SUO: Re: Peirce's MS 514
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John Velman wrote:
>
> The contributions of John S, Pat Hayes, Chris Menzel
> and others to this thread have helped clarify a lot
> of things that I thought I already understood.
> A short footnote to Pat's note --
>
> It is also amazing that there is such a large variety
> of useful (not necessarily complete) inference systems,
> involving various combinations of axioms, axiom schemata,
> and rules of inference. If one has only axioms, and no rules
> of inference, the theory is only the axioms (using theory to
> mean the body of statements that can be inferred, not the
> totality of what is entailed.)
All systems I know of that advertize themselves as having
no "rules of inference" (ROI's) still make use of principles
of substitution and replacement -- typically transposing these
two names in every next system that you run across -- and these
have a power that is analogous to modus ponens, if I recall aright
from the last time that I got intense about working on this issue --
memories like strawberries grows fuzzy with time, however ...
> In logic programming, the rules in a program are usually regarded as
> axioms (insofar as we're speaking of rules with only logical intent).
> In extending prolog to a certain version of paraconsistent logic
> Vladimir Lifschitz proposes instead to regard the rules as
> rules of inference. This provides a completely new
> perspective on the 'meaning' of the logic programs
> in question.
Many Regards,
Jon Awbrey
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