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• Directory:Jon Awbrey/Papers/Cactus Rules
  of k expressions is read as their k-adic logical conjunction, second, of the k expressions e_1, ..., e_k is false. I may sometimes refer to
  343 KB (13,950 words) - 02:46, 23 May 2009
• Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata
  ...evel of logic in the same way that differential calculus augments analytic geometry to handle change and diversity. There are several different introductions The parenthetical expressions on the right are the cactus forms for the boolean functions that correspond
  134 KB (16,535 words) - 15:30, 11 October 2013
• Latitude
  ...[[coplanar]], and all such [[Plane (mathematics)|plane]]s are [[Parallel (geometry)|parallel]] to the [[Equator]]. Lines of latitude other than the Equator a The expressions following assume [[ellipse|elliptical]] polar sections with the '''[[angula
  19 KB (2,694 words) - 21:23, 20 January 2008
• Differential Logic and Dynamic Systems • Part 1
  * A bracketed list of propositional expressions in the form <math>\texttt{(} e_1 \texttt{,} e_2 \texttt{,} \ldots \texttt{, * A concatenation of propositional expressions in the form <math>e_1 ~ e_2 ~ \ldots ~ e_{k-1} ~ e_k</math> indicates that
  98 KB (15,568 words) - 16:22, 2 February 2026
• User:Jon Awbrey/TRUTH
  ...for the sake of critical reflection, is that an examination of its verbal expressions can tell us something of signficance about any subject that is brought befo ...for the sake of critical reflection, is that an examination of its verbal expressions can tell us something of signficance about any subject that is brought befo
  237 KB (37,371 words) - 11:22, 20 August 2007
• Directory:Jon Awbrey/TRUTH
  ...for the sake of critical reflection, is that an examination of its verbal expressions can tell us something of signficance about any subject that is brought befo ...for the sake of critical reflection, is that an examination of its verbal expressions can tell us something of signficance about any subject that is brought befo
  237 KB (37,371 words) - 22:14, 25 January 2008
• Directory:Jon Awbrey/Papers/Differential Logic : Introduction
  ...that the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes. ...d of propositional expression is a parenthesized sequence of propositional expressions, written as <math>\texttt{(} e_1 \texttt{,} e_2 \texttt{,} \ldots \texttt{,
  131 KB (20,198 words) - 15:38, 2 December 2015
• User:Jon Awbrey/PROSPECT
  methods of differential geometry with the techniques of logic or descriptors can be any relevant signs or symbolic expressions: names,
  162 KB (25,941 words) - 13:28, 9 January 2008
• Introduction to Inquiry Driven Systems
  80 bytes (10 words) - 11:56, 6 October 2010
• Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 3.0
  ...d of propositional expression is a parenthesized sequence of propositional expressions, written as <math>\texttt{(} e_1 \texttt{,} e_2 \texttt{,} \ldots \texttt{, ...nd of propositional expression is a concatenated sequence of propositional expressions, written as <math>e_1\ e_2\ \ldots\ e_{k-1}\ e_k</math> and read to say tha
  519 KB (74,456 words) - 15:46, 3 October 2013
• Directory:Jon Awbrey/Papers/Differential Logic
  ...that the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes. However you draw it, these expressions follow because the expression <math>x + \mathrm{d}x,\!</math> where the plu
  145 KB (19,916 words) - 19:32, 11 December 2014
• Directory:Jon Awbrey/Papers/Introduction to Inquiry Driven Systems
  ...ultimately it becomes necessary for the system to have a formal syntax of expressions in which logical propositions about states can be represented and manipulat ...qualitative problem just stated with the questions treated in differential geometry and geometric dynamics.
  121 KB (16,341 words) - 04:34, 30 October 2015
• Directory:Jon Awbrey/Essays/Prospects For Inquiry Driven Systems
  ...My instrumental focus is placed on integrating the methods of differential geometry with the techniques of logic programming. I will attempt to embody this pr ...pointwise indicators or descriptors can be any relevant signs or symbolic expressions: names, code numbers, address pointers, or quoted phrases. A "vector fiel
  226 KB (34,541 words) - 14:20, 20 August 2016
• User:Jon Awbrey/Mathematical Notes
  ...hematical Notes#DIF. Differential Geometry For Engineers|DIF. Differential Geometry For Engineers]] analytic geometry, because instead of thinking about
  567 KB (86,909 words) - 21:00, 6 December 2016
• Differential Logic and Dynamic Systems
  * A bracketed list of propositional expressions in the form <math>\texttt{(} e_1, e_2, \ldots, e_{k-1}, e_k \texttt{)}</mat * A concatenation of propositional expressions in the form <math>e_1 ~ e_2 ~ \ldots ~ e_{k-1} ~ e_k</math> indicates that
  528 KB (75,728 words) - 21:56, 14 January 2021
• Directory:Jon Awbrey/Differential Logic and Dynamic Systems 2.0
  * A bracketed list of propositional expressions in the form <math>\texttt{(} e_1, e_2, \ldots, e_{k-1}, e_k \texttt{)}\!</m * A concatenation of propositional expressions in the form <math>e_1 ~ e_2 ~ \ldots ~ e_{k-1} ~ e_k</math> indicates that
  529 KB (75,750 words) - 14:32, 3 March 2023
• Differential Logic and Dynamic Systems • Part 3
  ...h to mark the relevant distinctions and to help us convert between related expressions at different levels of explicitness in their functionality. ...h> and Column&nbsp;5 simplifies these equations into the form of algebraic expressions. As always, <math>{}^{\backprime\backprime} + {}^{\prime\prime}</math> ref
  105 KB (14,158 words) - 17:48, 9 February 2026
• Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems
  While working with expressions solely in propositional calculus, the use of plain parentheses to represent One should be careful to observe that these last two expressions are not equivalent to the form (''A'',&nbsp;''B'',&nbsp;''C'').
  394 KB (54,134 words) - 14:30, 3 March 2023
• Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 4
  ...ates, ultimately it is necessary for the system to have a formal syntax of expressions in which propositions about states can be represented and manipulated. I h ...ated with the kinds of questions that are commonly treated in differential geometry and in geometric representations of dynamics.
  92 KB (15,197 words) - 20:40, 24 August 2025
• Directory:Jon Awbrey/Differential Logic : Various Sketches
  ...rom parsing the cactus string expressions, the ''painted and rooted cactus expressions'' (PARCE's). Finally, I will add a couple of venn diagrams that will serve ...describes <math>Q\!</math> is represented by the following graph and text expressions:
  369 KB (46,156 words) - 04:20, 27 December 2016

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