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*To*: address@hidden, address@hidden, address@hidden*Subject*: Re: what most every language is missing :-)*From*: Guy Steele - Sun Microsystems Labs <address@hidden>*Date*: Fri, 28 Mar 2003 15:22:45 -0500 (EST)*Cc*: address@hidden*Reply-to*: Guy Steele - Sun Microsystems Labs <address@hidden>*Sender*: address@hidden

Date: Fri, 28 Mar 2003 10:36:56 -0600 From: Trevis Rothwell <tjr@acm.org> To: Noel Welsh <noelwelsh@yahoo.com>, ll1-discuss@ai.mit.edu Subject: Re: what most every language is missing :-) Maybe if instead of giving a definite "true", it would work like this: schrodinger's-cat =? dead -> "hmmm... could be..." and schrodinger's-cat =? alive -> "hmmm... could be..." Either way, is there a semantic difference between saying "the cat might be alive" and "the cat might not be alive"? Certainly the first one sounds more positive and the second one more negative, but is there an actual difference? There can be. Suppose you are doing evaluation with a possible-world semantics, so that the value of an expression is actually the *set* of possible values that the expression might take on under a "normal" semantics. (This is a standard strategy; think, for example, of the standard technique for converting a nondeterministic finite-state automaton into a deterministic one: the states of the DFA correspond to *sets* of states of the NDFA, and the rest is fairly straightforward.) So, under this possible-world evaluation, the result of a boolean expression could be {true}, {false}, {true,false}, or {}. Then "the cat might be alive" is true if the possible-worlds result of the expression "the cat is alive" is either {true} or {true,false}, whereas "the cat might not be alive" is true if the possible-worlds result of the expression "the cat is alive" is either {false} or {true,false}. So in this context the two phrases do indeed have distinct meanings. They describe two different mappings from the possible-worlds domain {{}, {true}, {false}, {true,false}} to the ordinary boolean domain {true, false} All this is in turn related to the variety of modal logic that introduces the "possibly" and "necessarily" operators (which are usually symbolized by a square diamond and a square, respectively). --Guy

**Follow-Ups**:**Re: what most every language is missing :-)***From:*Dan Sugalski <dan@sidhe.org>

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