Decision making in ABLP logic ============================= .. header:: This is part of `A Model of Authority in the Web `_. Before we look in detail at Web protocols, let's look at an ordinary decision based on input from various sources of information: Sam has been considering refinancing his house for a while when his wife, Melissa, calls on the phone and says "The Fed rate is down to 4.5%; now is the time!" "Wow. Really? Are you sure?" says Sam. "Yes, I read it in this morning's Wall Street Journal," she says. Sam gets out a spreadsheet to figure out if that meets his goal of paying off the transaction cost within two years. A brochure from his bank, Citi Wide, shows they charge about $3,700 in transaction fees and they lend money at a quarter point (0.25%) over the Fed rate. The balance of his mortage is $200K and his present rate is 6.125%, which makes the monthly payment $1,215. At 4.75%, the payment would be $1,043, a savings of $172 per month, which makes up for the $3,700 in fees in 22 months. So yes, now is the time. Application of ABLP logic ------------------------- We can evaluate the soundness of Sam's reasoning using ABLP logic. .. sidebar:: Webizing ABLP logic We borrow relationships such as `says` from ABLP and give them URIs in the Semantic Web using using Notation3. The primer [N3P]_ explains basic statements and abbreviating URIs with namespaces. The default prefix is bound to ```` and we use ``@keywords`` to elide colons as explained in [N3Spec]_:: @keywords is, of, a. @prefix : . The `c:` prefix is mnemonic for *communication*:: @prefix c: . To express ABLP modal statements such as :: :Melissa c:says { :Fed :rate 4.5 }. we use Notation3 formula terms as explained in [N3Logic]_. .. examples A basic relation in this logic is `says` as in:: Melissa c:says _:something. Sam actually does not hear directly from Melissa, but rather from a telephone connection:: MelissaByPhone c:says _:something. Sam takes for granted that when Melissa calls, statements that come over that phone were said by Melissa:: { MelissaByPhone c:says ?X } => { Melissa c:says ?X }. .. output That is, the phone connection `speaks for` Melissa:: MelissaByPhone c:speaks_for Melissa. .. examples Sam wasn't sure whether to take Melissa's word for it that the Fed rate was down to 4.5%, but he does accept that the Wall Street Journal is an accurate source of this information; that is, the WSJ `controls` the Fed rate:: WSJ c:controls { Fed rate ?R }. *TODO: perhaps elaborate WSJ c:controls { Fed rate ?R }. using quoting* .. output Due to limitations in our reasoner, we'll actually use a more specific version of controls:: WSJ c:controls_property rate. which means that WSJ controls all statements of the form { ?X rate ?Y }. .. sidebar:: Functions and operators in Notation3 Read ``[ is c:quoting of (Melissa WSJ ) ]`` as `quoting(Melissa, WSJ)` following the Notation3 convention of writing `op(arg1, arg2)` as **[is op of (arg1 arg2)]** where **op** is an ``owl:FunctionalProperty``. This applies to `arg1 op arg2` as well; in the ABLP papers, `quoting(A, B)` is written `A|B`. Sam didn't read the WSJ himself; Melissa read it to him; i.e. over the phone, Sam heard Melissa `quoting` the WSJ:: MelissaByPhone c:says { [ is c:quoting of (Melissa WSJ ) ] c:says { Fed rate 4.5 } }. The City Wide brochure gives rates and fees for refinancing:: Citi_Wide_brochure c:says { City_Wide offers City_Wide_refi. City_Wide_refi cost 3700; rate_offset 0.25. }. Sam got the brochure from the bank, so he knows the bank will stand by what it says, and the bank is a reliable source of rates and transaction costs:: Citi_Wide_brochure c:speaks_for City_Wide. City_Wide c:controls_property rate_offset, cost. Like any spreadsheet user, Sam trusts his software to do financial calculations:: Spreadsheet c:controls_property payoff_wait. @forAll M1, M2 . { M1 rate 6.125; balance 200000 . Fed rate 4.5. M2 rate_offset 0.25; cost 3700 . } => { Spreadsheet c:says { (M1 M2) payoff_wait 22 } }. Sam knows his mortgage rate and balance:: Sam_mortgage rate 6.125; balance 200000 . His goal is to find an offer that pays off within 2 years:: @prefix math: . { (Sam_mortgage ?M) payoff_wait [ math:notGreaterThan 24 ] } => { ?M a GoodOffer }. And indeed, the premises above (available in `refi_ex.n3 `_), combined with the `speech.n3 `_ encoding of ABLP logic, do entail the conclusion: City_Wide_refi a GoodOffer. A `mechanically generated proof `_ shows the details of the reasoning. References ---------- .. [N3P] `Primer: Getting into RDF & Semantic Web using N3`__ Berners-Lee, Hawke, and Connolly WWW2003 (Budapest) tutorial __ http://www.w3.org/2000/10/swap/Primer .. [N3Spec] `Notation3 (N3): A readable RDF syntax`__ Berners-Lee work in progress 2000-2006 __ http://www.w3.org/DesignIssues/Notation3.html .. [N3Logic] `N3Logic: A Logical Framework for the World Wide Web`__ Berners-Lee, Tim, Connolly, Dan, Kagal, Lalana, Hendler, Jim, and Schraf, Yosi Journal of Theory and Practice of Logic Programming (TPLP), Special Issue on Logic Programming and the Web, 2008 __ http://arxiv.org/abs/0711.1533 .. [TTL] `Turtle - Terse RDF Triple Language`__ David Beckett and Tim Berners-Lee 14 January 2008 http://www.w3.org/TeamSubmission/2008/SUBM-turtle-20080114/ __ http://www.w3.org/TeamSubmission/2008/SUBM-turtle-20080114/