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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)
Revision as of 15:42, 4 July 2008
, 15:42, 4 July 2008→Review and Transition
It is important to note that the last expressions are not equivalent to the triple bracket <math>(x, y, z).\!</math>
It is important to note that the last expressions are not equivalent to the triple bracket <math>(x, y, z).\!</math>
{| align="center" border="1" cellpadding="8" cellspacing="1" style="text-align:center; width:96%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"
|+ '''Table 1. Syntax and Semantics of a Calculus for Propositional Logic'''
|+ '''Table 1. Syntax and Semantics of a Calculus for Propositional Logic'''
|- style="background:ghostwhite"
|- style="background:ghostwhite"
</blockquote>
</blockquote>
It was only later that Peirce and Jevons treated inclusive disjunction as a fundamental operation, but these authors, with a respect for the algebraic properties that were already associated with the plus sign, used a variety of other symbols for inclusive disjunction (Sty, 177, 189). It seems to have been Schröder who later reassigned the plus sign to inclusive disjunction (Sty, 208). Additional information, discussion, and references can be found in (Boole) and (Sty, 177–263). Aside from these historical points, which never really count against a current practice that has gained a life of its own, this usage does have a further disadvantage of cutting or confounding the lines of communication between algebra and logic. For this reason, it is best to avoid it here.
It was only later that Peirce and Jevons treated inclusive disjunction as a fundamental operation, but these authors, with a respect for the algebraic properties that were already associated with the plus sign, used a variety of other symbols for inclusive disjunction (Sty, 177, 189). It seems to have been Schröder who later reassigned the plus sign to inclusive disjunction (Sty, 208). Additional information, discussion, and references can be found in (Boole) and (Sty, 177–263). Aside from these historical points, which never really count against a current practice that has gained a life of its own, this usage does have a further disadvantage of cutting or confounding the lines of communication between algebra and logic. For this reason, it will be avoided here.
==A Functional Conception of Propositional Calculus==
==A Functional Conception of Propositional Calculus==