Operator “l-” and FOL

The purpose of this essay is not to give some opinion on every curiosity and controversy associated with the semantics of the operator “l-“; far from it. The purpose is just to suggest one possible clear, rigorous way to reconcile the syntactic flexibility of “l-” with standard FOL and to account in a general way for the fact of its seemingly non-FOL semantics. The approach will be to define some function underlying “l-” that maps arbitrary formulas to one-place “singleton” predicates. It will be seen that the approach does not force any particular semantics onto “l-“; it does not, for example, either compel or bar intensional readings of l-expressions. In fact, there will be admitted many possible semantics for “l-“.

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The semantics of “ju” [version 2]

Version 2: “ju” with unary operator f-

The binary operator “ju” is similar to “je” except that it ensures that child formulas have the same event argument. In the simplest case it was initially proposed to mean

  • ju S1 S2 => lE smE je S1fE S2fE

where S1 and S2 were simple formulas and E was some unique anonymous variable (-f- was originally an argument suffix, but is now a unary operator; “sm” is the nonrestrictive predicate, but it’s been replaced in this proposal by “sv”, meaning “composed/simultaneous event”).  The meaning is “In composed event E, S1 is true and S2 is true” or very roughly “Simultaneously S1 and S2“.

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