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...is fifteen years of publications extend from theoretical articles on graph theory to basic manuals, expository texts, and philosophical contemplations in the ...ng to found the following important subfields of [[computer science]]: the theory of [[parsing]], the [[semantics]] of programming languages, automatic [[pro

[[Category:Computational Complexity]] [[Category:Graph Theory]]

...wikipedia.org/wiki/Chess" TARGET="_blank" ^[1]</a> The game-tree complexity of chess was first calculated by Claude Shannon as 10 120, a number known a

===Appendix 3. Computational Details=== [[Category:Computational Complexity]]

Managing the conceptual complexity of our considerations at this juncture put us in need of some conceptual to ...hat one might compile a theory from axioms without knowing what either the theory or the axioms were about &mdash; and the best way to sum up the state of in

A '''logical graph''' is a [[graph theory|graph-theoretic]] structure in one of the systems of graphical [[syntax]] t ==Computational representation==

...ken, forward course by following steps that are never unsure. Acquiring a theory of inquiry is not, in short, a purely deductive exercise. ...o positive proof can arise from so negative a recommendation. Acquiring a theory of inquiry is not, in sum, a purely inductive exercise.

==Computational representation== ...p, one layer, one piece at a time, and it's just as much the case when the complexity of the object is irreducible, that is, when the articulations of the repres

...cause it uses a species of graphs that are usually called "cacti" in graph theory. The last exposition of the cactus syntax that I've written can be found h The representational and computational efficiency of the cactus language for the tasks that are usually associated

...d on the pragmatic theory of inquiry and its relationship to the pragmatic theory of signs. ...re of inquiry processes, with an eye to those elements that can be given a computational basis.

Linear Topics. The Differential Theory of Qualitative Equations that are employed in mathematical systems theory

of systems theory and artificial intelligence to each other. in systems theory, working to extend its concepts and methods

...have especially nice properties, turning out to be not only useful from a computational standpoint but also quite interesting from a theoretical point of view. Th For computational purposes, it is convenient to have a middle ground or an intermediate langu

...of-theoretic purity somewhere in the middle of grinding this calculus into computational form, I never got around to finding the most elegant and minimal, or anythi ...other name for the theory of inquiry is ''logic'' and another name for the theory of signs is ''semiotics''. So I might as well have said that I am interest

...propositions. A calculus that is very efficient from both conceptual and computational standpoints is based on just two types of logical connectives, both of vari ...ast of which has been the lack of a syntax that was adequate to handle the complexity of expressions that evolve.

...day mathematical bearing, but also in way that's not unrelated to Peirce's theory of categories. ...ur consideration of logical graphs, as seems most fitting, within Peirce's theory of triadic sign relations, we have declared the first layers of our object,

...ast of which has been the lack of a syntax that was adequate to handle the complexity of expressions that evolve. ...hat will extend a gentle invitation to the mathematical subject of ''group theory'', and demonstrate its relevance to differential logic in a strikingly apt

of inquiry as a dynamic process of theory change. of inquiry as a dynamic process of theory change.

...In the current phase of investigation I am taking a standpoint in systems theory, working to extend its concepts and methods to cover increasingly interesti ...work of the past few years I have sought to apply the framework of systems theory to the problems of AI. I believe that viewing intelligent systems as dynam

...propositions. A calculus that is very efficient from both conceptual and computational standpoints is based on just two types of logical connectives, both of vari ...relations are desirable because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reaso

adequate to handle the complexity of expressions that evolve. to the mathematical subject of "group theory", and demonstrate its

...r of factors, not the least of which being a syntax adequate to handle the complexity of expressions that evolve. ...hat will extend a gentle invitation to the mathematical subject of ''group theory'', and demonstrate its relevance to differential logic in a strikingly apt

The '''Drake equation''' is a [[probability theory|probabilistic argument]] used to estimate the number of active, communicati ...d to find anything, even though radio telescopes, receiver techniques, and computational abilities have improved significantly since the early 1960s. It has, howeve

.../math> ought not to be misconstrued as a device for magically generating a theory of inquiry from nothing. Like any other inquiry, it requires an agent to i ...eptive way, hiding how early in the empirical process the "cloven hoof" of theory actually enters.

...intend to address crucial questions about the operation, organization, and computational facilitation of inquiry, taking inquiry to encompass the general trend of a ...variety of formal systems and then implementing these representations in a computational medium as a way of clarifying the more complex descriptions that evolve.

...relations are desirable because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reaso ...atment of types, and they both have to do with our being able to take full computational advantage of certain dimensions of flexibility in the types that apply to t

...relations are desirable because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reaso ...atment of types, and they both have to do with our being able to take full computational advantage of certain dimensions of flexibility in the types that apply to t

...relations are desirable because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reaso ...atment of types, and they both have to do with our being able to take full computational advantage of certain dimensions of flexibility in the types that apply to t

...lly used, characteristically and as a matter of principle, to describe P's theory of R. ...T-theory of R, then we should say that "S describes P's theory of R as a T-theory of R".

...terms to mathematical quantities, is the very core of what "quantification theory" is all about, and definitely more to the point than the mere "innovation" ...g what may be called a ''principle of correspondence'' between probability theory and its limiting case in the forms of logic.

====Linear Topics : The Differential Theory of Qualitative Equations==== ...asses of mathematical structures that are employed in mathematical systems theory to model dynamical systems of very general sorts.

: [[User:Jon Awbrey/Mathematical Notes#CAT. Category Theory|CAT. Category Theory]] : [[User:Jon Awbrey/Mathematical Notes#GRAPH. Graph Theory|GRAPH. Graph Theory]]

...ncourage an ''ordinary language'' (OL), a ''formal language'' (FL), or a ''computational language'' (CL) approach, have their relevant properties illustrated in the ...ed in this section. Throughout this work as a whole, the subject of group theory serves in both illustrative and instrumental roles, providing, besides a ro

and computational facilitation of inquiry, taking inquiry to encompass and then implementing these representations in a computational medium as a

adequate to handle the complexity of expressions that evolve. to the mathematical subject of "group theory", and demonstrate its

...ey/Philosophical Notes#RTOK. Russell's Theory Of Knowledge|RTOK. Russell's Theory Of Knowledge]] | doctrine, which is in harmony with the above theory