# Meaning generalization

The meaning of a linguistic sign is generalized by a reduction of its intension and a corresponding widening of its extension. Assume the meaning of a linguistic sign to consist of a set of propositions, in the logical sense of the term. These are syntagmatically related to each other by means of truth-value functors. Three relations of propositional calculus are of particular relevance here. Ceteris paribus,

1. the disjunction of `p ∨ q`, as opposed to mere `p`, enhances the extension of meaning;
2. the conjunction of `p ∧ q`, as opposed to mere `p`, enhances the intension of a meaning;
3. the entailment of `p → q`, as opposed to mere `q` (or equivalently, given that `p → p`, the substitution of `q` by `p`), enhances the intension of meaning.

From a logical point of view, there are, thus, three ways that a meaning can be generalized:

1. To `p`, `q` is added as an alternative, converting it into `p ∨ q`;
2. in `p ∧ q`, `p` is lost;
3. in `p → q`, `p` is lost.

Observe that while in `p ∧ q`, either `p` or `q` may be lost, in `p → q`, `q` cannot be lost ceteris paribus, since if `p` remains what it was, it would always entail `q`.

Examples:

1. At a first stage, printer(x) is only an agent noun, meaning ‘somebody who prints’: ‘prints(x) ∧ human(x)’. At a second stage, it is also an instrument noun, meaning ‘something that prints’; thus: ‘prints(x) ∧ (human(x) ∨ artefact(x))’
2. In Middle English, dog (x) means ‘canine(x) ∧ big(x)’. In Modern English, it only means ‘canine(x)’.
3. Vulgar Latin arripare (x, y) means ‘(x goes by ship) ∧ (the ship reaches y) ∧ (y is [the bank or shore of] some land)’. This set of propositions entails ‘x arrives at y’. In Italian (and analogously in French and English), arrivare (x, y) means ‘x arrives at y’.

# Desemanticization

The desemanticization (or desemantization) of a sign is an extreme generalization of its meaning, to the extent that only very generic predicates remain in its intension. Assuming an ontology in the form of a taxonomy, extremely general and abstract concepts such as ‘entity’, ‘action’, ‘relation’ etc. are at its top. These are, at the same time, typical grammatical meanings. Here are some simplified examples:

• When the Anglo-Saxon demonstrative that(x) evolves into the definite article the(x), the semantic component of distal deixis is lost. What remains is the component ‘x is in the universe of discourse’.
• Latin (x,y) means ‘x is oriented down from y’. Here x is a movement and y is a physical object. In the Romance languages, the preposition de (Italian di) just means ‘x is related to y’. There are no selection restrictions on either x or y. Thus, the more recent meaning is fully entailed by the ancient meaning. And it is maximally general in that it carries no meaning of its own, but merely serves to syntagmatically relate two other expressions x and y.

Desemantization is an aspect of grammaticalization.