Differential Propositional Calculus • 19
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https://inquiryintoinquiry.com/2023/12/10/differential-propositional-calcul…
Failing to fetch me at first keep encouraged,
Missing me one place search another,
I stop some where waiting for you
— Walt Whitman • Leaves of Grass
Life on Easy Street —
The finite character of the extended universe [E†A†] makes
the task of solving differential propositions relatively
straightforward. The solution set of the differential
proposition q : EA → B is the set of models q⁻¹(1) in EA.
Finding all models of q, the extended interpretations in
EA which satisfy q, can be carried out by a finite search.
Being in possession of complete algorithms for propositional calculus
modeling, theorem checking, and theorem proving makes the analytic task
fairly simple in principle, even if the question of efficiency in the
face of arbitrary complexity remains another matter entirely.
The NP‑completeness of propositional satisfiability may weigh against
the prospects of a single efficient algorithm capable of covering the
whole space [E†A†] with equal facility but there appears to be much
room for improvement in classifying special forms and in developing
algorithms tailored to their practical processing.
Resources —
Differential Logic and Dynamic Systems
•
https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part…
Differential Logic • Life on Easy Street
•
https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part…
Regards,
Jon
cc:
https://www.academia.edu/community/LGZ3eV