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Third, the notion of "value" (Wert) here clearly means the truth-value of a whole proposition, not its propositional content specifically, which explains why a modal predicate "contributes nothing to the content of a judgment," i.e., it contributes nothing to the specific content of a judgment over and above its truth-value.
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Modal predicate logics can also be formed by making analogous additions to LPC instead of to PC.
Validity can also be defined for various modal predicate logics by combining the definition of LPC-validity given earlier (see above Validity in LPC) with the relevant accounts of validity for modal systems, but a modal logic based on LPC is, like LPC itself, an undecidable system.
The logical framework of abstractionism is modal predicate logic.
However, the main interest was in modal syllogistic and modal predicate logic.
In any event, the modal predicate is future-projecting.
The modal predicate is always future-projecting, although the prospective event is located in the past.
In both the deontic and the epistemic reading of 必 bì, the modal predicate is predominantly future-projecting.
The subject of the modal predicate is a third person [+/−HUMAN] subject which renders a deontic interpretation less likely.54.54
In example 17b, the reference time is located in the past and precedes the speech time, and two different times are involved in the modal predicate.49 Nevertheless, the modal is still future-projecting.50.50
Hence, if possible world semantics is supplemented with abstractionist definitions of possible worlds, then the logical framework of possible world semantics becomes modal predicate logic as well and, as a consequence, the extensionality of the semantics is lost once again.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com