## Object Specification Logic (1995)

Venue: | Journal of Logic and Computation |

Citations: | 63 - 12 self |

### BibTeX

@ARTICLE{Sernadas95objectspecification,

author = {Amílcar Sernadas and Cristina Sernadas},

title = {Object Specification Logic},

journal = {Journal of Logic and Computation},

year = {1995},

volume = {5}

}

### OpenURL

### Abstract

A logic for specifying and reasoning about object classes and their instances (aspects) is presented and illustrated. This logic is an extension of a rather standard linear temporal, many-sorted, first-order predicate logic with equality. The extensions where designed to be as simple as possible while supporting the envisaged locality of arguments, object specialization and object aggregation. Objects are specified through their aspects. Each aspect establishes a local vocabulary (signature). The logic works at two levels: first, we can specify and prove assertions about a given object aspect in isolation (local reasoning), eg persons, or patients, or cars; second, we can specify interaction constraints and make inferences between aspects within the same community of objects (global reasoning), eg carry the theorems of persons onto patients (specialization inheritance), or carry the theorems of persons onto the aggregations of persons and cars (incorporation inheritance). Some reflecti...

### Citations

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Citation Context ...ll need non-monotonic features [BL91, CSS94]. We assume that the reader is conversant with the field of temporal logic specification (for instance at the level of [McA76, Gol87]). For an overview see =-=[Eme90]-=-. We also use a little bit of category theory (the reader may find all relevant concepts in the introductory chapters of any textbook on the matter, eg [AHS90]): the more exotic notion of freely gener... |

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Citation Context ...taken(u) occurs in the instance b of book then the observation available(true) holds in that same instance b. The notion of aspect specification as a theory presentation is as usual (see for instance =-=[GB92]-=-). Definition 3.6 An aspect specification is a pair spec = h\Phi; Axi where \Phi is an object aspect signature and Ax ` L \Phi . In this context, the elements of Ax are called (local) aspect axioms. E... |

420 | Simplification by cooperating decision procedures
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Citation Context ...theorem proving in mind (see [GSGA93]). A prototype is running for a significant fragment of the proposed logic. Concerning reasoning about numbers the prototype uses the simplex algorithm (following =-=[NO79]-=-). The proposed logic has been shown to be useful for providing a (proof-theoretic) semantics of object-oriented specification languages: see for instance [Jun93]. 7 Appendix: Freely generated cartesi... |

269 |
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Citation Context ... of [McA76, Gol87]). For an overview see [Eme90]. We also use a little bit of category theory (the reader may find all relevant concepts in the introductory chapters of any textbook on the matter, eg =-=[AHS90]-=-): the more exotic notion of freely generated cartesian category is reviewed in the Appendix (for more details see [Sza78]). We also assume that the reader is familiar with the use of many-sorted form... |

208 |
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Citation Context ...he schema language is almost the standard many-sorted, linear temporal first-order with equality language within the context at hand of aspect signatures. For the temporal constructs see for instance =-=[Gol87]-=-: as usual, X is the next operator, F is the sometime operator, G is the always operator and U is the until operator. Note only the unary predicates allowing the recognition that a term of a given sup... |

166 | Object Oriented software Construction - Meyer - 1997 |

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Citation Context ...x (for more details see [Sza78]). We also assume that the reader is familiar with the use of many-sorted formalisms for specification purposes, either in the algebraic abstract data type setting (see =-=[EM85]-=-), or in the program correctness context (see [TZ88]). For a recent account of many sorted logic and its applications see [MT93]. Before entering the presentation of the logic, Section 2 discusses the... |

111 | Object Oriented Programming: An Evolutionary Approach - Cox - 1987 |

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Citation Context ...t the reader is familiar with the use of many-sorted formalisms for specification purposes, either in the algebraic abstract data type setting (see [EM85]), or in the program correctness context (see =-=[TZ88]-=-). For a recent account of many sorted logic and its applications see [MT93]. Before entering the presentation of the logic, Section 2 discusses the underlying object framework (following [ES91]) and ... |

29 |
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Citation Context ... corresponding to a state-dependent menu of enabled actions (at each state the set of actions in which the object is "willing" to involve itself). At this naive level of analysis, already pr=-=oposed in [SFSE89b]-=-, the specification of an object should include the list of its attributes (with the indication of their codomain sorts), the list of its actions (with the indication of their parameter sorts if any) ... |

28 | Temporal Aspects of Logical Procedure Definition - Sernadas - 1980 |

23 |
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Citation Context ... (see [TZ88]). For a recent account of many sorted logic and its applications see [MT93]. Before entering the presentation of the logic, Section 2 discusses the underlying object framework (following =-=[ES91]-=-) and outlines the main requirements for a logic of aspects. The local logic of object aspects is established in Section 3: language, semantics and deductive system. Section 4 presents the auxiliary n... |

20 | An institution of object behaviour - Sernadas, Costa, et al. - 1994 |

20 | In-the-large object-oriented design of information systems - Sernadas, Resende, et al. - 1991 |

19 |
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Citation Context ...of the object aspect and community specific axioms and rules. This is an interesting topic for further research, maybe by coding first the entire logic into a pure many-sorted, first-order logic (see =-=[Man93]-=-). Notwithstanding these limitations, the proposed logic does provide a useful setting for specifying and reasoning about object classes, their aggregations and specializations. We have been experimen... |

18 |
Temporal theories as modularization units for concurrent system specification
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(Show Context)
Citation Context ... the general direction of using temporal logic for (information) system specification triggered by [Pnu77, Ser80] and later explored for instance in [FS88, SFSE89b, CS91, FSMS91, FM92]. Compared with =-=[FM92]-=- our approach puts an emphasis on object classes (and their instances) and deals with interaction in a different way. Instead of using theory morphisms and colimit constructions for describing interac... |

18 | Proof-theoretic semantics of object-oriented speci constructs - Fiadeiro, Sernadas, et al. - 1991 |

18 | H.-D.: Abstract Object Types: A Temporal Perspective - Sernadas, Fiadeiro, et al. - 1988 |

17 |
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(Show Context)
Citation Context ...evant concepts in the introductory chapters of any textbook on the matter, eg [AHS90]): the more exotic notion of freely generated cartesian category is reviewed in the Appendix (for more details see =-=[Sza78]-=-). We also assume that the reader is familiar with the use of many-sorted formalisms for specification purposes, either in the algebraic abstract data type setting (see [EM85]), or in the program corr... |

16 |
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(Show Context)
Citation Context ... uses the simplex algorithm (following [NO79]). The proposed logic has been shown to be useful for providing a (proof-theoretic) semantics of object-oriented specification languages: see for instance =-=[Jun93]-=-. 7 Appendix: Freely generated cartesian categories We shortly describe the functor F cc : PO ! Cat that maps each partial order into its canonical cartesian extension. Let P = hjP j; i be a partial o... |

14 | Modular verification of asynchronous networks - Jonsson - 1987 |

13 | Object inheritance beyond subtyping
- Costa, Sernadas, et al.
- 1994
(Show Context)
Citation Context ...oach may not be sufficient. For instance, specialization with overriding is non-monotonic. This question should be addressed in subsequent work, maybe along the lines proposed for semantic domains in =-=[CSS94]-=- using the notion of partial morphism. However, it does not seem trivial to lift such a notion to the level of theories. Work in this direction is already presented in [BLR93] based upon an earlier ve... |

12 | There Is a Silver Bullet - Cox - 1990 |

12 |
Many-Sorted Logic and its Applications
- Meinke, Tucker
- 1993
(Show Context)
Citation Context ...ation purposes, either in the algebraic abstract data type setting (see [EM85]), or in the program correctness context (see [TZ88]). For a recent account of many sorted logic and its applications see =-=[MT93]-=-. Before entering the presentation of the logic, Section 2 discusses the underlying object framework (following [ES91]) and outlines the main requirements for a logic of aspects. The local logic of ob... |

11 | Objects semantics of temporal logic specification - Fiadeiro, Costa, et al. - 1991 |

10 | Specification of object behaviour with defaults
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(Show Context)
Citation Context ... for semantic domains in [CSS94] using the notion of partial morphism. However, it does not seem trivial to lift such a notion to the level of theories. Work in this direction is already presented in =-=[BLR93]-=- based upon an earlier version of the logic presented herein. Another limitation of the proposed logic is the impossibility of having consistent specializations with side-effects (that is, where a new... |

10 | Denotational semantics of object specification within an arbitrary temporal logic institution
- Sernadas, Sernadas
- 1993
(Show Context)
Citation Context ...is topic, adapting to the proposed framework the ideas already present in the literature (see for instance [Fra86, Jon90, MP92]). Some interesting results concerning fair aggregation are presented in =-=[SS93]-=-, where an institution of objects is established for any given temporal logic of specification. In the institutional front see also [SCS94, FCSM93]. To this end it seems useful to bring in the distinc... |

7 |
Specification and Verification of Database Dynamics
- Fiadeiro, Sernadas
- 1988
(Show Context)
Citation Context ...(SDT \Theta AS) + . The predicate occc refers to the actual occurrence (happening) of c. We refrain to consider here the enabling predicate enbc indicating when the action c is enabled as proposed in =-=[FS88]-=-. Indeed, such a distinction would imply the adoption of a more complicated semantics (at least multilinear). We return to this issue in the concluding remarks. Terms are built using the usual constru... |

5 |
Tableaux for reasoning about objects
- Gouveia, Sernadas, et al.
- 1993
(Show Context)
Citation Context ...amples within the context of a large-scale application and we are now working towards a more machine-oriented deductive system with automatic (or at least computer-aided) theorem proving in mind (see =-=[GSGA93]-=-). A prototype is running for a significant fragment of the proposed logic. Concerning reasoning about numbers the prototype uses the simplex algorithm (following [NO79]). The proposed logic has been ... |

5 | Reasoning about objects using a tableau method - Li, Sernadas - 1991 |

3 | Formal techniques for systems specification and verification - Carmo, Sernadas - 1991 |

2 |
Gentzen-type system for verification in conceptual modeling and knowledge representation
- Sernadas, Gouveia, et al.
- 1991
(Show Context)
Citation Context ...nteractions between persons and cars. The proposed logic is given in an axiomatic style. We decided to refrain from considering in this paper more practical versions, for instance sequent-based as in =-=[SGL92]-=- or tableau-based as in [LS91, GSGA93] where only local reasoning has been considered. Also, we only establish soundness. It should be possible to obtain a (relative) completeness result but that is a... |

1 |
An order-sorted predicate logic with closely coupled taxonomic information
- Beierle, Hedtstuck, et al.
- 1993
(Show Context)
Citation Context ...hence the many-sorted first-order approach. This approach should be ordered for aspect types so that the specialization sub-supertype relationships can be made explicit (this idea is also explored in =-=[BHPS93]-=-). The specification logic must also provide the means for describing the behaviour of each individual, hence the temporal approach. The signature of each aspect should include its attributes and acti... |

1 | Process semantics of temporal logic specification - Nierstrasz - 1989 |