lin-0132

10.1 Reasoning as the evolution of a maintained model

Conventional presentations often identify reasoning with a list of propositions

\[ p_0,p_1,\ldots ,p_n. \]

Such a list suppresses the structure that makes an inference meaningful: the types of its terms, the rule connecting one statement to another, the scope of its evidence, the alternatives it ruled out, and the authority that licensed revision.

lincs instead treats reasoning as controlled evolution of a maintained realization

\[ D_0\rightsquigarrow D_1\rightsquigarrow \cdots \rightsquigarrow D_n. \]

The dashed arrows are not assumed to be logical implications or optimizer steps. Each is a governed transition with a diagnostic history. A state can retain unresolved obstructions; a rejected proposal can leave the state unchanged; and an abstention can request a new observation rather than force a conclusion.

Definition 10.1 CoLT reasoning state

A CoLT reasoning state is a tuple

\[ \mathfrak C_k= (\mathbb S_k,D_k,\mathcal T_k,\pi _k,\mathcal U_k, \mathcal R_k,\mathcal A_k,\mathcal E_k), \]

where

  • \(\mathbb S_k\) is the current structural declaration and \(D_k\) its maintained realization;

  • \(\mathcal T_k\) is the admitted tangent site of meaningful probes;

  • \(\pi _k\) is the quotient that removes declared null variation;

  • \(\mathcal U_k\) is the cover used to localize and glue evidence;

  • \(\mathcal R_k\) is the registered repair language;

  • \(\mathcal A_k\) is the admission contract; and

  • \(\mathcal E_k\) is an evidence and provenance registry.

The declaration can contain propositions, but it can also contain causal mechanisms, database relations, policies, argument roles, source bindings, or interfaces among agents. CoLT therefore applies to reasoning with models, not only to deduction in a fixed propositional language.