Introduction of natural implication to propositional calculus
needs no modal operators, as C.
Shannon developed the statistical theory of information, the application of propositional calculus
to switching circuits, and has results on the efficient synthesis of switching circuits, the design of machines that learn, cryptography, and the theory of Turing machines.
And by making Owen a writer of code, Updike lets himself munch on and ruminate whole new pastures of language, from propositional calculus
, advanced topology, and invariant Betti groups to Turing tests, Markov chains, and random variables.
But we cannot in turn define a proof of C [disyuncion] D from premise A as 'a proof of C from premise A or a proof of D from premise A', because that would legitimate the law of distribution of [flecha diestra] into [disyuncion], which is strongly non-constructive, and certainly not deducible in the intuitionistic propositional calculus
The reader will find similar brief and tantalizing introductions to perceptions (the simplest sort of neural network), to Kripke's propositional calculus
, to Marschak-Radner team theory and its relation to games of imperfect recall, to Turing machines, and to a host of other ideas including Rubinstein's own famous concept of complexity in automata games.
The resulting system is cumbersome; for example, the proof of Cesare applies transformation rules 26 times, even assuming five theses of propositional calculus
not among the axioms.
In propositional calculus
, 0 and 1 are called truth values: 0 for a false statement; 1 for a true one.