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.

Applications

Carnap's *Linguistic Frameworks*

Hegel's *Dialectical Method* and *Science of Logic*

A *conceptual variable* denotes a *logic*.