## Algebraic Semiotics, ProofWebs, and Distributed Cooperative Proving (1997)

Venue: | Proceedings, User Interfaces for Theorem Provers |

Citations: | 10 - 9 self |

### BibTeX

@INPROCEEDINGS{Goguen97algebraicsemiotics,,

author = {Joseph Goguen and Akira Mori and Kai Lin},

title = {Algebraic Semiotics, ProofWebs, and Distributed Cooperative Proving},

booktitle = {Proceedings, User Interfaces for Theorem Provers},

year = {1997},

pages = {25--34}

}

### OpenURL

### Abstract

: We describe a new approach to interface design called algebraic semiotics, combining semiotics with algebraic specification to give a rigorous theory of representation quality, and we apply it to the tatami distributed cooperative proving project. This project uses standard html, Java, etc. for remote proof browsing, servers for remote proof execution, a protocol to maintain truth of distributed cooperative proofs, and a tool combining proof assistance with website editing. Its proof paradigm reduces theorems to problems solvable by proof servers. ProofWebs integrate browsing, execution, animation, and informal explanation with formal proofs, and their design has been driven by semiotic ideas. 1 Introduction The landscape of theorem proving can be seen as two main peaks with a great plane between. These peaks represent fully automatic theorem provers and proof checking theorem provers; the plane represents the difficulty of combining their virtues. The peaks are steep and dark bec...

### Citations

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Citation Context ...ency to preserve higher levels at the expense of lower levels. This may be surprising, because of emphasis by cognitive psychologists on the "basic level" of lexical concepts (e.g., "bi=-=rd", see Rosch [13, 14]-=-). The sentential level of natural language was long considered basic, but research like that of [5] shows that the discourse level is higher in our technical sense, and thus more important. This sugg... |

111 | A hidden agenda
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Citation Context ... far from being a proof checker as it is from being an automatic theorem prover 3 . Our target application is behavioral proofs for concurrent distributed systems, using new coinduction proof methods =-=[7]-=-. The tremendous progress of theorem proving system performance makes it arguable that the most pressing open problems now concern user interfaces. Technology-driven approaches to interface design are... |

103 |
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Citation Context ...tematically addressed quality of representation, and has not taken sufficient account of social context. We address these problems with algebraic semiotics [2], which combines algebraic specification =-=[6]-=- with social semiotics in the sense of [3]. We have built a proof planning and website 5 construction tool called kumo [4]. We are also building a 1 The research reported in this paper has been suppor... |

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Citation Context ...ency to preserve higher levels at the expense of lower levels. This may be surprising, because of emphasis by cognitive psychologists on the "basic level" of lexical concepts (e.g., "bi=-=rd", see Rosch [13, 14]-=-). The sentential level of natural language was long considered basic, but research like that of [5] shows that the discourse level is higher in our technical sense, and thus more important. This sugg... |

57 | Institution morphisms
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Citation Context ...n a mathematically rigorous way, has not systematically addressed quality of representation, and has not taken sufficient account of social context. We address these problems with algebraic semiotics =-=[2]-=-, which combines algebraic specification [6] with social semiotics in the sense of [3]. We have built a proof planning and website 5 construction tool called kumo [4]. We are also building a 1 The res... |

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Citation Context ... of 30, 60, 30 minutes, with "plot points" to move action from one act to the next. Proofs that are structured this way might be easier to understand. Another resource is the theory of stori=-=es. Labov [9] says oral narr-=-atives have a precise structure, involving a sequence of "narrative clauses" describing events whose order corresponds to their order in the story, interleaved with "evaluative material... |

41 | Towards a Social, Ethical Theory of Information
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Citation Context ...ation, and has not taken sufficient account of social context. We address these problems with algebraic semiotics [2], which combines algebraic specification [6] with social semiotics in the sense of =-=[3]-=-. We have built a proof planning and website 5 construction tool called kumo [4]. We are also building a 1 The research reported in this paper has been supported in part by the CafeOBJ project of the ... |

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Citation Context ... more understandable and interesting by recording the local conflicts that motivate difficult proof steps on ProofWebs; as Aristotle said, "Drama is conflict." Syd Field's screen writing boo=-=ks (e.g., [1]) give a p-=-recise but naive dramatic structure: Hollywood plots should have three acts, for setup, conflict, and resolution, of 30, 60, 30 minutes, with "plot points" to move action from one act to the... |

15 |
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Citation Context ...ys better than text, and that some multimedia combination is often better than any single medium [12]. For example, a clickable proof graph can be difficult to use for all but the smallest proofs 4 ; =-=[11]-=- considers why many serious users may prefer command line interfaces to direct manipulation. General insights from HCI do not give enough insight; we need specific work on the nature of proving, like ... |

11 |
Akira Mori, Grigore Rosu, and Akiyoshi Sato. Distributed cooperative formal methods tools
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- 1997
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Citation Context ...problems with algebraic semiotics [2], which combines algebraic specification [6] with social semiotics in the sense of [3]. We have built a proof planning and website 5 construction tool called kumo =-=[4]-=-. We are also building a 1 The research reported in this paper has been supported in part by the CafeOBJ project of the Information Promotion Agency (IPA), Japan, as part of its Advanced Software Tech... |

10 |
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Citation Context ...barista server; later there will be servers for other provers and sites around the world, and of course more proofs, including correctness of our tatami protocol and of an optimizing compiler for OBJ =-=[8]-=-. A prototype of kumo is also available over the web. Akiyoshi Sato is building a generator for kumo-like systems; he is also implementing the tatami protocol, so that we can experiment with distribut... |

10 |
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Citation Context ...rs why many serious users may prefer command line interfaces to direct manipulation. General insights from HCI do not give enough insight; we need specific work on the nature of proving, like that in =-=[10]-=-. This paper tackles user interface problems using semiotics, the study of signs. Unfortunately, this area has not developed in a mathematically rigorous way, has not systematically addressed quality ... |

8 | Why computer interfaces are not like paintings: the user as a deliberate reader
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Citation Context ...are common, and graphical user interfaces are popular. But HCI research shows that graphics is not always better than text, and that some multimedia combination is often better than any single medium =-=[12]-=-. For example, a clickable proof graph can be difficult to use for all but the smallest proofs 4 ; [11] considers why many serious users may prefer command line interfaces to direct manipulation. Gene... |

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Citation Context ...ogical complexity (i.e., effort of pronunciation). "Designer" orderings that combine various preservation properties in a specific way may be useful for specific applications. Experiments re=-=ported in [5]-=- show that preserving high levels is more important than preserving priorities, which in turn is more important than preserving content. They also show a strong tendency to preserve higher levels at t... |