Changes

<li>Another approach examines the nature of the objects that are invoked.</li></ol></ol>

<li>Another approach examines the nature of the objects that are invoked.</li></ol></ol>

   

   

<p align="center">'''Fragments'''</p>

<p align="center">'''Fragments'''</p>

In previous work I developed a version of propositional calculus based on C.S. Peirce's ''existential graphs'' and implemented this calculus in computational form as a ''sentential calculus interpreter''.  Taking this calculus as a point of departure, I devised a theory of ''differential extensions'' for propositional domains that can be used, figuratively speaking, to put universes of discourse &ldquo;in motion&rdquo;, in other words, to provide qualitative descriptions of processes taking place in logical spaces.  See (Awbrey, 1989 and 1994) for an account of this calculus, documentation of its computer program, and a detailed treatment of differential extensions.

In previous work I developed a version of propositional calculus based on C.S. Peirce's "existential graphs" (PEG) and implemented this calculus in computational form as a "sentential calculus interpreter" (SCI).  Taking this calculus as a point of departure, I devised a theory of "differential extensions" for propositional domains that can be used, figuratively speaking, to put universes of discourse "in motion", in other words, to provide qualitative descriptions of processes taking place in logical spaces.  See (Awbrey, 1989 & 1994) for an account of this calculus, documentation of its computer program, and a detailed treatment of differential extensions.

In previous work (Awbrey, 1989) I described a system of notation for propositional calculus based on C.S. Peirce's "existential graphs" (PEG), documented a computer implementation of this formalism, and showed how to provide this calculus with a "differential extension" (DEX) that can be used to describe changing universes of discourse.  In subsequent work (Awbrey, 1994) the resulting system of "differential logic" was applied to give qualitative descriptions of change in discrete dynamical systems.  This section draws on that earlier work, summarizing the conceptions that are needed to give logical representations of sign relations and recording a few changes of a minor nature in the typographical conventions used.

In previous work (Awbrey, 1989) I described a system of notation for propositional calculus based on C.S. Peirce's ''existential graphs'', documented a computer implementation of this formalism, and showed how to provide this calculus with a ''differential extension'' that can be used to describe changing universes of discourse.  In subsequent work (Awbrey, 1994) the resulting system of ''differential logic'' was applied to give qualitative descriptions of change in discrete dynamical systems.  This section draws on that earlier work, summarizing the conceptions that are needed to give logical representations of sign relations and recording a few changes of a minor nature in the typographical conventions used.

Abstractly, a domain of propositions is known by the axioms it satisfies.  Concretely, one thinks of a proposition as applying to the objects it is true of.

Abstractly, a domain of propositions is known by the axioms it satisfies.  Concretely, one thinks of a proposition as applying to the objects it is true of.

Logically, a domain of properties or propositions is known by the axioms it is subject to.  Concretely, a property or proposition is known by the things or situations it is true of.  Typically, the signs of properties and propositions are called "terms" and "sentences", respectively.

Logically, a domain of properties or propositions is known by the axioms it is subject to.  Concretely, a property or proposition is known by the things or situations it is true of.  Typically, the signs of properties and propositions are called ''terms'' and ''sentences'', respectively.

===6.20. Three Views of Systems===

===6.20. Three Views of Systems===