Add commentary on 3 papers.
Chris Pressey
6 months ago
| 162 | 162 | TODO |
| 163 | 163 | ---- |
| 164 | 164 | |
| 165 | * For commentary links on secondary entries: either don't show them, or have the link | |
| 166 | go to the proper (primary) topic's commentary page. | |
| 165 | 167 | * Match wayback machine links, show "(wayback)" on them |
| 166 | 168 | * Match PDF links, show "(PDF)" on them |
| 167 | 169 | * Questions, as seperate from Webpages |
| 133 | 133 | |
| 134 | 134 | * rating: 2 |
| 135 | 135 | |
| 136 | . | |
| 136 | I found this interesting but didn't write many coherent notes, just highlighted | |
| 137 | some paragraphs. The one coherent note I left is a paraphrase of one thing in it: | |
| 138 | ||
| 139 | The question of wether RA completely axiomatizes the | |
| 140 | equational theory of binary relations was answered in | |
| 141 | the negative by Lyndon in 1950, but given that the | |
| 142 | equations that it cannot capture are complicated to | |
| 143 | describe, one might interpret this as a technicality | |
| 144 | only, and consider RA to be "pragmatically" complete. | |
| 145 | ||
| 146 | R.C. Lyndon. The representation of relational algebras. | |
| 147 | Ann. of Math., Ser 2, 51:707–729, 1950. | |
| 148 | ||
| 149 | I would be really interested in understanding the structure of the | |
| 150 | equations it cannot capture. | |
| 137 | 151 | |
| 138 | 152 | ### The Algebra of Logic Tradition (Stanford Encyclopedia of Philosophy) |
| 139 | 153 |
| 50 | 50 | |
| 51 | 51 | * rating: 1 |
| 52 | 52 | |
| 53 | Only skimmed. Historical overview. Not bad but more information than I probably need. | |
| 53 | Only skimmed. It's a historical survey of the development | |
| 54 | of modal logic, whcih seems pretty decent, but contains | |
| 55 | more information than I probably need. | |
| 56 | ||
| 57 | One thing that changed between Kripke's first and second formulations of Kripke-style models | |
| 58 | seems a little interesting. The set of "possible worlds" changed to being an arbitrary | |
| 59 | set, allowing different worlds to assign the same truth values to atomic formulas. There | |
| 60 | seems to be a parallel to situation calculus here, where multiple distinct situations (histories) | |
| 61 | can result in the same world-state (all fluents evaluate to the same values in both situations; | |
| 62 | they either describe the same world, or identical worlds.) | |
| 54 | 63 | |
| 55 | 64 | ### Topological semantics of modal logic |
| 56 | 65 |
| 63 | 63 | |
| 64 | 64 | * rating: 1 |
| 65 | 65 | |
| 66 | . | |
| 66 | The authors present natural deduction-based logical systems that represent | |
| 67 | various parsing algorithms for context-free grammars (CYK, recursive descent, | |
| 68 | LR parsing, Earley's algorithm) and then some more sophisticated grammars -- | |
| 69 | Augmented Phrase-Structure Grammar (which is unification-based), | |
| 70 | Combinatory Categorial Grammars (which is Lambek-ish), | |
| 71 | Tree Adjoining Grammar (which is just weird). | |
| 72 | ||
| 73 | They present these to buttress their claim that parsing algorithms can be | |
| 74 | represented directly as deduction systems. | |
| 75 | ||
| 76 | These presentations could be used to form simple (but inefficient) implementations | |
| 77 | of these parsing algorithms in Prolog. At any rate, it elucidates the algorithms to | |
| 78 | some degree. | |
| 79 | ||
| 80 | Section 4.4 I also found interesting, but for different reasons. It's about the | |
| 81 | sequent calculus. They say their preceding presentations based on natural deduction | |
| 82 | can be implemented by bottom-up execution. Then they note Lambek calculus is | |
| 83 | presented as a sequent calculus system. Then they note that it is difficult to | |
| 84 | apply their techniques to sequent calculus systems, because | |
| 85 | "computationally they are designed to be used in a top-down direction". | |
| 86 | ||
| 87 | I would have thought both ND and SC were relational systems, and that "executing" | |
| 88 | them in one direction or the other would always necessitate search of some sort | |
| 89 | to deal with the nondeterminism. It's surprising to see them hold what looks like | |
| 90 | a markedly different view. Not sure if it has something to do with the connection | |
| 91 | to parsing, or not. | |
| 67 | 92 | |
| 68 | 93 | ### Taming Context-Sensitive Languages with Principled Stateful Parsing |
| 69 | 94 |