Third tidbit - see propositional stability
Also, propositional abstraction

Logical Modules

We assume a logical module or grammatical fragment suitable for first and higher-order implementations. More precisely, I define a module m per the following:

(1) A negation operator {¬}.
(2) A set of conceptual variables {λ1, …, λn}.
(3) A belief operator {●}.
(4) A set of temporal operators {t1, …, tn}.
(5) A time indexing operator {@}.
(6) The following grammatical rules:

(where wff is any well-formed formula in the language of implementation)

(i) ¬wff is a well-formed formula.
(iia) ●( λa , λb ) is a well-formed formula
(iib) ●( λa ) is a well-formed formula
(iic) where λa , λb range over conceptual variables.
(iii) wff @ ta is a well-formed formula where ta ranges over temporal operators.

A module m is implemented by a language L whenever:

(7) The syntactic marks (symbols) in (1) – (5) are in L’s vocabulary.
(8) The grammatical rules in (6) are consistent with and part of L’s grammar.

I define plug and play with respect to a language L as an attribute of a module whenever it, the module, can satisfy conditions (7) and (8) with respect to L.

Tertiary bits (no pun): a module m interfaces whenever it is implemented by two languages L1, L2. Usually we think of this as a morphism (a kind of relation) between two languages. I’d prefer to focus on the module here.


Carnap's Linguistic Frameworks
Hegel's Dialectical Method and Science of Logic

A conceptual variable denotes a logic.