| … | … | @@ -92,7 +92,7 @@ |
| 92 | 92 | \begin_body |
| 93 | 93 | |
| 94 | 94 | \begin_layout Title |
| 95 | | Aggregate |
| 95 | Aggregate Satisfaction |
| 96 | 96 | \end_layout |
| 97 | 97 | |
| 98 | 98 | \begin_layout Date |
| … | … | @@ -104,7 +104,8 @@ Linas Vepštas |
| 104 | 104 | \end_layout |
| 105 | 105 | |
| 106 | 106 | \begin_layout Abstract |
| 107 | | Stuff |
| 107 | Diary entry, attempting to work out some ideas. |
| 108 | |
| 108 | 109 | \end_layout |
| 109 | 110 | |
| 110 | 111 | \begin_layout Section* |
| … | … | @@ -112,7 +113,76 @@ Introduction |
| 112 | 113 | \end_layout |
| 113 | 114 | |
| 114 | 115 | \begin_layout Standard |
| 115 | | P |
| 116 | What follows will be free-form unstructured writing about aggregate satisfiabili |
| 117 | ty. |
| 118 | It is an attempt to reconcile a number of quite common and inter-related |
| 119 | ideas, and to develop a mathematical frammework for them. |
| 120 | The key ingredients are: |
| 121 | \end_layout |
| 122 | |
| 123 | \begin_layout Itemize |
| 124 | The Ising model as a motivational example. |
| 125 | This pulls in assorted concepts from physics that can be elaborated on. |
| 126 | \end_layout |
| 127 | |
| 128 | \begin_layout Itemize |
| 129 | Link Grammar parsing, in which syntactic jigdaw pieces are assembled to |
| 130 | create parses, called |
| 131 | \begin_inset Quotes eld |
| 132 | \end_inset |
| 133 | |
| 134 | linkages |
| 135 | \begin_inset Quotes erd |
| 136 | \end_inset |
| 137 | |
| 138 | , that are assigned a score. |
| 139 | The lower the linkage cost, the more likely correct linkage is correct. |
| 140 | \end_layout |
| 141 | |
| 142 | \begin_layout Itemize |
| 143 | Aggregate satisfiability, in that satisfiability refers to discrete logical |
| 144 | expressions, while aggregate suggests that there is some mean that indicates |
| 145 | the best possible solution. |
| 146 | \end_layout |
| 147 | |
| 148 | \begin_layout Standard |
| 149 | There are also some other inter-related concepts, which may of may not the |
| 150 | ideas to be developed here. |
| 151 | These include ideas like: |
| 152 | \end_layout |
| 153 | |
| 154 | \begin_layout Itemize |
| 155 | Markov Logic Networks: perhaps what I intend to describe will end up being |
| 156 | a Markov Logic Network. |
| 157 | Or maybe not. |
| 158 | \end_layout |
| 159 | |
| 160 | \begin_layout Itemize |
| 161 | Hopfield networks: these have commonality with regard to assorted physics |
| 162 | concepts. |
| 163 | Maybe they connect with what I intend to describe, and maybe they don't. |
| 164 | \end_layout |
| 165 | |
| 166 | \begin_layout Itemize |
| 167 | Mean field theory. |
| 168 | Who knows. |
| 169 | A knee-jerk reaction is that mean–field theory will describe the rsults. |
| 170 | I suppose. |
| 171 | Seems plausible. |
| 172 | \end_layout |
| 173 | |
| 174 | \begin_layout Itemize |
| 175 | Ensembles. |
| 176 | Of course, everything to be considered is meant to be an ensemble. |
| 177 | But I won't list this as a central point. |
| 178 | \end_layout |
| 179 | |
| 180 | \begin_layout Standard |
| 181 | So here we go. |
| 182 | \end_layout |
| 183 | |
| 184 | \begin_layout Section* |
| 185 | Ising Model |
| 116 | 186 | \end_layout |
| 117 | 187 | |
| 118 | 188 | \begin_layout Section* |