From: Simon Raboczi <raboczi@tucanatech.com>

Date: Tue, 15 Jun 2004 09:37:55 -0700

To: public-rdf-dawg@w3.org

Message-Id: <5A56257E-BEEA-11D8-828A-000A95C5686E@tucanatech.com>

Received on Tuesday, 15 June 2004 12:38:33 UTC

Date: Tue, 15 Jun 2004 09:37:55 -0700

To: public-rdf-dawg@w3.org

Message-Id: <5A56257E-BEEA-11D8-828A-000A95C5686E@tucanatech.com>

Consider variable binding results a sum-of-products expressions as follows: A single variable binding: [?x = "apple"] A single result: AND( [?x = "apple"], [?y = "30 cents"] ) A complete query result: OR( AND [?x = "apple"], [?y = "30 cents"] ), AND [?x = "banana"], [?y = "25 cents"] )) The tabular form is a shorthand for the sum-of-products expression: ?x ?y +----------+------------+ | "apple" } "30 cents" | +----------+------------+ | "banana" | "25 cents" | +----------+------------+ A conjunction AND( P1, P2 ... Pn ) is logically true unless any of the conjoined propositions is false. Therefore, a conjunction of zero propositions must be logically true. A disjunction OR( P1, P2, ... Pn ) is logically false unless any of the disjoined propositions is true. Therefore, a disjunction of zero propositions must be logically false. If you have zero variables to bind, there are only two possible sum of products expressions: The false result: OR() The true result: OR( AND() ) In tabular form, the false result has zero columns (variables) and zero rows. The true result has zero columns and one row. It doesn't make any sense to have more than one row, because additional rows would necessarily be duplicates of the first.

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