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...equational theory of two values, and observes the equivalence of both the lattice and ring definitions to this more elementary one.'' ...rt respectively a logical and an arithmetic character to the subject. The lattice basis originated in the 19th century with the work of [[Boole]], [[Peirce]]

{{DISPLAYTITLE:Functional Logic : Higher Order Propositions}} ...sitions about things in <math>X,</math> the first of a series of '''higher order propositions''' based on <math>X.</math>

===Higher Order Propositional Expressions=== ...with a bit of concrete material, I begin with a consideration of ''higher order propositional expressions'', in particular, those that stem from the propos

...c cone, or the pencil that is generated by a point in a lattice or partial order, with no real connection to physics intended, at least, not so directly as ...st one aspect of Peirce's theory, but we can refine it as we go. The next order of business, though, is to balance these abstract speculations with a few w

...alogy, placing it in relation to his overall theory of inquiry. The first order of business is to introduce the three fundamental types of reasoning that P ===Higher Order Propositional Expressions===

===Zeroth order inquiry=== ...the gentlest availing slope, we may well begin at the level of ''[[zeroth-order inquiry]]'', in effect, taking the syllogistic approach to inquiry only so

...ve term'' and a ''disjunctive term'' might look if they were cast within a lattice-theoretic frame. ...ctive term, "spherical, bright, fragrant, juicy, tropical fruit", within a lattice framework. We have these six terms:

by our ambler in any particular order, but we might suppose moderately well by blocking it out as a "zeroth order theory (ZOT):

...Awbrey/Mathematical Notes#HOC. Higher Order Categorical Logic|HOC. Higher Order Categorical Logic]] | example is the linear order !w! [omega]. As a category, it consists of

In order to discuss questions of this type, it is useful to define several "operator That's the basic idea. The next order of business is to develop the logical side of the analogy a bit more fully,

These concepts and notations may now be explained in greater detail. In order to begin as simply as possible, let us distinguish two levels of analysis a ===Propositions as Types and Higher Order Types===

These concepts and notations can now be explained in greater detail. In order to begin as simply as possible, I distinguish two levels of analysis and se ===Propositions as Types and Higher Order Types===

These concepts and notations may now be explained in greater detail. In order to begin as simply as possible, let us distinguish two levels of analysis a ===Propositions as Types and Higher Order Types===

These concepts and notations may now be explained in greater detail. In order to begin as simply as possible, let us distinguish two levels of analysis a ===Propositions as Types and Higher Order Types===

...is expected to serve, and then by analyzing these formal specifications in order to design computer programs that fulfill them. ...esearch (AIR), involving the conceptual and operational analysis of higher-order cognitive capacities with an eye toward the modeling, grounding, and suppor

In order to describe the universe in which these operators operate, the (first order) "enlargement" of f is the

operational analysis of higher-order cognitive capacities with an eye logic (the normative study of how we ought to think in order to accomplish

05:07 < Ironholds> the right question is "how do I get lattice-based graphs to accept coordinate-based input" or, alternately, "how do I g ...g it subject-oriented instead of article-oriented? this means using an "in order to understand the subject, an understanding of the following subjects is re