This post first appeared on **Postlib.com**.

An updated, more general, abstraction of the concept originally introduced in the section below.

A *logical module* defined. (More abstract, more fully general, newer, definition.)

- A set of
*symbols*within some lexicon L. - A
*grammar*system (rules of formation for wff) for L.

A *logical interface* defined.

Given two languages L₁, L₂ sharing the same proof system S :

- A module
*m strongly interfaces*between L₁, L₂ whenever:

`i.`

Each symbol in L₁ is in L₂.

`ii.`

Each symbol in L₂ is in L₁.

`iii.`

The grammar system defining wff in m is in L₁.

`iv.`

The grammar system defining wff in m is in L₂.

- A module
*m weakly interfaces*between L₁, L₂ whenever:

`i.`

Each symbol in L₁ is in L₂.

`ii.`

The grammar system defining wff in m is in L₁.

`iii.`

The grammar system defining wff in m is in L₂.

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

- A
*negation operator*{¬}. - A set of
*conceptual variables*{λ1, …, λn}. - A
*belief operator*{●}. - A set of
*temporal operators*{t1, …, tn}. - A
*time indexing operator*{@}. - The following grammatical rules (where wff is any well-formed formula in the language of implementation):

`i.`

Where ¬wff is a well-formed formula.

`ii.`

Where ●( λa , λb ) is a well-formed formula.

`iii.`

Where ●( λa ) is a well-formed formula.

`iv.`

where λa, λb range over *conceptual variables*.

`v.`

Where wff @ ta is a well-formed formula where ta ranges over *temporal operators*.

A *module* m is implemented by a language L whenever:

The syntactic marks

*negation operator*,*conceptual variables*,*belief operator*,*temporal operators*, and*time indexing operator*are in L's vocabulary.The grammatical rules above 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 the two conditions (immediately preceding this one) with respect to L.

Tertiary bits (no pun):

A module

`m`

interfaceswhenever 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 themodulehere.

- Carnap's
*Linguistic Frameworks*. - Hegel's
*Dialectical Method*and*Science of Logic*. - A
*conceptual variable*denotes a*logic*.

- Non-Eternalist Logic
- Transactional Logic
- Logical Module
- Dimensional and Hyper-Dimensional Logics
- Dimensional and Hyper-Dimensional Logics #2
- Language of God
- Propositional Stability and Cohen Forcing

##### post: 8/4/2016

##### update: 8/10/2016

##### update: 9/3/2019

##### update: 4/2/2020

##### update: 7/11/2021