oid's were introduced in [58, 60] and, subsequently, were utilized in =-=[35, 16]-=- and other works. The concept of object identity was widely discussed in database literature. An early attempt to bring this notion into the fold of a logical theory was reported by Maier [73]. Reflec...

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...6) becomes a simple, albeit lengthy, task. Examples of this kind of proofs can be found in [108, 34]. 2 The idea that object-based logics can be encoded in classical predicate logic first appeared in =-=[35]-=-, but embeddings of this sort were known in the Prolog community for quite some time. For instance, some prologs provide syntactic sugar that, roughly, amounts to the incorporation of what we earlier ...

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...can be an efficient evaluation procedure for F-logic queries. The answer to this question is believed to be positive: several major evaluation strategies developed for deductive databases (e.g., OLDT =-=[98, 38, 106]-=- or Magic Sets [19, 91]) are applicable here as well. Another important point is that one does not need to use some of the inference rules at run time. For instance, in proof-theoretic terms, the purp...

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...ds, (i) entails that variables can range over sets, thereby rendering the semantics second-order in the sense of [34]. Fortunately, the experience with object-oriented database systems, such as Orion =-=[61] and O 2 [-=-71], suggests that complex values are used in fairly restricted ways---primarily as weak entities of the EntityRelationship Approach. In other words, they are used as "second-rate objects," ...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...e to multiple inheritance, any one of the canonic models can be selected non-deterministically and then used to answer queries. In a different setting, non-monotonic inheritance was also discussed in =-=[69, 70, 24, 4]. Accordin-=-g to these approaches, a logical object (or a class) is a set of rules that represent "knowledge" embodied by the object (resp., class). These rules can be inherited by objects that are plac...

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...ectness in F-logic arose because existing theories are not sufficiently general to adequately type many kinds of F-programs (although some could be adapted for restricted classes of F-programs, e.g., =-=[49]-=-). A semantically rich logical theory, like F-logic, calls for a semantical, model-based notion of type-correctness---a notion that would apply to all meaningful untyped programs and one that would be...

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...ogic is left to the reader as an easy exercise; the above example already illustrates the main ideas behind such translation. A more complete discussion of path expressions in F-logic can be found in =-=[43]-=-. 16.5 Primary Classes and Immediate Superclasses Many object-oriented systems have the notion of object's primary class, which is the unique, lowest class in the class hierarchy where the object belo...

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...Gamma \Gamma \Gamma\Psi \Phi \Phi \Phi�� @ @ @I H H H H H Hj \Omega \Omega \Omega \Omega AE @ @ @R @ @ @R Q Q Q Qs Q Q Q Qk P P P Pq Exodus [30] O 2 [71] F-logic O-logic [60] C-logic [35] IQL [3] =-=FQL [27]-=- Daplex [95] Orion [61] Pascal-R [94] Glue [87] Relational algebra Prolog [36] LDL [85] NAIL! [83] Deductive Functional Procedural oriented Object Relational Programming paradigm paradigm Data represe...

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...a refutation of S. Proof: By Herbrand's Theorem, we can assume that S is finite. Suppose S is unsatisfiable. We will show that there is a refutation of S using a technique due to Anderson and Bledsoe =-=[9]. The proo-=-f is carried out by induction on the parameter excess(S), the number of "excess literals" in S: excess(S) def = ( the number of occurrences of literals in S) \Gamma (the number of clauses in...

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...se names themselves may have a rather complex structure and, in particular, the usual first-order terms (with variables) may appear in predicate positions. Many applications of HiLog are described in =-=[34, 110, 92]-=- and it is clear that extending F-logic in this direction is a good idea. In Section 12.4.1, we have seen one example---graph restructuring---where a combination of HiLog and F-logic may be useful. We...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...) a derivation step that turns the result of the previous step into a model. These operations are repeated until inheritance can be done no more. In this connection, we should mention the recent work =-=[39]-=-, which also proposes a semantics for inheritance in a language derived from F-logic. In particular, this work allows inheritance and deduction to interact in certain ways, but it does not deal with n...

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...e to multiple inheritance, any one of the canonic models can be selected non-deterministically and then used to answer queries. In a different setting, non-monotonic inheritance was also discussed in =-=[69, 70, 24, 4]. Accordin-=-g to these approaches, a logical object (or a class) is a set of rules that represent "knowledge" embodied by the object (resp., class). These rules can be inherited by objects that are plac...

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...spects of object-oriented systems, which are the focus of this paper. There has been extensive work on formalizing updates within logic. The reader is referred to the recent work on Transaction Logic =-=[21, 22, 23]-=- for a comprehensive discussion of the problem, for an overview of the related work in the field, and for solutions to many of the previously outstanding problems. In Section 17.4, we briefly touch up...

Citation Context

...e to multiple inheritance, any one of the canonic models can be selected non-deterministically and then used to answer queries. In a different setting, non-monotonic inheritance was also discussed in =-=[69, 70, 24, 4]. Accordin-=-g to these approaches, a logical object (or a class) is a set of rules that represent "knowledge" embodied by the object (resp., class). These rules can be inherited by objects that are plac...

Citation Context

...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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... Declarative Programming A number of researchers argued that object-oriented languages are fundamentally different from (and even incompatible with) other paradigms, especially with logic programming =-=[102, 75]-=-. This point of view was reflecting disappointment with the lack of early success in formalizing a number of central aspects of object-oriented programming. Compounding the problem was the lack of a f...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...re nixon : quaker is known to hold, nixon [policy ! hawk] is no longer a certainty but, rather, just one of two possibilities. Nonmonotonic inheritance has been a subject of intensive research (e.g., =-=[41, 100, 101, 50, 25, 99, 65, 45, 64, 88]-=-) for many years. The main difference between our approach and the above works is that we are developing an inheritance theory for a general-purpose object-oriented logical language. In contrast, most...

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...re nixon : quaker is known to hold, nixon [policy ! hawk] is no longer a certainty but, rather, just one of two possibilities. Nonmonotonic inheritance has been a subject of intensive research (e.g., =-=[41, 100, 101, 50, 25, 99, 65, 45, 64, 88]-=-) for many years. The main difference between our approach and the above works is that we are developing an inheritance theory for a general-purpose object-oriented logical language. In contrast, most...

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...ing Database Schema The higher-order syntax of F-logic makes it possible to query and manipulate certain meta-information about the database, such as its schema. Schema querying was also discussed in =-=[63]-=- and recently in [34]. However, the treatment in [63] is not as general and integrated as in F-logic, while [34] is a relational rather than an object-oriented language. Typically, database queries ar...

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... Declarative Programming A number of researchers argued that object-oriented languages are fundamentally different from (and even incompatible with) other paradigms, especially with logic programming =-=[102, 75]-=-. This point of view was reflecting disappointment with the lack of early success in formalizing a number of central aspects of object-oriented programming. Compounding the problem was the lack of a f...

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...ion may often be necessary. This means that the user has to apply intuitive or exploratory search through the structure of the scheme and the database at the same time and even in the same query (cf. =-=[84]-=-). Many user interfaces to commercial databases support browsing to some extent. The purpose of the following examples is to demonstrate that F-logic provides a unifying framework for data and schema ...

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...e to multiple inheritance, any one of the canonic models can be selected non-deterministically and then used to answer queries. In a different setting, non-monotonic inheritance was also discussed in =-=[69, 70, 24, 4]. Accordin-=-g to these approaches, a logical object (or a class) is a set of rules that represent "knowledge" embodied by the object (resp., class). These rules can be inherited by objects that are plac...

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...s. While the idea of encapsulation is simple, its logical rendition is not. In [79], Miller suggested a way to represent modules in logic programming via the intuitionistic embedded implication. Chen =-=[32]-=- defines modules as second-order objects, where data encapsulation inside modules is represented using existential quantifiers. In their present form, these approaches are not sufficiently general for...

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...d-terms, then I j=sT : =S if and only if (T ) = (S). 10 So, the term "F-molecule" will now include P-molecules. 11 In this paper, we do not deal with signatures of P-molecules, as they are s=-=tudied in [59, 108]-=-. 7 PROPERTIES OF F-STRUCTURES 22 To fully integrate P-molecules into F-logic, we now let F-formulae to be built using all kinds of molecules introduced so far. Truth of formulas in F-structures and t...

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...re nixon : quaker is known to hold, nixon [policy ! hawk] is no longer a certainty but, rather, just one of two possibilities. Nonmonotonic inheritance has been a subject of intensive research (e.g., =-=[41, 100, 101, 50, 25, 99, 65, 45, 64, 88]-=-) for many years. The main difference between our approach and the above works is that we are developing an inheritance theory for a general-purpose object-oriented logical language. In contrast, most...

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...re nixon : quaker is known to hold, nixon [policy ! hawk] is no longer a certainty but, rather, just one of two possibilities. Nonmonotonic inheritance has been a subject of intensive research (e.g., =-=[41, 100, 101, 50, 25, 99, 65, 45, 64, 88]-=-) for many years. The main difference between our approach and the above works is that we are developing an inheritance theory for a general-purpose object-oriented logical language. In contrast, most...

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...re nixon : quaker is known to hold, nixon [policy ! hawk] is no longer a certainty but, rather, just one of two possibilities. Nonmonotonic inheritance has been a subject of intensive research (e.g., =-=[41, 100, 101, 50, 25, 99, 65, 45, 64, 88]-=-) for many years. The main difference between our approach and the above works is that we are developing an inheritance theory for a general-purpose object-oriented logical language. In contrast, most...

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...inal objects in class c. Set comparison. Grouping is not only easy to express in F-logic, but it is also computationally more efficient than in some other languages, such as LDL [85], COL [2], or LPS =-=[67]-=-. The reason for this is that, in those languages, grouping is a second-order operation that requires stratification. We refer the reader to [60] for a more complete discussion. However, this gain in ...

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...fore, saying that all canonic F-models of a program must be typed is tantamount to saying that the program does not imply data atoms that do not comply with the signatures implied by that program. In =-=[33]-=-, this property is called semantic adequacy. 19 Such a class, called employmentGroup, was introduced towards the end of Section 3. 20 As determined by the chosen theory of canonic models, such as the ...

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...uided, lacking direction and needing a spokesman, like Codd, who could "coerce the researchers in this area into using a common set of terms and defining a common goal that they are hoping to ach=-=ieve [86].&quo-=-t; Our contention is that the problem lies deeper than that. When Codd made his influential proposal, he was relying on a large body of knowledge in classical predicate logic. He had the insight to se...

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...re nixon : quaker is known to hold, nixon [policy ! hawk] is no longer a certainty but, rather, just one of two possibilities. Nonmonotonic inheritance has been a subject of intensive research (e.g., =-=[41, 100, 101, 50, 25, 99, 65, 45, 64, 88]-=-) for many years. The main difference between our approach and the above works is that we are developing an inheritance theory for a general-purpose object-oriented logical language. In contrast, most...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...V ersion [: : :] 17 EXTENSIONS TO F-LOGIC 76 where arg is a suitable encoding of the desired version. Yet another way to do versioning is to parameterize attributes with version id's, as suggested in =-=[52]-=-. 17 Extensions to F-logic In this section, we outline several extensions to F-logic. Some of these could have been included in the main text, but they were left out to help us focus on the main issue...

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... @ @ @R Q Q Q Qs Q Q Q Qk P P P Pq Exodus [30] O 2 [71] F-logic O-logic [60] C-logic [35] IQL [3] FQL [27] Daplex [95] Orion [61] Pascal-R [94] Glue [87] Relational algebra Prolog [36] LDL [85] NAIL! =-=[83]-=- Deductive Functional Procedural oriented Object Relational Programming paradigm paradigm Data representation Figure 1: A Classification of Database Programming Languages is not necessarily a drawback...

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...ach [13, 96, 113, 107, 10]. One of the important driving forces behind the interest in object-oriented languages in databases is the promise they show in overcoming the, so called, impedance mismatch =-=[74, 113]-=- between programming languages for writing applications and languages for data retrieval. At the same time, a different, deductive approach gained enormous popularity. Since logic can be used as a com...

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...straction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g., =-=[1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]-=-) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra-logical featur...

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...e list cons(Obj; Rest) if Obj has Z and Z is a common object that X shares with the rest of the list. Our second example describes similarities among classes, specified via the like-relationship (cf. =-=[48, 12]). For instance, one-=- can say, "The concept of a Whale is like the concept of a Fish via habitat" or, "A Pig-Like-Person is like a Pig via nose and legs." Like-similarity can be expressed by means of a...

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...nteresting to see, though, if these approaches can be extended to make them suitable for method encapsulation in an object-oriented logic. We should also mention the recent work by Bugliesi and Jamil =-=[26]-=-. While their language and the notion of encapsulation are more limited than ours, encapsulation is made part of the syntax, semantics, and the proof theory, which could be a promising direction in th...