Definitions of loglanghood
When the term loglang first came into being, in the 1990s, it meant language 'based' on formal logic, the then prototypical examples being Loglan and Lojban. This wiki does not presuppose any particular definition of loglanghood, but nevertheless some loglangers have proposed more precise definitions (at least in their own loglangologizing).
And Rosta: predicate-argument structures
And Rosta has for many years defined loglang as a language that unambiguously encodes a limitless range of predicate-argument structures
- In other words, a language that unambiguously encodes the syntax of Propositional Thought.
- 'unambiguously' = what John Clifford has termed monoparsing. At minimum this requires that, where sentences are pairings of phonological form and logical form, no two sentences share the same phonological form.
Maiku: syntax-semantics isomorphism
Some crude thoughts to be developed:
My view of the definition of loglang is heavily influenced by Richard Montague's work, which in my opinion was a product of pure loglanging, albeit carried out in the opposite direction of usual loglanging: rather than starting with a grammar and adding a phonology and building up a speakable language, Montague started with an already existing natural language (namely English), focused on a "fragment" of that language, and attempted to demonstrate the formal properties of various elements of that fragment, including quantifiers, articles, and conjunctions. Open-class English content-words such as "fish", "walk", "tall" etc. were treated as predicates as might be found in any loglang, and Montague uses category theory to develop a syntactic schema to explain the allowed combinations of English's various parts of speech.
Montague's program contains a lot of important concepts, but one I'll touch on here is the idea of syntax-semantics isomorphism, which can also be called model-theoretic semantics, which embodies the idea of a loglang not merely having a formal grammar but having an interpreted formal grammar. What this means is that every syntactic unit from sentence down to word or morpheme has an interpretation in the "model", i.e. something that the syntactic unit points to in the domain of discourse. So a sentence like "le mlatu cu xekri" expresses the proposition that the cat is black. This sentence can be decomposed into "le mlatu", which expresses a first-order entity, namely the cat, and "cu xekri" which is roughly a mapping from first-order entities to truth values, or to propositions (i.e., a predicate). "Le mlatu" can be further decomposed into the choice operation "le" and another predicate "mlatu". Thus, the overall structure of the sentence observes Frege's principle of compositionality from top to bottom. In constructing loglangs, the loglanger carries this principle to the furthest limit -- ideally, there is one formal rule of semantic interpretation for each formal rule of grammar (morphology and above). This one-for-one ideal is one that has been all too often neglected in the history of loglanging, but in my humble opinion it's the ultimate goal, without which formal grammars amount to rather pointless string rewriting rules.