## 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

### Citations

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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 ...ogical frameworks in order to relate them. This leads to a category of logical frameworks. In 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], inst... |

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179 |
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Citation Context ...erogeneous specifications with components written in different logical frameworks [13, 25, 3], -- switch between different types of logical framework by borrowing missing logical structure along maps =-=[7]-=-, e.g. endow an institution with an entailment relation and a proof calculus, -- compare expressiveness of different logical frameworks (within one type of logical framework, of course) [17], -- use l... |

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Citation Context ...roof calculus, -- compare expressiveness of different logical frameworks (within one type of logical framework, of course) [17], -- use logical framework independent specification language constructs =-=[22, 6]-=- being preserved by maps. But if we do not follow some neat structuring principle in the meta theory (i. e. types of logical framework), there is the danger to end in the same Babylonian realm of 1 Th... |

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Citation Context ...meworks is that of encoding, or representing one logical framework into another one. 1 With this, one can -- write heterogeneous specifications with components written in different logical frameworks =-=[13, 25, 3]-=-, -- switch between different types of logical framework by borrowing missing logical structure along maps [7], e.g. endow an institution with an entailment relation and a proof calculus, -- compare e... |

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Citation Context ...(t 1 e = t 1 \Gamma! t 1 e = t 2 )s(t 2 e = t 2 \Gamma! t 1 e = t 2 ). A more complex example is the conjunctive simple map of institutions 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 translat... |

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39 |
Initial Computability, Algebraic Specifications, and Partial Algebras
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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 ... |

23 |
Relationships between logical formalisms
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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... |

20 |
Relationships between logical frameworks
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- 1992
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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 ...along maps [7], e.g. endow an institution with an entailment relation and a proof calculus, -- compare expressiveness of different logical frameworks (within one type of logical framework, of course) =-=[17]-=-, -- use logical framework independent specification language constructs [22, 6] being preserved by maps. But if we do not follow some neat structuring principle in the meta theory (i. e. types of log... |

17 |
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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 ...meworks is that of encoding, or representing one logical framework into another one. 1 With this, one can -- write heterogeneous specifications with components written in different logical frameworks =-=[13, 25, 3]-=-, -- switch between different types of logical framework by borrowing missing logical structure along maps [7], e.g. endow an institution with an entailment relation and a proof calculus, -- compare e... |

9 |
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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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Citation Context ... category of logical frameworks. In 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 relat... |

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Citation Context ...types of logical framework), there is the danger to end in the same Babylonian realm of 1 There also are categories of logical frameworks with the purpose of building one framework above another, see =-=[13, 25, 24, 18]-=-. PCalc proofs LogSys proof theory combinations Ent entailment Log Inst satisfaction model theory SpecFram models ent fflffl pcalc l l l l l l l l l l l l l 55 log fflffl ent LS R R R R R R R R R R R ... |

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Citation Context ...ons [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 logical frameworks, and each type of logical framework (together with a type of arrow bet... |