## Moving Between Logical Systems (1998)

Venue: | Recent Trends in Data Type Specification |

Citations: | 55 - 4 self |

### BibTeX

@INPROCEEDINGS{Tarlecki98movingbetween,

author = {Andrzej Tarlecki},

title = {Moving Between Logical Systems},

booktitle = {Recent Trends in Data Type Specification},

year = {1998},

pages = {478--502},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

: This paper presents a number of concepts of a mapping between logical systems modelled as institutions, discusses their mutual merits and demerits, and sketches their role in the process of system specification and development. Some simple properties of the resulting categories of institutions are given. 1 Introduction We have to live with a multitude of logical systems used in various approaches to software specification and development. The proliferation of logical systems in the area is not just researchers' fancy, but results from the very practical needs to capture various aspects of software systems and to cater for various programming paradigms. Each of them leads to a different notion of a semantic model capturing the semantic essence of the adopted view of software systems. For instance, standard (many-sorted) algebras [BL70], [GTW78] provide a satisfactory framework for modelling data types where all operations always yield well-defined results. However, if general recursi...

### Citations

1624 | The Definition of Standard ML
- Milner, Tofte, et al.
- 1990
(Show Context)
Citation Context ... semantics determines its (obvious) signature Sig [SORT ] and class of models Mod [SORT ]. Here is an example of a specification built over the institution PLNG (where a notation based on Standard ML =-=[MTH90]-=- is used as the underlying programming language, with natural numbers and their lists among built-in data types): SORT IMP = hide insert in opns sort: list -? list insert: nat * list -? list axioms in... |

716 | A framework for defining logics
- Harper, Honsell, et al.
- 1993
(Show Context)
Citation Context ...ow whether it is cocomplete, but again, this does not seem directly interesting). It seems important to study the following typical situation, occuring in general logical frameworks like Edinburgh LF =-=[HHP93]: we choos-=-e a powerful logical system, a "universal logic" in which other logics we want to work with would be encoded. Then the encoded logics are combined using the limit construction as suggested a... |

282 | An initial algebra approach to the specification, correctness, and implementation of abstract data types - Goguen, Thatcher, et al. - 1978 |

179 |
General Logics
- Meseguer
- 1989
(Show Context)
Citation Context ...f other systems? For instance, can a proof system developed for one logic be reused for another? This was already studied using the concept of institution morphism [GB92] and institution map [Mes89], =-=[CM93]-=-, as well as in [Tar87]. Yet another notion of institution representation seems most directly suited for this purpose. Some apparently slight technical change w.r.t. the formal definition of instituti... |

150 |
Putting theories together to make specifications
- BURSTALL, GOGUEN
- 1977
(Show Context)
Citation Context ...ides a convenient framework for putting logical systems together using the limit construction, much as the category of theories provides a framework for putting specifications together using colimits =-=[BG77]-=-. Such a process of building logical systems up in a systematic manner is of crucial importance even if we are able to use a number of logical systems at the same time; their explicit combination ofte... |

145 | Toward formal development of programs from algebraic specifications: Implementations revisited
- Sannella, Tarlecki
- 1988
(Show Context)
Citation Context ... a number of logical systems and for developments migrating from one logical system to another, which goes beyond foundations for building specifications [ST88a] and modelling the development process =-=[ST88b]-=- in an arbitrary but fixed institution. Providing such a basis is one of the main goals of the work presented here. To make this possible, institutions involved must be linked in some way with each ot... |

103 | Simple consequence relations
- Avron
- 1991
(Show Context)
Citation Context ...iew of logic: the central concepts are those of model and of satisfaction relation between models and sentences. This does not mean that a view of logic based on the concept of an entailment relation =-=[Avr91]-=- is entirely banned. Most fundamentally, given an institution I = hSign; Sen; Mod; hj= \Sigma i \Sigma2jSignj i, for each signature \Sigma 2 jSignj, the \Sigma-satisfaction relation determines a seman... |

94 | Specifications in an arbitrary institution
- Sannella, Tarlecki
- 1988
(Show Context)
Citation Context ...ies the basic need for specifications spanning a number of logical systems and for developments migrating from one logical system to another, which goes beyond foundations for building specifications =-=[ST88a]-=- and modelling the development process [ST88b] in an arbitrary but fixed institution. Providing such a basis is one of the main goals of the work presented here. To make this possible, institutions in... |

55 |
A kernel language for algebraic specification and implementation
- Sannella, Wirsing
- 1983
(Show Context)
Citation Context ...igma; \Phii] = \Sigma and Mod[h\Sigma; \Phii] = fM 2 jMod(\Sigma)j j M j= \Phig. Further specification-building operations can be introduced to combine and modify presentations in a systematic manner =-=[SW83]-=-. Typical examples of such operations which can be defined over an arbitrary institution are studied in [ST88a]. Operations defined there are powerful enough to express the operations used in a somewh... |

54 | Toward formal development of ML programs: foundations and methodology - Sannella, Tarlecki - 1989 |

50 |
Bits and pieces of the theory of institutions
- Tarlecki
- 1986
(Show Context)
Citation Context ...ution morphism [GB92]. Institution morphisms capture a way in which a "richer" institution is built over a "simpler" one. The resulting category of institutions with institution mo=-=rphisms is complete [Tar86]-=- (we do not know if it is cocomplete, even when small institutions only are considered, but this does not seem of practical importance) and so potentially it provides a convenient framework for puttin... |

44 |
A study in the foundations of programming methodology: Specifications, institutions, charters and parchments
- Goguen, Burstall
- 1985
(Show Context)
Citation Context ... be no hope that limits in the category of institutions, where no analysis of the structure of sentences is available whatsoever, would yield desired results. We believe that a category of parchments =-=[GB86]-=- may provide a more appropriate framework for this. 4.2 Comparing consequence relations Another aspect of potential use of institution morphisms is that since we do translate sentences from one instit... |

29 |
Implementation and behavioural equivalence: A survey
- Orejas, Navarro, et al.
(Show Context)
Citation Context ...a way of translating models of some specifications to models of some other specifications, and so, in essence it can be viewed as a constructor in the sense of constructor implementations of [ST88b], =-=[ONS93]-=-. Therefore, it can be meaningfully used in a formal development process to reduce the task of realising a specification from one institution to realising a specification in another institution linked... |

27 |
Partial abstract data types
- Broy, Wirsing
- 1982
(Show Context)
Citation Context ...ions always yield well-defined results. However, if general recursion is allowed as a mechanism to define operations then we have to admit the potential of their non-termination, and partial algebras =-=[BW82]-=- become more appropriate as semantic models; if we want to capture system infinitary behaviour then perhaps continuous algebras [TW86] are appropriate; if we want to conveniently describe abstract err... |

23 |
Relationships between logical formalisms
- Cerioli
- 1993
(Show Context)
Citation Context ...e of type ( ! / ! ), institution representations are of type ( ! ! / ), Section 5.3 hints at some morphisms of type ( ! ! ! ). Classification of other types of mappings studied in the literature (see =-=[Cer93]-=- for a careful overview) is more difficult due to the use of partial and multi-valued translations of models and sentences. Various forms of satisfaction condition used add extra complexity. One basic... |

19 | A.: Foundations of Algebraic Specification and Formal Program Development - Sannella, Tarlecki - 2011 |

17 | Equivalences among various logical frameworks of partial algebras
- Mossakowski
- 1995
(Show Context)
Citation Context ...ms provide some rudimentary way of comparing logics: intuitively, an institution morphism ��: I 0 ! I captures a way in which "richer" institution I 0 is built over more "poor"=-= institution I (but see [Mos95a]-=- for a careful study of relationship between various logics for partial algebras based on a more refined notion of institution equivalence). This suggests that an appropriate category of institutions ... |

15 | Structured theory presentations and logic representations
- Harper, Sannella, et al.
- 1994
(Show Context)
Citation Context ...rules. Families of entailment relations indexed by signatures may be put in the institutional framework provided they are preserved under translation along signature morphisms, cf. [FS88], [Mes89] or =-=[HST94]-=-. This basic property does indeed hold for the semantic consequence relations: Proposition 2.2 Semantic consequence is preserved by signature morphisms: for any signature morphism oe: \Sigma ! \Sigma ... |

13 | Galleries and institutions - Mayoh - 1985 |

11 |
Algebraic and operational semantics of specifications allowing exceptions and errors. Theoretical Computer Science 34
- Gogolla, Drosten, et al.
- 1984
(Show Context)
Citation Context ... as semantic models; if we want to capture system infinitary behaviour then perhaps continuous algebras [TW86] are appropriate; if we want to conveniently describe abstract errors then error algebras =-=[GDLE84]-=- may be handy, etc. Various properties, and hence various sets of formulae capturing these properties, are then essential for basic specification of systems modelled as such algebras --- again, for ea... |

7 | Context institutions
- Pawlowski
- 1996
(Show Context)
Citation Context ...ategory to combine logic presentations in a systematic way. This may prove especially useful if open formulae and free variables are properly accommodated for, as for instance in context institutions =-=[Paw95]-=-. Consequently, this paper can be viewed merely as a presentation of a necessary but preliminary work preceding a more subtle and technically involved but similar treatment of parchments (perhaps with... |

6 |
A.: Structuring theories on consequence. Recent Trends in Data Type Specification
- Fiadeiro, Sernadas
- 1988
(Show Context)
Citation Context ...nce a set of proof rules. Families of entailment relations indexed by signatures may be put in the institutional framework provided they are preserved under translation along signature morphisms, cf. =-=[FS88]-=-, [Mes89] or [HST94]. This basic property does indeed hold for the semantic consequence relations: Proposition 2.2 Semantic consequence is preserved by signature morphisms: for any signature morphism ... |

6 | Using colimits of parchments to systematically construct institutions of partial algebras - Mossakowski - 1995 |

5 |
Model--theoretic foundations for formal program development: basic concepts and motivation
- Sannella, Tarlecki
- 1995
(Show Context)
Citation Context ...rea can and hence should be carried out in the framework of an arbitrary institution. Indeed, much work has been done along this lines, and many essential ideas have been presented in such a way; see =-=[ST95]-=- and references there. However, working in an arbitrary but fixed logical system (institution) is not always adequate. We often need a number of logical systems to be used in the same specification an... |

5 |
Institution representation. Unpublished note
- Tarlecki
- 1987
(Show Context)
Citation Context ...nstance, can a proof system developed for one logic be reused for another? This was already studied using the concept of institution morphism [GB92] and institution map [Mes89], [CM93], as well as in =-=[Tar87]-=-. Yet another notion of institution representation seems most directly suited for this purpose. Some apparently slight technical change w.r.t. the formal definition of institution morphisms brings a r... |

4 |
M.: Continuous abstract data types. Fundamenta Informaticae 9:95--125
- Tarlecki, Wirsing
- 1986
(Show Context)
Citation Context ...dmit the potential of their non-termination, and partial algebras [BW82] become more appropriate as semantic models; if we want to capture system infinitary behaviour then perhaps continuous algebras =-=[TW86]-=- are appropriate; if we want to conveniently describe abstract errors then error algebras [GDLE84] may be handy, etc. Various properties, and hence various sets of formulae capturing these properties,... |

3 | Structural properties of some categories of institutions
- Tarlecki
- 1996
(Show Context)
Citation Context ...es intuitively (though not formally) dual to those of the category INS of institutions with institution morphisms. For example, INS repr is complete, with limits defined "dually" to those in=-= INS, see [Tar96]-=-. However, unlike in the case of the category of institutions with institution morphisms, this does not seem of any fundamental importance. Limits in INS provide some rudimentary way of combining inst... |

2 |
J.D.: Heteregeneous algebras
- Birkhoff, Lipson
- 1970
(Show Context)
Citation Context ...ogramming paradigms. Each of them leads to a different notion of a semantic model capturing the semantic essence of the adopted view of software systems. For instance, standard (many-sorted) algebras =-=[BL70]-=-, [GTW78] provide a satisfactory framework for modelling data types where all operations always yield well-defined results. However, if general recursion is allowed as a mechanism to define operations... |

2 |
Institutions: asbtract model theory for computer science
- Goguen, Burstall
- 1984
(Show Context)
Citation Context ...ilable, etc. The resulting wealth of logical systems to choose is as much an advantage as a burden, sometimes leading to unnecessary repetitive work. To avoid this repetitiveness, Goguen and Burstall =-=[GB92]-=- introduced the concept of institution to formally capture the informal notion of logical system and provide a basis for doing much of the work on software specification and development independently ... |