## Different Types of Arrow Between Logical Frameworks (1996)

Venue: | Proc. ICALP 96, LNCS 1099, 158--169 |

Citations: | 5 - 2 self |

### BibTeX

@INPROCEEDINGS{Mossakowski96differenttypes,

author = {Till Mossakowski},

title = {Different Types of Arrow Between Logical Frameworks},

booktitle = {Proc. ICALP 96, LNCS 1099, 158--169},

year = {1996},

pages = {158--169},

publisher = {Springer Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

this paper we argue that these different types of arrow can be generated by one basic type of arrow and monadic constructions on categories of logical frameworks, with the effect of automatically having functors relating the new categories of logical frameworks with the old ones. The paper is organized as follows: in Sect. 2, some types of logical framework and some categorical notions are recalled. Section 3 then introduces, using monads and adjunctions, one well-known and three new notions of maps between institutions, which vary in the strictness of keeping the signature--sentence distinction. In each case, we briefly show the application to different logical frameworks. Section 4 concludes the paper. Due to lack of space, we omit proofs, which will appear elsewhere. 2 Preliminaries

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Citation Context ...distinction between the notion of signature and of sentence. But there are many choices for what should be included into the signature part, and what into the sentences. For example, in type theories =-=[15]-=-, typing information is put into the sentences, while in HEP-theories [20], not only typing, but also definedness axioms are put into the signatures. The problem now arises when considering maps. Plai... |

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Citation Context ... many choices for what should be included into the signature part, and what into the sentences. For example, in type theories [15], typing information is put into the sentences, while in HEP-theories =-=[20]-=-, not only typing, but also definedness axioms are put into the signatures. The problem now arises when considering maps. Plain maps (of institutions or entailment systems), which keep signatures and ... |

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Citation Context ...], pre-institutions with transformations [21], institutional frames [27], - and -institutions [12, 23], institutions with contexts [19], etc. Some of these were related by Maura Cerioli in her thesis =-=[6]-=-. Thus, there are quite different types of logical frameworks, and each type of logical framework (together with a type of arrow between logical frameworks) leads to a new category of logical framewor... |

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Citation Context ...the literature, there are described not only one, but many categories of logical frameworks: institutions [13] with maps of institutions [16], specification frames [10], institutions with simulations =-=[2]-=-, pre-institutions with transformations [21], institutional frames [27], - and -institutions [12, 23], institutions with contexts [19], etc. Some of these were related by Maura Cerioli in her thesis [... |

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Citation Context ...y one, but many categories of logical frameworks: institutions [13] with maps of institutions [16], specification frames [10], institutions with simulations [2], pre-institutions with transformations =-=[21]-=-, institutional frames [27], - and -institutions [12, 23], institutions with contexts [19], etc. Some of these were related by Maura Cerioli in her thesis [6]. Thus, there are quite different types of... |

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Citation Context ...ions from the institution of set-valued left exact sketches (see [4]) to the institution of limit theories (an extension of Horn theories with unique-existential quanfitication in the conclusion, see =-=[9]-=-) which is described in [17]. A diagram over a sketch is translated to a set of equations, while a cone over a sketch is translated to the statement that the cone is a limiting cone, which can be expr... |

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